@Preamble{"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi"}
@String{ack-do = "Dianne O'Leary,
Department of Computer Science,
University of Maryland,
College Park, MD, USA,
email: \path|oleary@cs.umd.edu|"}
@String{ack-gg = "Grant Gustafson,
Department of Mathematics,
University of Utah,
Salt Lake City, UT 84112, USA,
Tel: +1 801 581 6879,
e-mail: Internet: \path|gustafso@math.utah.edu|"}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
@String{ack-nj = "Norbert Juffa,
2445 Mission College Blvd.
Santa Clara, CA 95054
USA
email: \path=norbert@iit.com="}
@String{ack-sf = "Stefano Foresti,
Center for High-Performance Computing,
University of Utah,
Salt Lake City, UT 84112, USA,
Tel: +1 801 581 3173,
FAX: +1 801 585 5366,
e-mail: \path|stefano@chpc.utah.edu|"}
@String{inst-ANL = "Argonne National Laboratory"}
@String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL
60439-4801, USA"}
@String{inst-CORNELL = "Cornell University"}
@String{inst-CORNELL:adr = "Ithaca, NY, USA"}
@String{inst-CS-U-MARYLAND = "Department of Computer Science,
University of Maryland"}
@String{inst-CS-U-MARYLAND:adr = "College Park, MD, USA"}
@String{inst-CSRD = "Center for Supercomputing Research
and Development"}
@String{inst-CSRD:adr = "University of Illinois at
Urbana-Champaign, Urbana, IL, USA"}
@String{inst-STANFORD-CS = "Department of Computer Science,
Stanford University"}
@String{inst-STANFORD-CS:adr = "Stanford, CA"}
@String{inst-U-MARYLAND = "University of Maryland"}
@String{inst-U-MARYLAND:adr = "College Park, MD, USA"}
@String{inst-U-MARYLAND-CS = "Department of Computer Science,
University of Maryland"}
@String{inst-U-MARYLAND-CS:adr = "College Park, MD, USA"}
@String{j-ACTA-NUMERICA = "Acta Numerica"}
@String{j-ALMAGEST = "Almagest: International Journal for
the History of Scientific Ideas"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-AMER-STAT = "The American Statistician"}
@String{j-ANN-HIST-COMPUT = "Annals of the History of Computing"}
@String{j-ANN-MATH-STAT = "Annals of Mathematical Statistics"}
@String{j-ANN-NUM-MATH = "Annals of Numerical Mathematics"}
@String{j-ANN-STAT = "Annals of Statistics"}
@String{j-APL-MAT = "Aplicace Mathematicky"}
@String{j-APPL-MATH-OPTIM = "Applied Mathematics and Optimization"}
@String{j-APPL-NUM-MATH = "Applied Numerical Mathematics"}
@String{j-BAMS-NS = "Bulletin (new series) of the American
Mathematical Society"}
@String{j-BIOINFORMATICS = "Bioinformatics"}
@String{j-BIOMETRICS = "Biometrics"}
@String{j-BIT = "BIT"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BULL-AUSTRAL-MATH-SOC = "Bulletin of the Australian Mathematical Society"}
@String{j-CACM = "Communications of the Association
for Computing Machinery"}
@String{j-CALCOLO = "Calcolo"}
@String{j-COMPUT-METH-APPL-MECH-ENG = "Computer Methods in Applied Mechanics and
Engineering"}
@String{j-COMPUT-MATH-APPL = "Computers and Mathematics with Applications"}
@String{j-COMPUT-SYST-ENG = "Computing Systems in Engineering"}
@String{j-COMPUTING = "Computing"}
@String{j-DOKL-MATH = "Doklady Mathematics"}
@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
Analysis"}
@String{j-EURASIP-J-ADV-SIGNAL-PROCESS = "EURASIP Journal on Advances in Signal
Processing"}
@String{j-FOUND-COMPUT-MATH = "Foundations of Computational Mathematics"}
@String{j-IEEE-ANN-HIST-COMPUT = "IEEE Annals of the History of Computing"}
@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE Signal Processing Letters"}
@String{j-IEEE-TRANS-AUTOMAT-CONTR = "IEEE Transactions on Automatic Control"}
@String{j-IEEE-TRANS-CIRC-SYS = "IEEE Transactions on Circuits and Systems"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE Transactions on Circuits and
Systems. 2, Analog and Digital Signal
Processing"}
@String{j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH = "IEEE Transactions on Circuits
and Systems for Video Technology"}
@String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"}
@String{j-IEEE-TRANS-IMAGE-PROCESS = "IEEE Transactions on Image Processing"}
@String{j-IEEE-TRANS-MED-IMAG = "IEEE Transactions on Medical Imaging"}
@String{j-IEEE-TRANS-SIG-PROC = "IEEE Transactions on Signal Processing"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-IMA-VOL-MATH-APPL = "The IMA volumes in mathematics and its
applications"}
@String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical
Methods in Engineering"}
@String{j-INT-J-NUMER-METHODS-FLUIDS = "International Journal for Numerical
Methods in Fluids"}
@String{j-INTERNET-MATH = "Internet Mathematics"}
@String{j-INVERSE-PROBLEMS = "Inverse Problems"}
@String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical
Association"}
@String{j-J-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-J-COMPUT-GRAPH-STAT = "Journal of Computational and Graphical
Statistics"}
@String{j-J-COMPUT-PHYS = "Journal of Computational Physics"}
@String{j-J-ECONOMETRICS = "Journal of Econometrics"}
@String{j-J-FLUID-MECH = "Journal of Fluid Mechanics"}
@String{j-J-MATH-ANAL-APPL = "Journal of Mathematical Analysis and Applications"}
@String{j-J-STAT-COMPUT-SIMUL = "Journal of Statistical Computation and
Simulation"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-LECT-NOTES-MATH = "Lecture Notes in Mathematics"}
@String{j-LINEAR-ALGEBRA-APPL = "Linear Algebra and its Applications"}
@String{j-MAA-STUD-MATH = "MAA studies in mathematics"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-PROG = "Mathematical Programming"}
@String{j-MITT-MATH-GES-HAMBURG = "Mitteilungen der Mathematischen
Gessellschaft in Hamburg"}
@String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for
informationsbehandling"}
@String{j-NUM-LIN-ALG-APPL = "Numerical Linear Algebra with Applications"}
@String{j-NUM-MATH = "Numerische Mathematik"}
@String{j-NUMER-ALGORITHMS = "Numerical Algorithms"}
@String{j-PAMM = "Proceedings in Applied Mathematics and
Mechanics"}
@String{j-PROC-IEEE = "Proceedings of the IEEE"}
@String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of
Sciences of the United States of America"}
@String{j-PROC-SPIE = "Proceedings of the SPIE --- The
International Society for Optical
Engineering"}
@String{j-ROCKY-MOUNTAIN-J-MATH = "Rocky Mountain Journal of Mathematics"}
@String{j-SIAM = "Journal of the Society for Industrial
and Applied Mathematics"}
@String{j-SIAM-J-ALG-DISC-METH = "SIAM Journal of Algebraic Discrete
Methods"}
@String{j-SIAM-J-APPL-MATH = "SIAM Journal on Applied Mathematics"}
@String{j-SIAM-J-MAT-ANA-APPL = "SIAM Journal on Matrix Analysis and
Applications"}
@String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"}
@String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and
Applied Mathematics: Series B, Numerical
Analysis"}
@String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"}
@String{j-SIAM-J-SCI-STAT-COMP = "SIAM Journal on Scientific and
Statistical Computing"}
@String{j-SIAM-NEWS = "SIAM News"}
@String{j-SIAM-REVIEW = "SIAM Review"}
@String{j-SIGNUM = "ACM SIGNUM Newsletter"}
@String{j-SIGPLAN = "ACM SIGPLAN Notices"}
@String{j-SYST-CONTROL = "Systems and Control"}
@String{j-SYST-CONTROL-LETT = "Systems and Control Letters"}
@String{j-TECHNOMETRICS = "Technometrics"}
@String{j-TOMS = "ACM Transactions on Mathematical
Software"}
@String{j-Z-ANGE-MATH-MECH = "{Zeitschrift f{\"u}r Angewandte Mathematik
und Mechanik}"}
@String{j-Z-ANGE-MATH-PHYS = "Z. Angew. Math. Phys"}
@String{prep-latex = "Prepared with {\LaTeX}."}
@String{pub-ACADEMIC = "Academic Press"}
@String{pub-ACADEMIC:adr = "New York, NY, USA"}
@String{pub-ACM = "ACM Press"}
@String{pub-ACM:adr = "New York, NY 10036, USA"}
@String{pub-AMS = "American Mathematical Society"}
@String{pub-AMS:adr = "Providence, RI, USA"}
@String{pub-BIRKHAUSER = "Birkh{\"a}user Verlag"}
@String{pub-BIRKHAUSER:adr = "Basel, Switzerland"}
@String{pub-CUP = "Cambridge University Press"}
@String{pub-CUP:adr = "Cambridge, UK"}
@String{pub-ELS = "Elsevier"}
@String{pub-ELS:adr = "Amsterdam, The Netherlands"}
@String{pub-ENH = "Elsevier North-Holland, Inc."}
@String{pub-ENH:adr = "New York, NY, USA"}
@String{pub-ESP = "Elsevier Science Publishers"}
@String{pub-ESP:adr = "Amsterdam, The Netherlands"}
@String{pub-EYROLLES = "Editions Eyrolles"}
@String{pub-EYROLLES:adr = "Paris, France"}
@String{pub-IEEE = "IEEE Computer Society Press"}
@String{pub-IEEE:adr = "1109 Spring Street, Suite 300, Silver
Spring, MD 20910, USA"}
@String{pub-JOHNS-HOPKINS = "The Johns Hopkins University Press"}
@String{pub-JOHNS-HOPKINS:adr = "Baltimore, MD, USA"}
@String{pub-KLUWER = "Kluwer Academic Publishers Group"}
@String{pub-KLUWER:adr = "Norwell, MA, USA, and Dordrecht,
The Netherlands"}
@String{pub-LONGMAN = "Longman Scientific and Technical"}
@String{pub-LONGMAN:adr = "Essex, UK"}
@String{pub-MATH-ASSOC-AMER = "Mathematical Association of America"}
@String{pub-MATH-ASSOC-AMER:adr = "Washington, DC, USA"}
@String{pub-NH = "North-Holland Publishing Co."}
@String{pub-NH:adr = "Amsterdam, The Netherlands"}
@String{pub-NORTH-OXFORD = "North Oxford Academic"}
@String{pub-NORTH-OXFORD:adr = "Oxford, England"}
@String{pub-OXFORD = "Oxford University Press"}
@String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"}
@String{pub-PHYSICA = "Physica-Verlag"}
@String{pub-PHYSICA:adr = "Wien, Austria"}
@String{pub-PRINCETON = "Princeton University Press"}
@String{pub-PRINCETON:adr = "Princeton, NJ, USA"}
@String{pub-ROCQUENCOURT = "Rocquencourt"}
@String{pub-ROCQUENCOURT:adr = "Centre de Rocquencourt, France"}
@String{pub-SIAM = "Society for Industrial and Applied
Mathematics"}
@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SPARTAN = "Spartan Books"}
@String{pub-SPARTAN:adr = "London, England"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
Germany~/ London, UK~/ etc."}
@String{pub-TEUBNER = "Teubner"}
@String{pub-TEUBNER:adr = "Stuttgart, Germany; Leipzig, Germany"}
@String{pub-U-ILLINOIS-PRESS = "University of Illinois Press"}
@String{pub-U-ILLINOIS-PRESS:adr = "Urbana, IL, USA"}
@String{pub-US-ARO = "U.S. Army Research Office"}
@String{pub-US-ARO:adr = "Research Triangle Park, NC, USA"}
@String{pub-WATERLOO = "University of Waterloo"}
@String{pub-WATERLOO:adr = "Waterloo, Ontario, Canada"}
@String{pub-WESTERN-PERIODICALS = "Western Periodicals Co.,"}
@String{pub-WESTERN-PERIODICALS:adr = "North Hollywood, CA"}
@String{pub-WORLD-SCI = "World Scientific Publishing
Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road,
Singapore 9128, and River Edge, NJ, USA"}
@String{ser-LECT-NOTES-MATH = "Lecture Notes in Mathematics"}
@PhdThesis{Golub:1959:UCM,
author = "Gene Howard Golub",
title = "The Use of {Chebyshev} Matrix Polynomials in the
Iterative Solution of Linear Equations Compared to the
Method of Successive Overrelaxation",
type = "Ph.D. Thesis in Mathematics",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "vi + 134",
month = mar,
year = "1959",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/university-of-illinois-urbana-champagne.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Also published as Technical Report UIUC-DCS-R-59-85.
Abstracted in Dissertation Abstracts, v. 20 (1959), no.
5.",
acknowledgement = ack-nhfb,
advisor = "Abraham Haskel Taub",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "numerical analysis; numerical calculations; relaxation
methods (mathematics)",
remark = "Gene Golub received a Master's degree with coursework,
but no thesis, in 1954 at UIUC \cite[page
13]{Haigh:2005:IGG}. In that interview, Golub expresses
hard feelings about his thesis advisor.",
}
@Article{Golub:1961:CSIa,
author = "Gene H. Golub and Richard S. Varga",
title = "{Chebyshev} Semi-Iterative Methods, Successive
Overrelaxation Iterative Methods, and Second Order
{Richardson} Iterative Methods. {I}",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "147--156",
month = dec,
year = "1961",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "26\#3207",
MRreviewer = "J. R. Cannon",
bibdate = "Sun Jan 14 10:09:19 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "nla, relaxation, iter, semi-iterative method,
Richardson's method",
}
@Article{Golub:1961:CSIb,
author = "Gene H. Golub and Richard S. Varga",
title = "{Chebyshev} Semi-Iterative Methods, Successive
Overrelaxation Iterative Methods, and Second Order
{Richardson} Iterative Methods. {II}",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "157--168",
month = dec,
year = "1961",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "26\#3208",
MRreviewer = "J. R. Cannon",
bibdate = "Sun Jan 14 10:09:24 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "nla, relaxation, iter, semi-iterative method,
Richardson's method",
}
@Article{Golub:1962:BET,
author = "Gene H. Golub",
title = "Bounds for Eigenvalues of Tridiagonal Symmetric
Matrices Computed by the {LR} Method",
journal = j-MATH-COMPUT,
volume = "16",
number = "80",
pages = "438--445",
month = oct,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.40",
MRnumber = "29 \#732",
MRreviewer = "P. Henrici",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2003134",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Golub:1962:BRE,
author = "Gene H. Golub",
title = "Bounds for the Round-Off Errors in the {Richardson}
Second Order Method",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "4",
pages = "212--223",
month = dec,
year = "1962",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940168",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "29\#2958",
MRreviewer = "A. S. Householder",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=212",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Golub:1963:CVM,
author = "Gene H. Golub",
title = "Comparison of the Variance of Minimum Variance and
Weighted Least Squares Regression Coefficients",
journal = j-ANN-MATH-STAT,
volume = "34",
number = "3",
pages = "984--991",
month = sep,
year = "1963",
CODEN = "AASTAD",
DOI = "https://doi.org/10.1214/aoms/1177704021",
ISSN = "0003-4851 (print), 2168-8990 (electronic)",
ISSN-L = "0003-4851",
MRclass = "62.55",
MRnumber = "27\#5336",
MRreviewer = "A. C. Cohen",
bibdate = "Sat May 31 09:11:02 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/annmathstat.bib",
URL = "http://projecteuclid.org/euclid.aoms/1177704021",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
}
@Article{Golub:1963:LBR,
author = "Gene H. Golub",
title = "On a Lower Bound for the Rank of a Partitioned Square
Matrix",
journal = j-MATH-COMPUT,
volume = "17",
number = "82",
pages = "186--188",
month = apr,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "15.05",
MRnumber = "28\#1209",
MRreviewer = "Ky Fan",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2003639",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Golub:1963:RBG,
author = "Gene H. Golub",
title = "Review: {{\booktitle{A Guide to ALGOL Programming}},
by Daniel D. McCracken}",
journal = j-J-AM-STAT-ASSOC,
volume = "58",
number = "304",
pages = "1202--1202",
month = dec,
year = "1963",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:37 MST 2012",
bibsource = "http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314185;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1960.bib",
URL = "http://www.jstor.org/stable/2283384",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Golub:1964:RPP,
author = "G. H. Golub",
title = "Recent Publications and Presentations: {{\em An
Introduction to Computational Methods}}, by {K. A.
Redish}",
journal = j-AMER-MATH-MONTHLY,
volume = "71",
number = "10",
pages = "1145--1145",
month = dec,
year = "1964",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:42 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Businger:1965:LLS,
author = "Peter A. Businger and Gene H. Golub",
title = "Linear Least Squares Solutions by {Householder}
Transformations",
journal = j-NUM-MATH,
volume = "7",
number = "3",
pages = "269--276",
month = jun,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.20",
MRnumber = "31\#862",
bibdate = "Sun Jan 14 10:04:47 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Also in \cite[pp. 111--118]{Wilkinson:1971:LA}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Householder transformation; lsq; nla; qrd; software",
}
@Article{Forsythe:1965:SVS,
author = "George E. Forsythe and Gene H. Golub",
title = "On the Stationary Values of a Second-Degree Polynomial
on the Unit Sphere",
journal = j-SIAM,
volume = "13",
number = "4",
pages = "1050--1068",
month = dec,
year = "1965",
CODEN = "JSIMAV",
ISSN = "0368-4245 (print), 1095-712X (electronic)",
MRclass = "65.30",
MRnumber = "MR0195250 (33 \#3453)",
MRreviewer = "A. V. Balakrishnan",
bibdate = "Sun Jan 14 10:01:11 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR
database",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
URL = "http://www.jstor.org/stable/2946425",
ZMnumber = "0168.03005",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "forms; linear algebra; nla; updating",
}
@Article{Golub:1965:CSV,
author = "G. H. Golub and W. Kahan",
title = "Calculating the Singular Values and Pseudo-Inverse of
a Matrix",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "2",
number = "2",
pages = "205--224",
month = "????",
year = "1965",
ISSN = "0887-459X (print), 1095-7170 (electronic)",
ISSN-L = "0887-459X",
MRclass = "65.35",
MRnumber = "32 \#587",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of the Society for Industrial and Applied
Mathematics: Series B, Numerical Analysis",
journal-URL = "http://epubs.siam.org/loi/sjnaam.1",
keywords = "nla, svd, ginv",
}
@InProceedings{Golub:1965:IRL,
author = "G. H. Golub and J. H. Wilkinson",
title = "Iterative Refinement of Least Square Solution",
crossref = "Kalenich:1965:IPP",
pages = "606--607",
year = "1965",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, lsq, iterative refinement",
}
@Article{Golub:1965:NMSa,
author = "Gene H. Golub",
title = "Numerical methods for solving linear least squares
problems",
journal = j-APL-MAT,
volume = "10",
number = "??",
pages = "213--216",
month = "????",
year = "1965",
CODEN = "APMTAK",
ISSN = "0373-6725",
MRclass = "65.20",
MRnumber = "31\#5324",
MRreviewer = "W. J. Kotz{\'e}",
bibdate = "Sun Jan 14 10:03:53 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Aplikace Matematiky",
}
@Article{Golub:1965:NMSb,
author = "G. H. Golub",
title = "Numerical Methods for Solving Linear Least Squares
Problems",
journal = j-NUM-MATH,
volume = "7",
number = "3",
pages = "206--216",
month = jun,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.20",
MRnumber = "31\#5323",
MRreviewer = "W. J. Kotz{\'e}",
bibdate = "Sun Jan 14 10:03:43 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Householder transformation; lsq; nla; qrd; updating",
}
@Article{Golub:1966:NIR,
author = "G. H. Golub and J. H. Wilkinson",
title = "Note on the Iterative Refinement of Least Squares
Solution",
journal = j-NUM-MATH,
volume = "9",
number = "2",
pages = "139--148",
month = dec,
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.20",
MRnumber = "35 \#3849",
MRreviewer = "W. J. Kotz{\'e}",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "condition; iterative refinement; la; lsq; nla; pert",
}
@Article{Bjorck:1967:API,
author = "{\AA}ke Bj{\"o}rck and Gene H. Golub",
title = "{Algol} programming: Iterative Refinement of Linear
Least Squares Solutions by {Householder}
Transformation",
journal = j-BIT,
volume = "7",
number = "4",
pages = "322--337",
month = dec,
year = "1967",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939326",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:10 MST 2006",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=7&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=7&issue=4&spage=322",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "nla, lsq, iterative refinement, Householder
transformation",
}
@Article{Golub:1967:GBA,
author = "G. H. Golub and T. N. Robertson",
title = "A generalized {Bairstow} algorithm",
journal = j-CACM,
volume = "10",
number = "6",
pages = "371--373",
month = jun,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "39 \#2315",
bibdate = "Sat Nov 26 10:31:36 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Bartels:1968:ACS,
author = "Richard H. Bartels and Gene H. Golub",
title = "{Algorithm 328}: {Chebyshev} Solution to An
Overdetermined Linear System [{F4}]",
journal = j-CACM,
volume = "11",
number = "6",
pages = "428--430",
month = jun,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:20 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
note = "See certification \cite{Schryer:1969:CA}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
editorsnote = "The following algorithm by Barrels and Golub relates
to the paper by the same authors in the Numerical
Analysis department of this issue on pages 401--406
\cite{Bartels:1968:NAS}. This is the first instance of
this type of concurrent publication in Communications
under the policy announced by the Editors of the two
departments, J. G. Herriot and J. F. Traub, in the
March 1967 issue.",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Bartels:1968:NAS,
author = "Richard H. Bartels and Gene H. Golub",
title = "Numerical Analysis: Stable numerical methods for
obtaining the {Chebyshev} solution to an overdetermined
system of equations",
journal = j-CACM,
volume = "11",
number = "6",
pages = "401--406",
month = jun,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.35",
MRnumber = "39\#2302",
bibdate = "Thu Dec 08 06:16:41 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
note = "See algorithm \cite{Bartels:1968:ACS}.",
abstract = "An implementation of Stiefel's exchange algorithm for
determining a Chebyshev solution to an overdetermined
system of linear equations is presented, that uses
Gaussian LU decomposition with row interchanges. The
implementation is computationally more stable than
those usually given in the literature. A generalization
of Stiefel's algorithm is developed which permits the
occasional exchange of two equations simultaneously.",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "Chebyshev solutions; exchange algorithm; linear
equations; overdetermined linear systems",
}
@Article{Golub:1968:LSS,
author = "G. H. Golub",
title = "Least Squares, Singular Values, and Matrix
Approximations",
journal = j-APL-MAT,
volume = "13",
number = "??",
pages = "44--51",
month = "????",
year = "1968",
CODEN = "APMTAK",
ISSN = "0373-6725",
MRclass = "65.35",
MRnumber = "37 \#4944",
MRreviewer = "L. W. Ehrlich",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Aplikace Matematiky",
keywords = "nla, lsq, regr, svd, Schmidt-Mirsky theorem",
}
@Article{Bartels:1969:ASM,
author = "Richard H. Bartels and Gene H. Golub",
title = "{Algorithm 350}: simplex method procedure employing
{LU} decomposition [{H}]",
journal = j-CACM,
volume = "12",
number = "5",
pages = "275--278",
month = may,
year = "1969",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362946.362982",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Nov 26 10:31:36 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm.bib",
note = "ACM Algorithm 350.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Bartels:1969:SML,
author = "Richard H. Bartels and Gene H. Golub",
title = "The Simplex Method of Linear Programming Using {LU}
Decomposition",
journal = j-CACM,
volume = "12",
number = "5",
pages = "266--268",
month = may,
year = "1969",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362946.362974",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Nov 26 10:31:36 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "nla, nlop, lud, linear programming, updating",
}
@Article{Businger:1969:AAS,
author = "Peter A. Businger and Gene H. Golub",
title = "{Algorithm 358}: singular value decomposition of a
complex matrix [{F1}, 4, 5]",
journal = j-CACM,
volume = "12",
number = "10",
pages = "564--565",
month = oct,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Nov 26 10:31:36 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm.bib",
note = "ACM Algorithm 358.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Golub:1969:CGQ,
author = "Gene H. Golub and John H. Welsch",
title = "Calculation of {Gauss} Quadrature Rules",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "221--230 + s1--s10",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database; Theory/Matrix.bib",
note = "Loose microfiche suppl A1--A10. Reprinted in
\cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/2004418",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "na, Gaussian quadrature",
}
@TechReport{Golub:1969:MDSa,
author = "G. H. Golub",
title = "Matrix Decompositions and Statistical Calculations",
type = "Technical Report",
number = "124",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
month = "????",
year = "1969",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "stat, nla, lsq, qrd, svd",
}
@InCollection{Golub:1969:MDSb,
author = "G. H. Golub",
title = "Matrix Decompositions and Statistical Computation",
crossref = "Milton:1969:CSC",
pages = "365--397",
year = "1969",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Golub:1969:SVR,
author = "G. H. Golub and R. Underwood",
title = "Stationary Values of the Ratio of Quadratic Forms
Subject to Linear Constraints",
type = "Technical Report",
number = "CS-142",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
month = "????",
year = "1969",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, geig, regularization",
}
@InCollection{Bartels:1970:NTM,
author = "R. H. Bartels and G. H. Golub and M. A. Saunders",
title = "Numerical Techniques in Mathematical Programming",
crossref = "Rosen:1970:SNP",
pages = "123--176",
year = "1970",
MRclass = "90.58 (65.00)",
MRnumber = "42 \#7277",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, qrd, rank determination",
}
@Article{Buzbee:1970:DMS,
author = "B. L. Buzbee and G. H. Golub and C. W. Nielson",
title = "On Direct Methods for Solving {Poisson}'s Equations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "7",
number = "4",
pages = "627--656",
month = dec,
year = "1970",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65.66",
MRnumber = "44 \#4920",
MRreviewer = "G. T. McAllister",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "nla, pde, direct Poisson solver, sparse",
}
@TechReport{Golub:1970:LAS,
author = "G. H. Golub and R. Underwood and J. H. Wilkinson",
title = "The {Lanczos} Algorithm for the Symmetric {$ A x =
\lambda B x $} problem",
type = "Technical report",
number = "142",
institution = "Computer Science Department, Stanford University",
address = "Stanford, CA, USA",
year = "1970",
bibdate = "Fri Nov 10 07:11:31 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007); James H. Wilkinson (27 September 1919--5 October
1986)",
}
@InProceedings{Golub:1970:LLS,
author = "G. H. Golub and M. A. Saunders",
title = "Linear Least Squares and Quadratic Programming",
crossref = "Abadie:1970:INP",
pages = "229--256",
year = "1970",
MRclass = "90C20",
MRnumber = "55 \#9983",
bibdate = "Fri Dec 20 16:55:01 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nlop, qrd, lsq, quadratic programming",
}
@TechReport{Golub:1970:SUL,
author = "G. H. Golub",
title = "Some uses of the {Lanczos} algorithm in numerical
linear algebra",
type = "Report",
number = "STAN-CS-72-302",
institution = "Computer Science Department, Stanford University",
address = "Stanford, CA, USA",
year = "1970",
bibdate = "Fri Nov 10 07:15:29 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
remark = "Republished in \cite{Golub:1973:SUL}",
}
@Article{Golub:1970:SVD,
author = "G. H. Golub and C. Reinsch",
title = "Singular Value Decomposition and Least Squares
Solutions",
journal = j-NUM-MATH,
volume = "14",
number = "5",
pages = "403--420",
month = apr,
year = "1970",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Also in \cite[pp. 134--151]{Wilkinson:1971:LA}.
Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022);
Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "lsq; nla; rank determination; regularization;
software; svd",
}
@Article{Golub:1970:SVR,
author = "Gene H. Golub and Richard Underwood",
title = "Stationary Values of the Ratio of Quadratic Forms
Subject to Linear Constraints",
journal = j-Z-ANGE-MATH-PHYS,
volume = "21",
number = "??",
pages = "319--326 (or 318--326??)",
month = "????",
year = "1970",
CODEN = "ZAMPDB",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
MRclass = "65.40",
MRnumber = "42\#7056",
MRreviewer = "J. D. P. Donnelly",
bibdate = "Sun Jan 14 09:57:25 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik = Journal of Applied Mathematics and Physics}",
journal-URL = "http://link.springer.com/journal/33",
}
@Article{Buzbee:1971:DSD,
author = "B. L. Buzbee and F. W. Dorr and J. A. George and G. H.
Golub",
title = "The Direct Solution of the Discrete {Poisson} Equation
on Irregular Regions",
journal = j-SIAM-J-NUMER-ANAL,
volume = "8",
number = "4",
pages = "722--736",
month = dec,
year = "1971",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65Q05",
MRnumber = "45 \#1403",
MRreviewer = "J. R. Kuttler",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "nla, pde, direct Poisson solver, sparse",
}
@Article{Golub:1971:AAC,
author = "G. H. Golub and L. B. Smith",
title = "{ACM} Algorithm 414: {Chebyshev} Approximation of
Continuous Functions by a {Chebyshev} System of
Functions",
journal = j-CACM,
volume = "14",
number = "11",
pages = "737--746",
month = nov,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Sep 20 19:46:04 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm.bib",
note = "ACM Algorithm 414.",
acknowledgement = ack-nj,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@InCollection{Golub:1971:DMS,
author = "G. H. Golub",
title = "Direct methods for solving elliptic difference
equations",
crossref = "Morris:1971:STN",
pages = "1--19",
year = "1971",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1971:MMM,
author = "Gene Golub",
title = "Matrix methods in mathematical programming",
journal = j-LECT-NOTES-MATH,
volume = "193",
pages = "21--39",
year = "1971",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0060342",
ISBN = "3-540-05422-7 (print), 3-540-36538-9 (e-book)",
ISBN-13 = "978-3-540-05422-1 (print), 978-3-540-36538-9
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Fri May 9 19:07:44 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0060342/",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
book-DOI = "https://doi.org/10.1007/BFb0060340",
book-URL = "http://www.springerlink.com/content/978-3-540-36538-9",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Golub:1971:SME,
author = "G. H. Golub",
title = "Some modified eigenvalue problems",
journal = j-LECT-NOTES-MATH,
volume = "228",
pages = "56--56",
year = "1971",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0069447",
ISBN = "3-540-05656-4 (print), 3-540-36976-7 (e-book)",
ISBN-13 = "978-3-540-05656-0 (print), 978-3-540-36976-9
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Fri May 9 19:07:43 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0069447",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
book-DOI = "https://doi.org/10.1007/BFb0069442",
book-URL = "http://www.springerlink.com/content/978-3-540-36976-9",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Dahlquist:1972:BEL,
author = "Germund Dahlquist and Stanley C. Eisenstat and Gene H.
Golub",
title = "Bounds for the error of linear systems of equations
using the theory of moments",
journal = j-J-MATH-ANAL-APPL,
volume = "37",
number = "1",
pages = "151--166",
month = jan,
year = "1972",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(72)90264-8",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "65F99",
MRnumber = "45 1368",
MRreviewer = "J. G. Herriot",
bibdate = "Sun Jan 14 09:56:10 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
}
@TechReport{Golub:1972:LAS,
author = "G. H. Golub and R. Underwood and J. H. Wilkinson",
title = "The {Lanczos} Algorithm for the Symmetric {$ A x =
\lambda B x $} Problem",
type = "Technical Report",
number = "STAN-CS-72-270",
institution = "Computer Science, Stanford University",
address = "Stanford, CA, USA",
pages = "24",
year = "1972",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007); James H. Wilkinson (27 September 1919--5 October
1986)",
keywords = "nla, geig, Lanczos algorithm",
}
@Article{Bjorck:1973:NMC,
author = "{\AA}ke Bj{\"o}rck and Gene H. Golub",
title = "Numerical Methods for Computing Angles between Linear
Subspaces",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "579--594",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F30",
MRnumber = "50 1485",
MRreviewer = "J. Legras",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database; Parallel/par.lin.alg.bib;
Theory/Matrix.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/2005662",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "B0240 (Probability and statistics); B0290H (Linear
algebra); C1140 (Probability and statistics); C4140
(Linear algebra)",
corpsource = "Link{\"o}ping Univ., Sweden",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "angles between linear; canonical; computing;
correlations; matrix algebra; numerical methods;
rectangular matrices; statistics; subspaces",
kwds = "math, nla, gsvd, canonical angles, subspace metric",
treatment = "T Theoretical or Mathematical",
}
@Article{Concus:1973:UFD,
author = "Paul Concus and Gene H. Golub",
title = "Use of Fast Direct Methods for the Efficient Numerical
Solution of Nonseparable Elliptic Equations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "10",
number = "6",
pages = "1103--1120",
month = dec,
year = "1973",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65N05",
MRnumber = "49",
MRreviewer = "P. Laasonen",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2156207",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "nla, fast algorithm, elliptic pde, direct Poisson
solver",
}
@InCollection{Dantzig:1973:NSO,
author = "G. B. Dantzig and R. W. Cottle and B. C. Eaves and G.
H. Golub and F. S. Hillier and A. S. Manne and D. J.
Wilde and R. B. Wilson",
title = "On the need for a {Systems Optimization Laboratory}",
crossref = "Hu:1973:MPP",
pages = "1--32",
year = "1973",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
xxnote = "Is the cross-reference correct?? The original title
Mathematical Programming matches a great many library
catalog entries.",
}
@InProceedings{Golub:1973:CLI,
author = "G. H. Golub and W. Dent",
title = "Computation of the limited information maximum
likelihood estimator",
crossref = "Tarter:1973:PCS",
pages = "60--65",
year = "1973",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1973:CSD,
author = "G. H. Golub and E. Seneta",
title = "Computation of the stationary distribution of an
infinite {Markov} matrix",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "8",
number = "??",
pages = "333--341",
month = "????",
year = "1973",
CODEN = "ALNBAB",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "60J10 (68A10)",
MRnumber = "50 \#8710",
MRreviewer = "I. Vaduva",
bibdate = "Fri Dec 20 17:00:44 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
}
@Article{Golub:1973:DPI,
author = "G. H. Golub and V. Pereyra",
title = "The Differentiation of Pseudo-Inverses and Nonlinear
Least Squares Problems Whose Variables Separate",
journal = j-SIAM-J-NUMER-ANAL,
volume = "10",
number = "2",
pages = "413--432",
month = apr,
year = "1973",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15",
MRnumber = "49 \#1753",
MRreviewer = "R. P. Tewarson",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@InProceedings{Golub:1973:EPR,
author = "Gene H. Golub and Irwin Guttman and Rudolf Dutter",
title = "Examination of pseudo-residuals of outliers for
detecting spurosity in the general univariate linear
model",
crossref = "Kabe:1973:MSI",
pages = "63--108",
year = "1973",
MRclass = "62J05",
MRnumber = "51 9380",
MRreviewer = "Colin L. Mallows",
bibdate = "Sun Jan 14 09:51:59 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1973:NCU,
author = "Gene H. Golub and George P. H. Styan",
title = "Numerical computations for univariate linear models",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "2",
number = "3",
pages = "253--274",
year = "1973",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657308810051",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
MRclass = "62J05 (65F05)",
MRnumber = "51 11840",
MRreviewer = "Valery Fedorov",
bibdate = "Tue Apr 22 09:10:34 MDT 2014",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
keywords = "stat, nla, regr, lsq, qrd",
}
@InProceedings{Golub:1973:SAN,
author = "G. H. Golub and George P. H. Styan",
title = "Some aspects of numerical computations for linear
models",
crossref = "Kennedy:1973:PCS",
pages = "189--192",
year = "1973",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1973:SMM,
author = "Gene H. Golub",
title = "Some Modified Matrix Eigenvalue Problems",
journal = j-SIAM-REVIEW,
volume = "15",
number = "2",
pages = "318--334",
month = apr,
year = "1973",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1015032",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F15",
MRnumber = "48 7569",
MRreviewer = "J. F. Traub",
bibdate = "Thu Mar 27 09:06:49 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/15/2;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available at
\verb=ftp://math.liu.se/pub/references=. Reprinted in
\cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/2028604",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
error = "conflicting pages with your cv: 318-335",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "nla, eig, updating",
onlinedate = "April 1973",
xxpages = "318--344",
}
@InCollection{Golub:1973:SUL,
author = "G. H. Golub",
title = "Some uses of the {Lanczos} algorithm in numerical
algebra",
crossref = "Miller:1973:TNA",
pages = "173--184",
year = "1973",
MRclass = "65F15",
MRnumber = "50 \#11743",
MRreviewer = "F. Szidarovszky",
bibdate = "Fri Dec 20 17:46:23 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Fischer:1974:FTM,
author = "D. Fischer and G. Golub and O. Hald and C. Leiva and
O. Widlund",
title = "On {Fourier--Toeplitz} Methods for Separable Elliptic
Problems",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "349--368",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F05 (65N20)",
MRnumber = "54 \#4072",
MRreviewer = "R. H. Bartels",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "B0290P (Differential equations); B0220 (Mathematical
analysis); C4170 (Differential equations)",
corpsource = "New York Univ., NY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "differential equations; elliptic; fast; fast Fourier
transforms; Fourier Toeplitz method; Fourier transform;
numerical methods; separable elliptic problems;
Toeplitz factorizations",
treatment = "T Theoretical or Mathematical",
}
@Article{Gill:1974:MMM,
author = "P. E. Gill and G. H. Golub and W. Murray and M. A.
Saunders",
title = "Methods for Modifying Matrix Factorizations",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "505--535",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F05",
MRnumber = "49 \#8299",
MRreviewer = "L. W. Ehrlich",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database; Theory/Matrix.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Nat. Phys. Lab., Teddington, UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Cholesky factors; complete orthogonal factorisation;
matrix algebra; matrix factorizations; rank one
change",
kwds = "math, nla, qrd, lud, updating",
treatment = "T Theoretical or Mathematical",
}
@Article{Golub:1974:BMM,
author = "G. H. Golub",
title = "Bounds for matrix moments",
journal = j-ROCKY-MOUNTAIN-J-MATH,
volume = "4",
number = "2",
pages = "207--211",
month = "????",
year = "1974",
CODEN = "RMJMAE",
DOI = "https://doi.org/10.1216/RMJ-1974-4-2-207",
ISSN = "0035-7596 (print), 1945-3795 (electronic)",
ISSN-L = "0035-7596",
MRclass = "65F30",
MRnumber = "48 12803",
MRreviewer = "Walter Gautschi",
bibdate = "Sun Jan 14 09:54:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Proceedings of the International Conference on
Pad{\'e} Approximants, Continued Fractions and Related
Topics (Univ. Colorado, Boulder, Colo., 1972; dedicated
to the memory of H. S. Wall)",
URL = "http://projecteuclid.org/euclid.rmjm/1250130962",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Rocky Mountain Journal of Mathematics",
journal-URL = "http://projecteuclid.org/euclid.rmjm",
}
@Article{Golub:1974:CBS,
author = "G. H. Golub and J. M. Varah",
title = "On a Characterization of the Best $ l_2 $-Scaling of a
Matrix",
journal = j-SIAM-J-NUMER-ANAL,
volume = "11",
number = "3",
pages = "472--479",
month = jun,
year = "1974",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F35 (15A12)",
MRnumber = "55 \#9510",
MRreviewer = "H. Schwerdtfeger",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "nla, condition, scaling",
}
@Article{Golub:1974:CSD,
author = "G. H. Golub and E. Seneta",
title = "Computation of the stationary distribution of an
infinite stochastic matrix of special form",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "10",
number = "??",
pages = "255--261",
month = "????",
year = "1974",
CODEN = "ALNBAB",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "60J10",
MRnumber = "51 \#9212",
MRreviewer = "Dean Isaacson",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Bulletin of the Australian Mathematical Society",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=BAZ",
}
@InProceedings{Golub:1974:MCE,
author = "G. H. Golub",
title = "Methods for computing eigenvalues of sparse matrix
equations",
crossref = "Pereyra:1974:ADS",
pages = "127--148",
year = "1974",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Book{Miller:1974:TNA,
editor = "John J. H. Miller",
title = "Topics in Numerical Analysis {II}: Proceedings of the
Royal Irish Academy Conference on Numerical Analysis,
1974",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiv + 266",
year = "1974",
ISBN = "0-12-496952-6",
ISBN-13 = "978-0-12-496952-0",
LCCN = "QA297.R69 1974",
bibdate = "Sat Oct 22 18:09:20 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Concus:1975:GCG,
author = "Paul Concus and Gene H. Golub",
title = "A generalized conjugate gradient method for
non-symmetric systems of linear equations",
crossref = "Glowinski:1975:CMA",
pages = "56--65",
year = "1975",
MRclass = "65F10",
MRnumber = "57 7968",
MRreviewer = "David R. Kincaid",
bibdate = "Sun Jan 14 09:49:28 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Golub:1975:ICE,
author = "G. H. Golub and J. H. Wilkinson",
title = "Ill-Conditioned Eigensystems and the Computation of
the {Jordan} Canonical Form",
type = "Technical Report",
number = "STAN-CS-75-478",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
year = "1975",
bibdate = "Wed Aug 24 16:47:40 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Published as \cite{Golub:1976:ICE}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InCollection{Golub:1975:SMC,
author = "G. H. Golub",
title = "Sparse matrix computations: Eigenvalues and linear
equations",
crossref = "Anonymous:1975:SI",
pages = "117--140",
year = "1975",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1975:WPS,
author = "G. H. Golub and L. Jenning and W. H. Yang",
title = "Waves in periodically structured media",
journal = j-J-COMPUT-PHYS,
volume = "17",
number = "4",
pages = "349--357",
month = apr,
year = "1975",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(75)90039-X",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:17 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199917590039X",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@InProceedings{Cline:1976:CNM,
author = "A. K. Cline and G. H. Golub and G. W. Platzman",
title = "Calculation of Normal Modes of Oceans Using a
{Lanczos} Method",
crossref = "Bunch:1976:SMC",
pages = "409--426",
year = "1976",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, eig, Lanczos algorithm",
}
@TechReport{Concus:1976:GCGa,
author = "P. Concus and G. H. Golub",
title = "A Generalized {Conjugate Gradient} Method for
Nonsymmetric Systems of Linear Equations",
type = "Technical Report",
number = "STAN-CS-76-535",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
month = "????",
year = "1976",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Concus:1976:GCGb,
author = "Paul Concus and Gene H. Golub and Dianne P. O'Leary",
title = "A Generalized Conjugate Gradient Method for the
Numerical Solution of Elliptic Partial Differential
Equations",
crossref = "Bunch:1976:SMC",
pages = "309--332",
year = "1976",
MRclass = "65F10 (65P05)",
MRnumber = "58",
MRreviewer = "M. R. Hestenes",
bibdate = "Sun Jan 14 09:48:20 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, conjugate gradients, elliptic pde",
}
@TechReport{Concus:1976:NSN,
author = "Paul Concus and Gene H. Golub and Dianne P. O'Leary",
title = "Numerical solutions of nonlinear elliptic partial
differential equations by a generalized conjugate
gradient method",
type = "Technical Report",
number = "STAN-CS-76-585",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "43",
month = "????",
year = "1976",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "differential equations, elliptic --- numerical
solutions",
}
@Article{Golub:1976:CVO,
author = "G. H. Golub and M. Heath and G. Wahba",
title = "Cross-Validation and Optimum Ridge Regression",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "806--806",
month = "????",
year = "1976",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@InCollection{Golub:1976:DPI,
author = "G. H. Golub and V. Pereyra",
title = "Differentiation of Pseudo-Inverses, Separable
Nonlinear Least Squares Problems and Other Tales",
crossref = "Nashed:1976:GIA",
pages = "303--324",
year = "1976",
MRclass = "65F20 (15A09 65J05)",
MRnumber = "58 \#8200",
MRreviewer = "B. Levinger",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1976:ICE,
author = "G. H. Golub and J. H. Wilkinson",
title = "Ill-Conditioned Eigensystems and the Computation of
the {Jordan} Canonical Form",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "578--619",
month = "????",
year = "1976",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1018113",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F15 (15A21)",
MRnumber = "54 \#1570",
MRreviewer = "Robert Todd Gregory",
bibdate = "Fri Dec 20 17:05:12 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "nla, eig, Jordan form, condition, pert,
ill-conditioned problem",
}
@TechReport{Golub:1976:RDLa,
author = "Gene H. Golub and Virginia Klema and G. W. Stewart",
title = "Rank Degeneracy and Least Squares Problems",
type = "Technical Report",
number = "TR-456",
institution = inst-U-MARYLAND,
address = inst-U-MARYLAND:adr,
pages = "????",
month = jun,
year = "1976",
bibdate = "Wed May 28 17:40:15 2014",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/university-of-maryland.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
note = "Also published as Stanford University Computer Science
Department Technical Report STAN-CS-76-559.",
abstract = "This paper is concerned with least squares problems
when the least squares matrix \$A\$ is near a matrix
that is not of full rank. A definition of numerical
rank is given. It is shown that under certain
conditions when \$A\$ has numerical rank \$r\$ there is
a distinguished \$r\$ dimensional subspace of the
column space of \$A\$ that is insensitive to how it is
approximated by \$r\$ independent columns of \$A\$. The
consequences of this fact for the least squares problem
are examined. Algorithms are described for
approximating the stable part of the column space of
\$A\$.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, svd, qrd, condition estimation, rank
determination, pert, variable selection",
xxnote = "Check: is this the same as Golub:1976:RDLb? If so,
which report number is correct??",
}
@TechReport{Golub:1976:RDLb,
author = "G. H. Golub and Virginia Klema and G. W. {Stewart
III}",
title = "Rank Degeneracy and Least Squares Problems",
type = "Report",
number = "TR-751",
institution = inst-CS-U-MARYLAND,
address = inst-CS-U-MARYLAND:adr,
pages = "????",
month = "????",
year = "1976",
bibdate = "Thu May 29 16:12:45 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
GWS-number = "N6",
xxnote = "Check: is this the same as Golub:1976:RDLa? If so,
which report number is correct??",
}
@InProceedings{Golub:1976:SVD,
author = "G. H. Golub and F. Luk",
title = "Singular value decomposition: applications and
computations",
crossref = "ARO:1976:PAN",
pages = "??--??",
year = "1976",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Bjorck:1977:EMA,
author = "{\AA}ke Bj{\"o}rck and Gene H. Golub",
title = "Eigenproblems for Matrices Associated with Periodic
Boundary Conditions",
journal = j-SIAM-REVIEW,
volume = "19",
number = "1",
pages = "5--16",
month = jan,
year = "1977",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1019002",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F15",
MRnumber = "55 1716",
MRreviewer = "B. Levinger",
bibdate = "Sat Mar 29 09:52:39 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/19/1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://www.jstor.org/stable/2029322",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1977",
}
@TechReport{Boley:1977:IEPa,
author = "D. Boley and Gene H. Golub",
title = "Inverse eigenvalue problems for band matrices",
type = "Technical Report",
number = "STAN-CS-77-623",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "9",
month = "????",
year = "1977",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "eigenvalues; matrices",
}
@InCollection{Boley:1977:IEPb,
author = "D. Boley and G. H. Golub",
title = "Inverse eigenvalue problems for band matrices",
crossref = "Watson:1978:NAP",
pages = "??--??",
month = jun,
year = "1977",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InCollection{Buzbee:1977:VCS,
author = "B. Buzbee and G. Golub and J. Howell",
title = "Vectorizations for the {CRAY-1} of Some Methods for
Solving Elliptic Difference Equations",
crossref = "Kuck:1977:HSC",
pages = "255--271",
year = "1977",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/ovr.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{deBoor:1977:NSR,
author = "Carl de Boor and Gene H. Golub",
title = "The numerically stable reconstruction of a {Jacobi}
matrix from spectral data",
type = "Technical Report",
number = "STAN-CS-77-602",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "18",
month = "????",
year = "1977",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "jacobi varieties; matrices",
}
@InCollection{Golub:1977:BLM,
author = "G. H. Golub and R. Underwood",
title = "The Block {Lanczos} Method for Computing Eigenvalues",
crossref = "Rice:1977:MSI",
pages = "364--377 (or 361--377??)",
year = "1977",
MRclass = "65F15",
MRnumber = "57 \#14376",
MRreviewer = "Colette Lebaud",
bibdate = "Fri Dec 20 17:48:35 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, block algorithm, Lanczos algorithm, eig",
}
@TechReport{Golub:1977:GCV,
author = "Gene H. Golub and Michael Heath and Grace Wahba",
title = "Generalized cross-validation as a method for choosing
a good ridge parameter",
type = "Technical Report",
number = "STAN-CS-77-622",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "24",
month = "????",
year = "1977",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Also issued as Dept. of Statistics Technical Report
no. 491, University of Wisconsin, Madison, WI.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "graphic methods; regression analysis",
}
@InProceedings{Golub:1977:TTC,
author = "Gene H. Golub and Franklin T. Luk",
title = "Singular value decomposition: applications and
computations",
crossref = "Army:1977:TTC",
pages = "577--605",
year = "1977",
MRclass = "65F30",
MRnumber = "58 31784",
bibdate = "Sun Jan 14 09:45:27 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Golub:1977:TTS,
author = "Gene H. Golub and Franklin T. Luk",
title = "Singular value decomposition: applications and
computations",
crossref = "Army:1977:TTC",
pages = "577--605",
year = "1977",
MRclass = "65F30",
MRnumber = "58 \#31784",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Boley:1978:IEP,
author = "D. Boley and G. H. Golub",
title = "Inverse eigenvalue problems for band matrices",
crossref = "Watson:1978:NAP",
pages = "23--31",
year = "1978",
MRclass = "65F15",
MRnumber = "57 \#14375",
MRreviewer = "H. Hochstadt",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Boley:1978:MIEa,
author = "D. Boley and Gene H. Golub",
title = "The Matrix Inverse Eigenvalue Problem for Periodic
{Jacobi} Matrices",
type = "Technical Report",
number = "STAN-CS-78-684",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "[5] + 14",
month = "????",
year = "1978",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "eigenvalues; matrices",
}
@InProceedings{Boley:1978:MIEb,
author = "D. L. Boley and G. H. Golub",
title = "The Matrix Inverse Eigenvalue Problem for Periodic
{Jacobi} Matrices",
crossref = "Marek:1978:PFS",
pages = "63--76",
year = "1978",
MRclass = "15A21 (58F07 65F15 65F30)",
MRnumber = "81e:15005",
MRreviewer = "J. S. Joel",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Concus:1978:NSN,
author = "P. Concus and G. H. Golub and D. P. O'Leary",
title = "Numerical Solution of Nonlinear Elliptic Partial
Differential Equations by a Generalized Conjugate
Gradient Method",
journal = j-COMPUTING,
volume = "19",
number = "4",
pages = "321--339",
month = "????",
year = "1978",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02252030",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65H10 (65N99)",
MRnumber = "58 \#31799",
MRreviewer = "L. Hageman",
bibdate = "Fri Dec 20 17:41:37 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "nla, conjugate gradients",
}
@Article{Cottle:1978:SLS,
author = "Richard W. Cottle and Gene H. Golub and Richard S.
Sacher",
title = "On the solution of large structured linear
complementarity problems: the block partitioned case",
journal = j-APPL-MATH-OPTIM,
volume = "4",
number = "4",
pages = "347--363",
month = "????",
year = "1978",
CODEN = "AMOMBN",
ISSN = "0095-4616 (print), 1432-0606 (electronic)",
ISSN-L = "0095-4616",
MRclass = "90C30 (90C05)",
MRnumber = "80a:90120",
bibdate = "Mon Jan 15 09:15:16 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Applied Mathematics and Optimization",
journal-URL = "http://link.springer.com/journal/245",
}
@Article{deBoor:1978:NSR,
author = "C. de Boor and G. H. Golub",
title = "The numerically stable reconstruction of a {Jacobi}
matrix from spectral data",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "21",
number = "3",
pages = "245--260",
month = sep,
year = "1978",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (15A57)",
MRnumber = "80i:15007",
MRreviewer = "O. Pokorn{\'a}",
bibdate = "Tue Feb 16 18:50:27 MST 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/linala1970.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
URL = "http://www.sciencedirect.com/science/article/pii/0024379578900861",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@TechReport{Golub:1978:SHM,
author = "G. H. Golub and S. Nash and C. {Van Loan}",
title = "A {Schur-Hessenberg} Method for the Problem {$ {Ax +
xB = C} $}",
type = "Technical Report",
number = "TR 78-354",
institution = inst-CORNELL,
address = inst-CORNELL:adr,
month = oct,
year = "1978",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/cornell-university.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "mailto::lmc@cs.cornell.edu",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Golub:1978:UPD,
author = "G. H. Golub and C. {Van Loan}",
title = "Unsymmetric Positive Definite Linear Systems",
type = "Technical Report",
number = "TR 78-352",
institution = inst-CORNELL,
address = inst-CORNELL:adr,
month = sep,
year = "1978",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/cornell-university.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "mailto::lmc@cs.cornell.edu",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{VanLoan:1978:SUP,
author = "C. {Van Loan} and G. H. Golub",
title = "Solving Unsymmetric Positive Definite Linear Systems",
journal = j-SIAM-REVIEW,
volume = "20",
number = "3",
pages = "636--636",
month = "????",
year = "1978",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Bauer:1979:ES,
author = "F. L. Bauer and G. H. Golub and A. S. Householder and
K. Samelson",
title = "{Eduard L. Stiefel}: 4/21/1909--11/27/1978",
journal = j-NUM-MATH,
volume = "32",
number = "4",
pages = "480--481",
month = dec,
year = "1979",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "01A70",
MRnumber = "82e:01083",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "With a German translation.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Dahlquist:1979:BEL,
author = "Germund Dahlquist and Gene H. Golub and Stephen G.
Nash",
title = "Bounds for the error in linear systems",
crossref = "Hettich:1979:SIP",
pages = "154--172",
year = "1979",
MRclass = "65F10 (90C05)",
MRnumber = "154--172",
MRreviewer = "Jacques Dubois",
bibdate = "Sun Jan 14 09:41:57 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Dahlquist:1979:SIP,
author = "Germund Dahlquist and Gene H. Golub and Stephen G.
Nash",
title = "Bounds for the error in linear systems",
crossref = "Hettich:1979:SIP",
pages = "154--172",
year = "1979",
MRclass = "65F10 (90C05)",
MRnumber = "81b:65028",
MRreviewer = "Jacques Dubois",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Golub:1979:CMA,
author = "Gene H. Golub and Robert J. Plemmons",
title = "Sparse least squares problems",
crossref = "Glowinski:1979:CMA",
pages = "489--496",
year = "1979",
MRclass = "65F05",
MRnumber = "82a:65025",
MRreviewer = "D. S. Henderson",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1979:DSE,
author = "G. H. Golub and W. Langlois",
title = "Direct solution of the equation for the {Stokes}
stream function",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "19",
number = "3",
pages = "391--399",
month = sep,
year = "1979",
CODEN = "CMMECC",
DOI = "https://doi.org/10.1016/0045-7825(79)90066-5",
ISSN = "0045-7825 (print), 1879-2138 (electronic)",
ISSN-L = "0045-7825",
MRclass = "76D05 (65P05)",
MRnumber = "82c:76029",
MRreviewer = "C. Taylor",
bibdate = "Fri Dec 20 17:07:23 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
ajournal = "Comp. Methods in Appl. Mech. and Engrg.",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Computer Methods in Applied Mechanics and
Engineering",
journal-URL = "http://www.sciencedirect.com/science/journal/00457825",
}
@InProceedings{Golub:1979:EUV,
author = "Gene H. Golub and Randall J. LeVeque",
title = "Extensions and Uses of the Variable Projection
Algorithm for Solving Nonlinear Least Squares
Problems",
crossref = "ARO:1979:PAN",
pages = "1--12",
year = "1979",
MRclass = "65F20",
MRnumber = "81b:65036",
bibdate = "Sun Jan 14 09:40:39 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nlop, nllsq",
}
@Article{Golub:1979:GCV,
author = "Gene H. Golub and Michael T. Heath and Grace Wahba",
title = "Generalized Cross-Validation as a Method for Choosing
a Good Ridge Parameter",
journal = j-TECHNOMETRICS,
volume = "21",
number = "2",
pages = "215--223",
month = may,
year = "1979",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.1080/00401706.1979.10489751",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
MRclass = "62J07",
MRnumber = "81e:62079",
MRreviewer = "Colin L. Mallows",
bibdate = "Sun Jan 14 09:39:58 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available at
\verb=ftp://math.liu.se/pub/references=. Reprinted in
\cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/1268518",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html;
http://www.tandfonline.com/loi/utch20",
keywords = "nla, stat, ridge regression, cross validation,
regularization",
}
@TechReport{Golub:1979:HSMa,
author = "Gene H. Golub and Stephen Nash and Charles F. {Van
Loan}",
title = "A {Hessenberg--Schur} method for the problem {$ {AX +
XB = C} $}",
type = "Technical Report",
number = "STAN-CS-79-713",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "50",
month = "????",
year = "1979",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "matrix mechanics; numerical analysis",
}
@Article{Golub:1979:HSMb,
author = "G. H. Golub and S. Nash and C. {Van Loan}",
title = "A {Hessenberg--Schur} Method for the Matrix Problem {$
A X + X B = C $}",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "24",
number = "6",
pages = "909--913",
month = "????",
year = "1979",
CODEN = "IETAA9",
DOI = "https://doi.org/10.1109/TAC.1979.1102170",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
MRclass = "65F30 (93C05)",
MRnumber = "81a:65046",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
keywords = "nla, Sylvester equation, Hessenberg matrix, Schur
form, Lyapunov equation, matrix equation",
}
@InProceedings{Golub:1979:LSL,
author = "G. H. Golub and F. Luk and M. Pagano",
title = "A large sparse least squares problem in
photogrammetry",
crossref = "Gentleman:1979:PCS",
pages = "??--??",
year = "1979",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Golub:1979:SLS,
author = "G. H. Golub and R. Plemmons",
title = "Sparse least squares problems",
crossref = "ISCMASE:1979:PIF",
pages = "??--??",
year = "1979",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Golub:1979:TLS,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Total least squares",
crossref = "Gasser:1979:STC",
pages = "69--76",
year = "1979",
MRclass = "65D10 (65U05)",
MRnumber = "82a:65013",
MRreviewer = "Valery Fedorov",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, svd, total least squares",
}
@Article{Golub:1979:UPD,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Unsymmetric Positive Definite Linear Systems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "28",
number = "??",
pages = "85--97",
month = dec,
year = "1979",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(79)90122-8",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A23 (65F05)",
MRnumber = "80k:15016",
MRreviewer = "Colette Lebaud",
bibdate = "Tue Feb 16 18:50:44 MST 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/linala1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379579901228",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, linear system, positive definite matrix,
nonsymmetric matrix",
}
@TechReport{Golub:1980:ATLa,
author = "G. H. Golub and C. F. {Van Loan}",
title = "An Analysis of the Total Least Squares Problem",
type = "Technical Report",
number = "80-411",
institution = inst-CORNELL,
address = inst-CORNELL:adr,
month = feb,
year = "1980",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/cornell-university.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "mailto::lmc@cs.cornell.edu",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1980:ATLb,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "An Analysis of the Total Least Squares Problem",
journal = j-SIAM-J-NUMER-ANAL,
volume = "17",
number = "6",
pages = "883--893",
month = dec,
year = "1980",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0717073",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65D10",
MRnumber = "83g:65020",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
note = "Reprinted in \cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/2156807",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "statistics, least squares, math, nla, lsq, svd, deriv,
total least squares",
}
@Article{Golub:1980:LSG,
author = "Gene H. Golub and Robert J. Plemmons",
title = "Large-Scale Geodetic Least-Squares Adjustment by
Dissection and Orthogonal Decomposition",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "34",
pages = "3--28",
month = dec,
year = "1980",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(80)90156-1",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "86A30 (15A23 65F10)",
MRnumber = "81k:86010",
MRreviewer = "K. R. Koch",
bibdate = "Sun Jan 14 09:38:35 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, lsq, sparse, geodesy, qrd",
}
@Article{Golub:1980:RSD,
author = "G. Golub and V. Klema and S. C. Peters",
title = "Rules and Software for Detecting Rank Degeneracy",
journal = j-J-ECONOMETRICS,
volume = "12",
number = "1",
pages = "41--48",
month = "????",
year = "1980",
CODEN = "JECMB6",
DOI = "https://doi.org/10.1016/0304-4076(80)90051-2",
ISSN = "0304-4076 (print), 1872-6895 (electronic)",
ISSN-L = "0304-4076",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Econometrics",
journal-URL = "http://www.sciencedirect.com/science/journal/03044076",
}
@InProceedings{Golub:1980:SLS,
author = "Gene H. Golub and Robert J. Plemmons",
title = "Sparse least squares problems",
crossref = "Glowinski:1980:CMA",
pages = "489--496",
year = "1980",
MRclass = "65F05",
MRnumber = "82a:65025",
MRreviewer = "D. S. Henderson",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Ward:1980:NLA,
author = "Robert C. Ward and Gene H. Golub",
title = "Numerical linear algebra",
journal = j-SIGNUM,
volume = "15",
number = "3",
pages = "9--26",
month = sep,
year = "1980",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:09 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Bjorck:1981:EMA,
author = "{\AA}ke Bj{\"o}rck and Gene H. Golub",
title = "Eigenproblems for matrices associated with periodic
boundary conditions. ({Chinese})",
journal = "Yingyong Shuxue yu Jisuan Shuxue",
volume = "1",
number = "??",
pages = "10--18",
month = "????",
year = "1981",
MRclass = "65F15",
MRnumber = "83d:65110",
bibdate = "Sun Jan 14 09:34:26 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Translated from the English by Cheng Ming Huang",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1981:BDV,
author = "G. H. Golub and W. P. Tang",
title = "The Block Decomposition of a {Vandermonde} Matrix and
Its Applications",
journal = j-BIT,
volume = "21",
number = "??",
pages = "505--517",
year = "1981",
CODEN = "BITTEL",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "nla, block algorithm, Vandermonde matrix",
}
@Article{Golub:1981:BLM,
author = "Gene H. Golub and Franklin T. Luk and Michael L.
Overton",
title = "A Block {Lanczos} Method for Computing the Singular
Values and Corresponding Singular Vectors of a Matrix",
journal = j-TOMS,
volume = "7",
number = "2",
pages = "149--169",
month = jun,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355945.355946",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65F50 (65F15)",
MRnumber = "84h:65045",
bibdate = "Sun Jan 14 09:28:55 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "nla, svd, Lanczos algorithm, block Lanczos method,
singular values, singular vectors, large sparse matrix,
singular-value decomposition, upper-triangular band
matrix, nla, svd, Lanczos algorithm",
}
@Article{Tang:1981:BDV,
author = "W. P. Tang and G. H. Golub",
title = "The Block Decomposition of a {Vandermonde} Matrix and
Its Applications",
journal = j-BIT,
volume = "21",
number = "4",
pages = "505--517",
month = dec,
year = "1981",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932847",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F30 (15A06)",
MRnumber = "83e:65077",
MRreviewer = "V. Syamala Devi",
bibdate = "Wed Jan 4 18:52:17 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=4&spage=505",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "nla, block algorithm, Vandermonde matrix",
}
@TechReport{Chan:1982:ACS,
author = "T. F. Chan and G. H. Golub and R. J. {Le Veque}",
title = "Algorithms for Computing the Sample Variance: Analysis
and Recommendations",
type = "??",
number = "222",
institution = "Department of Computer Science, Yale University",
address = "??",
month = "????",
year = "1982",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "stat, na, variance, standard deviation",
}
@InProceedings{Chan:1982:UFP,
author = "T. F. Chan and G. H. Golub and R. J. LeVeque",
title = "Updating formulae and a pairwise algorithm for
computing sample variances",
crossref = "Caussinus:1982:CSH",
pages = "30--41",
year = "1982",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
descriptors = "Simulation; statistics; numeric calculation",
}
@InProceedings{Golub:1982:CTS,
author = "Gene H. Golub and Michael L. Overton",
title = "Convergence of a two-stage {Richardson} iterative
procedure for solving systems of linear equations",
crossref = "Watson:1982:NAP",
pages = "125--139",
year = "1982",
DOI = "https://doi.org/10.1007/BFb0093153",
MRclass = "65F10",
MRnumber = "83f:65045",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1982:NAV,
author = "Gene H. Golub and Stephen G. Nash",
title = "Nonorthogonal Analysis of Variance using a Generalized
Conjugate-Gradient Algorithm",
journal = j-J-AM-STAT-ASSOC,
volume = "77",
number = "377",
pages = "109--116",
month = mar,
year = "1982",
CODEN = "JSTNAL",
DOI = "https://doi.org/10.2307/2287776",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62J10 (65U05)",
MRnumber = "83i:62135",
MRreviewer = "Walter Schlee",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
URL = "http://www.jstor.org/stable/2287776",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
error = "in Gene's cv is Statistical Computing, but we found
this reference: The American Statistician",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "stat, anova, conjugate gradients",
}
@Article{Paige:1982:LAS,
author = "C. C. Paige and M. A. Saunders",
title = "{LSQR}: an algorithm for sparse linear equations and
sparse least squares",
journal = j-TOMS,
volume = "8",
number = "1",
pages = "43--71",
month = mar,
year = "1982",
CODEN = "ACMSCU",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "algorithms; measurement",
review = "ACM CR 39252",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Sparse and very large systems
\\ G.1.6 Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Least squares methods G Mathematics of
Computing, MATHEMATICAL SOFTWARE",
}
@Article{Chan:1983:ACS,
author = "Tony F. Chan and Gene H. Golub and Randall J.
LeVeque",
title = "Algorithms for computing the sample variance: Analysis
and recommendations",
journal = j-AMER-STAT,
volume = "37",
number = "3",
pages = "242--247",
month = aug,
year = "1983",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.2307/2683386",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRclass = "62-04",
MRnumber = "84k:62003",
bibdate = "Mon May 5 09:19:29 MDT 1997",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1983.bib;
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2683386",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
country = "USA",
date = "13/05/93",
descriptors = "Simulation; statistics; numeric calculation",
enum = "7109",
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
location = "SEL: Wi",
references = "0",
revision = "16/01/94",
}
@Article{Golub:1983:CGQ,
author = "G. H. Golub and J. Kautsk{\'y}",
title = "Calculation of {Gauss} quadratures with multiple free
and fixed knots",
journal = j-NUM-MATH,
volume = "41",
number = "2",
pages = "147--163",
month = jun,
year = "1983",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01390210",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D32 (65F15)",
MRnumber = "84i:65030",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Dept. of Computer Sci., Stanford Univ., Stanford, CA,
USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "algorithms; fixed knots; Gauss knots; Gauss
quadratures; integration; Jacobi matrix; quadratic
convergence; theory",
subject = "G.1.4 Mathematics of Computing, NUMERICAL ANALYSIS,
Quadrature and Numerical Differentiation, Gaussian
quadrature",
treatment = "T Theoretical or Mathematical",
}
@Book{Golub:1983:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
publisher = pub-JOHNS-HOPKINS # " and " # pub-NORTH-OXFORD,
address = pub-JOHNS-HOPKINS:adr # " and " # pub-NORTH-OXFORD:adr,
pages = "xvi + 476",
year = "1983",
ISBN = "0-8018-3010-9 (hardcover), 0-8018-3011-7 (paperback),
0-946536-00-7, 0-946536-05-8 (paperback)",
ISBN-13 = "978-0-8018-3010-5 (hardcover), 978-0-8018-3011-2
(paperback), 978-0-946536-00-9, 978-0-946536-05-4
(paperback)",
LCCN = "QA188 .G65 1983",
MRclass = "65Fxx (65-02)",
MRnumber = "85h:65063",
MRreviewer = "C. Ilioi",
bibdate = "Sun Jan 14 09:27:53 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "Johns Hopkins Series in the Mathematical Sciences",
URL = "http://www.jstor.org/stable/2008107;
http://www.jstor.org/stable/2030489;
http://www.jstor.org/stable/3616959",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "algebra --- matrices --- computation by digital
computer systems; matrices --- data processing",
remark = "See review by James W. Demmel in SIAM Review, Vol. 28,
No. 2 (Jul., 1986), pp. 252-255, review by David F.
Mayers, Mathematics of Computation, Vol. 47, No. 175
(Jul., 1986), pp. 376-377, and review by T. J. Randall,
The Mathematical Gazette, Vol. 69, No. 448 (Jun.,
1985), p. 152.",
tableofcontents = "Preface to the Third Edition \\
Software \\
Selected References \\
Matrix Multiplication Problems / 1 \\
Matrix Analysis / 48 \\
General Linear Systems / 87 \\
Special Linear Systems / 133 \\
Orthogonalization and Least Squares / 206 \\
Parallel Matrix Computations / 275 \\
The Unsymmetric Eigenvalue Problem / 308 \\
The Symmetric Eigenvalue Problem / 391 \\
Lanczos Methods / 470 \\
Iterative Methods for Linear Systems / 508 \\
Functions of Matrices / 555 \\
Special Topics / 579 \\
Bibliography / 637 \\
Index / 687",
}
@Book{Golub:1983:RNG,
author = "Gene H. Golub and G{\'e}rard A. Meurant",
title = "{R}{\'e}solution Num{\'e}rique des Grands Syst{\`e}mes
Lin{\'e}aires (English: Numerical solution of large
linear systems)",
volume = "49",
publisher = pub-EYROLLES,
address = pub-EYROLLES:adr,
pages = "x + 329",
year = "1983",
ISBN = "??",
ISBN-13 = "??",
LCCN = "??",
MRclass = "65-01 (65F10 65F20 65N20)",
MRnumber = "86b:65002",
MRreviewer = "G. Maess",
bibdate = "Sun Jan 14 09:26:25 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
series = "Collection de la Direction des Etudes et Recherches de
l'Electricit\'e de France",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "book, nla, linear system, sparse",
}
@InProceedings{Golub:1983:UPI,
author = "G. Golub and D. Mayers",
title = "The Use of Preconditioning Over Irregular Regions",
crossref = "Blackburn:1983:SIC",
pages = "??--??",
year = "1983",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/ovr.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Kautsky:1983:CJM,
author = "J. Kautsk{\'y} and G. H. Golub",
title = "On the Calculation of {Jacobi} Matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "52/53",
pages = "439--456",
year = "1983",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(83)90028-9",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F30 (15A99 33A65)",
MRnumber = "84g:65050",
MRreviewer = "Walter Gautschi",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, Jacobi matrix",
}
@Article{Boley:1984:LAA,
author = "D. L. Boley and G. H. Golub",
title = "The {Lanczos--Arnoldi} Algorithm and controllability",
journal = j-SYST-CONTROL-LETT,
volume = "4",
number = "6",
pages = "317--324",
month = sep,
year = "1984",
CODEN = "SCLEDC",
DOI = "https://doi.org/10.1016/S0167-6911(84)80072-9",
ISSN = "0167-6911 (print), 1872-7956 (electronic)",
ISSN-L = "0167-6911",
MRclass = "93B40 (93B05)",
MRnumber = "86a:93044",
bibdate = "Fri Dec 20 17:12:57 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Systems and Control Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01676911",
keywords = "nla, controllability, Lanczos algorithm, Arnoldi's
method, algorithms",
subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
Miscellaneous",
}
@Article{Boley:1984:MMR,
author = "Daniel Boley and Gene H. Golub",
title = "A modified method for reconstructing periodic {Jacobi}
matrices",
journal = j-MATH-COMPUT,
volume = "42",
number = "165",
pages = "143--150",
month = jan,
year = "1984",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007564",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15 (15A18)",
MRnumber = "85h:65078",
MRreviewer = "Alan L. Andrew",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2007564",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "B0210 (Algebra); C1110 (Algebra)",
corpsource = "Computer Sci. Dept., Univ. of Minnesota, Minneapolis,
MN, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algorithm; initial data items; matrix algebra;
numerically stable; periodic Jacobi matrices; spectral
data",
treatment = "T Theoretical or Mathematical",
}
@Article{Concus:1984:GCG,
author = "Paul Concus and Gene H. Golub and Dianne P. O'Leary",
title = "A generalized conjugate gradient method for the
numerical solution of elliptic partial differential
equations",
journal = j-MAA-STUD-MATH,
volume = "24",
number = "??",
pages = "178--198",
month = "????",
year = "1984",
CODEN = "MSTMBI",
ISSN = "0081-8208",
MRclass = "65N20 (65F10 65F15)",
MRnumber = "925 214",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "MAA studies in mathematics",
}
@Article{Gallant:1984:ICR,
author = "A. Ronald Gallant and Gene H. Golub",
title = "Imposing curvature restrictions on flexible functional
forms",
journal = j-J-ECONOMETRICS,
volume = "26",
number = "3",
pages = "295--321",
month = dec,
year = "1984",
CODEN = "JECMB6",
DOI = "https://doi.org/10.1016/0304-4076(84)90024-1",
ISSN = "0304-4076 (print), 1872-6895 (electronic)",
ISSN-L = "0304-4076",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Econometrics",
journal-URL = "http://www.sciencedirect.com/science/journal/03044076",
}
@InCollection{Golub:1984:UPI,
author = "Gene H. Golub and David Mayers",
title = "The use of preconditioning over irregular regions",
crossref = "Glowinski:1983:CMA",
pages = "3--14",
year = "1984",
MRclass = "65F10 (65F35)",
MRnumber = "87h:65059",
bibdate = "Sun Jan 14 09:23:24 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.grid.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Concus:1985:BPC,
author = "P. Concus and G. H. Golub and G. A. Meurant",
title = "Block Preconditioning for the Conjugate Gradient
Method",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "6",
number = "??",
pages = "220--252",
month = "????",
year = "1985",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0906018",
ISSN = "0196-5204",
MRclass = "65F10 (65N20)",
MRnumber = "87c:65035a",
MRreviewer = "Ian Gladwell",
bibdate = "Thu Apr 09 15:41:33 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "See corrigendum \cite{Concus:1985:CBP}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "nla, block algorithm, preconditioning, conjugate
gradients",
}
@Article{Concus:1985:CBP,
author = "P. Concus and G. H. Golub and G. Meurant",
title = "Corrigendum: {``Block preconditioning for the
conjugate gradient method''}",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "6",
number = "3",
pages = "791--791",
month = "????",
year = "1985",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "65F10 (65N20)",
MRnumber = "87c:65035b",
MRreviewer = "Ian Gladwell",
bibdate = "Thu Apr 09 15:41:30 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "See \cite{Concus:1985:BPC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
}
@Article{Golub:1985:SLS,
author = "G. H. Golub",
title = "Solution of Large Sparse Structured Least-Squares
Problem",
journal = j-BIOMETRICS,
volume = "41",
number = "3",
pages = "799--799",
month = "????",
year = "1985",
CODEN = "BIOMB6",
ISSN = "0006-341X (print), 1541-0420 (electronic)",
ISSN-L = "0006-341X",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/biometrics1980.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Biometrics",
journal-URL = "http://www.jstor.org/journal/biometrics",
}
@Article{Golub:1986:CBS,
author = "G. H. Golub and P. Manneback and Ph. L. Toint",
title = "A Comparison Between some Direct and Iterative Methods
for Large Scale Geodetic Least Squares Problems",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "7",
number = "3",
pages = "799--816",
month = jul,
year = "1986",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0907053",
ISSN = "0196-5204",
MRclass = "65F50 (65U05)",
MRnumber = "87g:65063",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "algorithms; conjugate gradients; geodesy; iter; lsq;
nested dissection; nla; sparse; theory; verification",
subject = "G.1.6 Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Least squares methods \\ J.2 Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Physics",
}
@Article{Golub:1986:CTS,
author = "Gene H. Golub and R. Kannan",
title = "Convergence of a two-stage {Richardson} process for
nonlinear equations",
journal = j-BIT,
volume = "26",
number = "2",
pages = "209--216",
month = jun,
year = "1986",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933747",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65H10 (47H17 65F10)",
MRnumber = "87f:65064",
MRreviewer = "V. Pereyra",
bibdate = "Wed Jan 4 18:52:19 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=2;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=2&spage=209",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@TechReport{Golub:1986:PBS,
author = "Gene H. Golub and Robert J. Plemmons and Ahmed Sameh",
title = "Parallel Block Schemes for Large Scale Least Squares
Computations",
type = "Technical Report",
number = "574",
institution = inst-CSRD,
address = inst-CSRD:adr,
pages = "20",
month = apr,
year = "1986",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/ovr.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "matrices; parallel processing (electronic computers)",
}
@Article{Golub:1986:UFG,
author = "Gene H. Golub and Carl D. {Meyer, Jr.}",
title = "Using the {$ {QR} $} Factorization and Group Inversion
to Compute, Differentiate, and estimate the Sensitivity
of Stationary Probabilities for {Markov} Chains",
journal = j-SIAM-J-ALG-DISC-METH,
volume = "7",
number = "2",
pages = "273--281",
month = apr,
year = "1986",
CODEN = "SJAMDU",
DOI = "https://doi.org/10.1137/0607031",
ISSN = "0196-5212 (print), 2168-345X (electronic)",
ISSN-L = "0196-5212",
MRclass = "60J10 (65F05)",
MRnumber = "87i:60073",
MRreviewer = "M. F. Neuts",
bibdate = "Sun Jan 14 09:22:16 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Algebraic and Discrete Methods",
journal-URL = "http://epubs.siam.org/loi/sjamdu",
keywords = "eig; ginv; Markov chain; nla; qrd; theory;
verification",
subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices \\ G.2.1 Mathematics
of Computing, DISCRETE MATHEMATICS, Combinatorics",
}
@TechReport{Arbenz:1987:SDH,
author = "P. Arbenz and G. H. Golub",
title = "On the Spectral Decomposition of {Hermitian} Matrices
Subject to Indefinite Low Rank Perturbations with
Applications",
type = "??",
number = "NA 87-07",
institution = "Computer Science, Stanford University",
address = "Stanford, CA",
month = "????",
year = "1987",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Boley:1987:SMI,
author = "Daniel Boley and Gene H. Golub",
title = "A survey of matrix inverse eigenvalue problems",
journal = j-INVERSE-PROBLEMS,
volume = "3",
number = "4",
pages = "595--622",
month = "????",
year = "1987",
CODEN = "INPEEY",
DOI = "https://doi.org/10.1088/0266-5611/3/4/010",
ISSN = "0266-5611 (print), 1361-6420 (electronic)",
ISSN-L = "0266-5611",
MRclass = "65F15",
MRnumber = "89m:65036",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Inverse Problems",
journal-URL = "http://iopscience.iop.org/0266-5611/",
}
@InProceedings{Ferziger:1987:BSA,
author = "J. H. Ferziger and G. H. Golub and M. C. Thompson",
title = "Block {SOR} applied to the cyclically-reduced
equations as an efficient solution technique for
convection-diffusion equations",
crossref = "Noye:1987:CTA",
pages = "??--??",
year = "1987",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1987:D,
author = "Gene H. Golub and Iain Duff and Cleve Moler",
title = "Dedication",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "1--12",
year = "1987",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "01A70",
MRnumber = "88e:01060",
bibdate = "Mon Jan 15 17:54:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Golub:1987:GEY,
author = "G. H. Golub and Alan Hoffman and G. W. Stewart",
title = "A generalization of the {Eckart--Young--Mirsky} matrix
approximation theorem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "317--327",
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90114-5",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "41A45 (15A60 62J05 65F99)",
MRnumber = "88f:41039",
MRreviewer = "R. A. Lorentz",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Golub:1987:JW,
author = "Gene H. Golub and Miki Neumann and James W. Demmel and
Paul Saylor and James M. Boyle and Iain Duff and Jack
Dongarra",
title = "{James Wilkinson} (1919--1986)",
journal = j-ANN-HIST-COMPUT,
volume = "9",
number = "2",
pages = "205--210",
month = apr # "\slash " # jun,
year = "1987",
CODEN = "AHCOE5",
ISSN = "0164-1239",
bibdate = "Sat Jul 14 18:11:40 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "From the introduction: ``A series of lightly edited
extracts from messages that were sent over various
computer networks during the period October 5,
1986--February 13, 1987''.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
keywords = "obituary",
}
@Article{Golub:1987:LAA,
author = "G. H. Golub and C. Moler",
title = "Linear Algebra and its Applications --- in Memory of
{James H. Wilkinson}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88--89",
pages = "1--3",
month = apr,
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90098-X",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@InProceedings{Golub:1987:LSL,
author = "G. H. Golub",
title = "Large scale least squares problems",
crossref = "Heiberger:1987:CSS",
pages = "3",
month = "????",
year = "1987",
bibdate = "Mon Sep 9 12:13:04 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Summary form only given as follows. With the advent of
satellites, it is possible to collect large sets of
data which are frequently analysed through least
squares methods. These problems can have over a million
observations and several hundred thousand unknowns.
Fortunately, the data is highly structured so that one
can combine direct and iterative methods for solving
the associated least squares problem. Furthermore, it
is possible to decompose the problem in such a way that
the computation can be performed in parallel. The
author discusses this computation and points out its
connection to other large scale least squares
problems.",
acknowledgement = ack-nhfb,
affiliation = "Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Associated least squares problem; Highly structured;
Iterative methods; Large scale least squares problems;
Least squares methods; Observations; Parallel;
Satellites; Unknowns",
thesaurus = "Least squares approximations; Mathematics computing",
}
@TechReport{Golub:1987:SHC,
author = "Gene H. Golub and Dianne P. O'Leary",
title = "Some history of the conjugate gradient and {Lanczos}
algorithms: 1948--1976",
type = "Technical Report",
number = "TR-1859, UMIACS-TR-87-20",
institution = inst-U-MARYLAND-CS,
address = inst-U-MARYLAND-CS:adr,
pages = "51",
month = "????",
year = "1987",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "Algorithms --- Bibliography",
}
@Article{Arbenz:1988:RRM,
author = "Peter Arbenz and Walter Gander and Gene H. Golub",
title = "Restricted Rank Modification of the Symmetric
Eigenvalue Problem: Theoretical Considerations",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "104",
pages = "75--95",
year = "1988",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(88)90309-6",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18)",
MRnumber = "89h:65052",
MRreviewer = "V. S. Zaja{\v{c}}kovski",
bibdate = "Sun Jan 14 09:18:09 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, eig, symmetric matrix, updating",
}
@Article{Arbenz:1988:SDH,
author = "Peter Arbenz and Gene H. Golub",
title = "On the Spectral Decomposition of {Hermitian} Matrices
Modified by Low Rank Perturbations with Applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "9",
number = "1",
pages = "40--58",
month = "????",
year = "1988",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0609004",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A57 (15A18 65F15)",
MRnumber = "89c:15028",
MRreviewer = "Moody T. Chu",
bibdate = "Tue Jan 21 07:54:58 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "algorithms; eig; indefinite matrix; nla; symmetric
matrix; theory; updating",
subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices \\ I.1.1 Computing
Methodologies, ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Simplification of expressions \\
G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
General, Stability (and instability) \\ G.1.3
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Error analysis",
}
@InProceedings{Gander:1988:CEP,
author = "Walter Gander and Gene H. Golub and Urs {von Matt}",
title = "A constrained eigenvalue problem",
crossref = "Golub:1991:NLA",
pages = "677--686",
year = "1988",
MRclass = "65F15",
MRnumber = "92k:65067",
bibdate = "Sun Jan 14 08:57:55 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Variants of this problem occur in many applications.
The authors show how to eliminate the linear
constraint. Three different methods are presented for
the solution of the resulting Lagrange equations.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Inf., ETH, Zurich, Switzerland",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0210 (Algebra); C1110 (Algebra)",
keywords = "Constrained eigenvalue problem; Lagrange equations;
Linear constraint",
thesaurus = "Eigenvalues and eigenfunctions; Matrix algebra",
}
@Article{Golub:1988:CIC,
author = "Gene H. Golub and Michael L. Overton",
title = "The Convergence of Inexact {Chebyshev} and
{Richardson} Iterative Methods for Solving Linear
Systems",
journal = j-NUM-MATH,
volume = "53",
number = "5",
pages = "571--593",
month = aug,
year = "1988",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01397553",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F10",
MRnumber = "90b:65054",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Chebyshev approximation; convergence; convergence of
numerical methods; error analysis; error bound;
experimentation; inexactness; iter; iterative methods;
linear algebra; linear system; linear systems;
measurement; nla; nonsymmetric inexact Chebyshev
iteration; numerical experiments; performance;
preconditioned iteration; Richardson iterative methods;
skew-symmetric iteration; spectral radius; theory;
verification",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods)",
treatment = "T Theoretical or Mathematical",
xxtitle = "The Convergence of Inexact {Tschebyscheff} and
{Richardson} Iterative Methods for Solving
Linear-Systems",
}
@Article{Golub:1988:GEY,
author = "G. H. Golub and A. Hoffman and G. W. Stewart",
title = "A Generalization of the {Eckart--Young--Mirsky}
Approximation Theorem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "317--328",
year = "1988",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Golub:1988:OPH,
author = "Gene H. Golub and Richard S. Varga",
title = "Obituary to {Peter Henrici (13. September 1923--13.
March 1987)}",
journal = j-NUM-MATH,
volume = "52",
number = "5",
pages = "481--482",
month = may,
year = "1988",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01400886",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "01A70",
MRnumber = "89i:01077",
bibdate = "Sun Jan 14 09:17:43 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
subject-dates = "Peter Karl Henrici (13 September 1923--13 March
1987)",
}
@InCollection{Golub:1988:PBS,
author = "Gene H. Golub and Robert J. Plemmons and Ahmed Sameh",
title = "Parallel Block Schemes for Large-Scale Least-Squares
Computations",
crossref = "Wilhelmson:1988:HSC",
pages = "171--179",
year = "1988",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
price = "US\$29.95",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "algorithms; design; theory",
subject = "J.2 Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Engineering \\ F.2.1 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices \\ G.1.0 Mathematics of
Computing, NUMERICAL ANALYSIS, General, Parallel
algorithms \\ G.1.6 Mathematics of Computing, NUMERICAL
ANALYSIS, Optimization, Least squares methods",
}
@TechReport{DeMoor:1989:GSV,
author = "Bart L. R. {De Moor} and Gene H. Golub",
title = "Generalized singular value decompositions: a proposal
for a standardized nomenclature",
type = "Technical Report",
number = "STAN-CS-TR-2002",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "12",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "decomposition (mathematics)",
}
@TechReport{DeMoor:1989:RSV,
author = "Bart L. R. {De Moor} and Gene H. Golub",
title = "The restricted singular value decomposition:
properties and applications",
type = "Technical Report",
number = "STAN-CS-TR-2001",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "69",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "decomposition (mathematics)",
}
@TechReport{Elhay:1989:UDO,
author = "Sylvan Elhay and Gene H. Golub and Jaroslav
Kautsk{\'y}",
title = "Updating and downdating of orthogonal polynomials with
data fitting applications",
type = "Technical Report",
number = "STAN-CS-89-04, NA-89-04",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "32",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "least squares; orthogonal polynomials",
}
@TechReport{Elman:1989:IMC,
author = "Howard C. Elman and Gene H. Golub",
title = "Iterative methods for cyclically reduced
non-self-adjoint linear systems {II}",
type = "Technical Report",
number = "STAN CS-TR-2238, UMIACS-TR-89-45",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "26",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "iterative methods (mathematics); linear systems",
}
@InProceedings{Elman:1989:LIM,
author = "Howard C. Elman and Gene H. Golub",
title = "Line iterative methods for cyclically reduced
non-self-adjoint elliptic problems",
crossref = "ARO:1990:TSA",
pages = "457--466",
year = "1989",
MRclass = "65F10 (65N20)",
MRnumber = "057 847",
bibdate = "Sun Jan 14 10:11:05 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Gander:1989:CEP,
author = "Walter Gander and Gene H. Golub and Urs {von Matt}",
title = "A constrained eigenvalue problem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "114/115",
pages = "815--839",
year = "1989",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(89)90494-1",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (15A23)",
MRnumber = "90e:15008",
MRreviewer = "Lajos L{\'a}szl{\'o}",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Gander:1989:DLS,
author = "Walter Gander and Gene H. Golub",
title = "Discussion: Linear Smoothers and Additive Models",
journal = j-ANN-STAT,
volume = "17",
number = "2",
pages = "529--532",
month = jun,
year = "1989",
CODEN = "ASTSC7",
DOI = "https://doi.org/10.1214/aos/1176347120",
ISSN = "0090-5364 (print), 2168-8966 (electronic)",
ISSN-L = "0090-5364",
bibdate = "Tue May 18 17:06:23 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://projecteuclid.org/euclid.aos/1176347120;
http://www.jstor.org/stable/2241565",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Annals of Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aos/",
}
@InCollection{Gander:1989:SLE,
author = "Walter Gander and Gene H. Golub and Dominik Gruntz",
title = "Solving linear equations by extrapolation",
crossref = "Kowalik:1989:S",
pages = "279--293",
year = "1989",
MRclass = "65F10",
MRnumber = "91j:65060",
MRreviewer = "R. P. Tewarson",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1989:CEP,
author = "Walter Gander and Gene H. Golub and Urs {von Matt}",
title = "A Constrained Eigenvalue Problem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "114/115",
pages = "815--839",
year = "1989",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (15A23)",
MRnumber = "90e:15008",
MRreviewer = "Lajos L{\'a}szl{\'o}",
bibdate = "Sun Jan 14 09:13:37 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, eig, constrained eigenvalue problem",
}
@Article{Golub:1989:EEI,
author = "Gene H. Golub and Mark D. Kent",
title = "Estimates of Eigenvalues for Iterative Methods",
journal = j-MATH-COMPUT,
volume = "53",
number = "188",
pages = "619--626",
month = oct,
year = "1989",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008724",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10 (65F15)",
MRnumber = "90e:65043",
MRreviewer = "Vasile I. Ionescu",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2008724",
abstract = "Describes a procedure for determining estimates of the
eigenvalues of operators used in various iterative
methods for the solution of linear systems of
equations. The authors show how to determine upper and
lower bounds for the error in the approximate solution
of linear equations, using essentially the same
information as that needed for the eigenvalue
calculations. The methods described depend strongly
upon the theory of moments and Gauss quadrature.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comp. Sci., Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "C4140 (Linear algebra); C4130 (Interpolation and
function approximation); C4160 (Numerical integration
and differentiation)",
corpsource = "Dept. of Comp. Sci., Stanford Univ., CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximate solution; approximation theory;
eigenvalues; eigenvalues and eigenfunctions; error;
estimates; Gauss quadrature; integration; iterative
methods; linear equations; linear systems; lower
bounds; theory of moments; upper bounds",
thesaurus = "Approximation theory; Eigenvalues and eigenfunctions;
Integration; Iterative methods",
treatment = "T Theoretical or Mathematical",
}
@Book{Golub:1989:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
volume = "3",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
edition = "Second",
pages = "xix + 642",
year = "1989",
ISBN = "0-8018-3772-3 (hardcover), 0-8018-3739-1 (paperback)",
ISBN-13 = "978-0-8018-3772-2 (hardcover), 978-0-8018-3739-5
(paperback)",
LCCN = "QA188 .G65 1989",
MRclass = "65Fxx (65-02)",
MRnumber = "90d:65055",
MRreviewer = "Perry Smith",
bibdate = "Mon Oct 26 07:31:01 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/bibnet/subjects/domain-decomp.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
price = "US\$14.50",
series = "Johns Hopkins Series in the Mathematical Sciences",
ZMnumber = "0733.65016",
abstract = "Thoroughly revised, updated, and expanded by more than
one third, this new edition of Golub and Van Loan's
landmark book in scientific computing provides the
vital mathematical background and algorithmic skills
required for the production of numerical software. New
chapters on high performance computing use matrix
multiplication to show how to organize a calculation
for vector processors as well as for computers with
shared or distributed memories. Also new are
discussions of parallel vector methods for linear
equations, least squares, and eigenvalue problems.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "book; math; matrices --- data processing; matrices ---
informatique; na; nla",
libnote = "Not yet in my library.",
remark = "See review by G. W. Steward in Mathematics of
Computation, Vol. 56, No. 193 (Jan., 1991), pp.
380--381.",
shorttableofcontents = "Preface to the Third Edition \\
Software \\
Selected References \\
Matrix Multiplication Problems / 1 \\
Matrix Analysis / 48 \\
General Linear Systems / 87 \\
Special Linear Systems / 133 \\
Orthogonalization and Least Squares / 206 \\
Parallel Matrix Computations / 275 \\
The Unsymmetric Eigenvalue Problem / 308 \\
The Symmetric Eigenvalue Problem / 391 \\
Lanczos Methods / 470 \\
Iterative Methods for Linear Systems / 508 \\
Functions of Matrices / 555 \\
Special Topics / 579 \\
Bibliography / 637 \\
Index / 687",
tableofcontents = "Preface to the First Edition / xi \\
Preface to the Second Edition / xv \\
Using the Book / xvii \\
1: Matrix Multiplication Problems / 1 \\
1.1 Basic Algorithms and Notations / 2 \\
1.2 Exploiting Structure / 16 \\
1.3 Block Matrices and Algorithms / 25 \\
1.4 Aspects of Vector Pipeline Computing / 35 \\
2: Matrix Analysis / 49 \\
2.1 Basic Ideas from Linear Algebra / 49 \\
2.2 Vector Norms / 53 \\
2.3 Matrix Norms / 55 \\
2.4 Finite Precision Matrix Computations / 60 \\
2.5 Orthogonality and the SVD / 70 \\
2.6 Projections and the CS Decomposition / 75 \\
2.7 The Sensitivity of Square Linear Systems / 79 \\
3: General Linear Systems / 86 \\
3.1 Triangular Systems / 86 \\
3.2 Computing the LU Factorization / 92 \\
3.3 Roundoff Analysis of Gaussian Elimination / 104 \\
3.4 Pivoting / 108 \\
3.5 Improving and Estimating Accuracy / 123 \\
4: Special Linear Systems / 133 \\
4.1 The $LDM^T$ and $LDL^T$ Factorizations / 134 \\
4.2 Positive Definite Systems / 139 \\
4.3 Banded Systems / 149 \\
4.4 Symmetric Indefinite Systems / 159 \\
4.5 Block Tridiagonal Systems / 170 \\
4.6 Vandermonde Systems / 178 \\
4.7 Toeplitz Systems / 183 \\
5: Orthogonalization and Least Squares / 193 \\
5.1 Householder and Givens Transformations / 194 \\
5.2 The $Q R$ Factorization / 211 \\
5.3 The Full Rank Least Squares Problem / 221 \\
5.4 Other Orthogonal Factorizations / 233 \\
5.5 The Rank Deficient Least Squares Problem / 241 \\
5.6 Weighting and Iterative Improvement / 250 \\
5.7 A Note on Square and Underdetermined Systems / 256
\\
6: Parallel Matrix Computations / 260 \\
6.1 Distributed Memory Gaxpy / 261 \\
6.2 Shared Memory Gaxpy / 276 \\
6.3 Parallel Matrix Multiplication / 288 \\
6.4 Ring Factorization Procedures / 301 \\
6.5 Mesh Factorization Procedures / 310 \\
6.6 Shared Memory Factorization Methods / 321 \\
7: The Unsymmetric Eigenvalue Problem / 331 \\
7.1 Properties and Decompositions / 332 \\
7.2 Perturbation Theory / 341 \\
7.3 Power Iterations / 351 \\
7.4 Hessenberg and Real Schur Forms / 361 \\
7.5 The Practical $Q R$ Algorithm / 373 \\
7.6 Invariant Subspace Computations / 382 \\
7.7 The $QZ$ Method for $A x = \lambda B x$ / 394 \\
8: The Symmetric Eigenvalue Problem / 409 \\
8.1 Properties, Decompositions, Perturbation Theory /
410 \\
8.2 The Symmetric $Q R$ Algorithm / 418 \\
8.3 Computing the SVD / 427 \\
8.4 Some Special Methods / 437 \\
8.5 Jacobi Methods / 444 \\
8.6 A Divide and Conquer Method / 459 \\
8.7 More Generalized Eigenvalue Problems / 466 \\
9: Lanczos Methods / 475 \\
9.1 Derivation and Convergence Properties / 476 \\
9.2 Practical Lanczos Procedures / 484 \\
9.3 Applications and Extensions / 494 \\
10: Iterative Methods for Linear Systems / 505 \\
10.1 The Standard Iterations / 506 \\
10.2 The Conjugate Gradient Method / 516 \\
10.3 Preconditioned Conjugate Gradient Methods / 527
\\
11: Functions of Matrices / 539 \\
11.1 Eigenvalue Methods / 540 \\
11.2 Approximation Methods / 546 \\
11.3 The Matrix Exponential / 555 \\
12: Special Topics / 561 \\
12.1 Some Constrained Least Squares Problems / 561 \\
12.2 Subset Selection Using the SVD / 571 \\
12.3 Total Least Squares / 576 \\
12.4 Comparing Subspaces Using the SVD / 581 \\
12.5 Some Modified Eigenvalue Problems / 587 \\
12.6 Updating the $Q R$ Factorization / 592 \\
Bibliography / 601 \\
Index / 635",
}
@TechReport{Golub:1989:MMI,
author = "Gene H. Golub and Martin H. Gutknecht",
title = "Modified moments for indefinite weight functions",
type = "Technical Report",
number = "STAN-CS-89-08, NA-89-08",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "19",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "orthogonal polynomials",
}
@Article{Golub:1989:SHC,
author = "Gene H. Golub and Dianne P. O'Leary",
title = "Some History of the Conjugate Gradient and {Lanczos}
Algorithms: 1948--1976",
journal = j-SIAM-REVIEW,
volume = "31",
number = "1",
pages = "50--102",
month = mar,
year = "1989",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1031003",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65-03 (00A15 01A60 65-00 65Fxx 90-03)",
MRnumber = "90b:65003",
bibdate = "Mon Jan 20 10:31:25 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib",
URL = "http://www.jstor.org/stable/2030847",
abstract = "The conjugate gradient and Lanczos algorithms for
solving linear systems of equations and eigenproblems
represent very important computational innovations of
the early 1950s. These methods came into wide use only
in the mid-1970s. Shortly thereafter, vector computers
and massive computer memories made it possible to use
these methods to solve problems which could not be
solved in any other way. Since that time, the
algorithms have been further refined and have become a
basic tool for solving a wide variety of problems on a
wide variety of computer architectures. The conjugate
gradient algorithm has also been extended to solve
nonlinear systems of equations and optimization
problems, and this has had tremendous impact on the
computation of unconstrained and constrained
optimization problems. This paper gives some of the
history of the conjugate gradient and Lanczos
algorithms and an annotated bibliography for the period
1948--1976.",
acknowledgement = ack-nhfb,
affiliation = "Stanford Univ",
affiliationaddress = "Stanford, CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "723; 921",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "Algorithms; Computer Programming--Algorithms;
Conjugate Gradient Algorithm; Lanczos Algorithm;
Mathematical Techniques; Optimization--Theory; Variable
Metric Algorithms",
mynote = "June 1987 Maryland TR-1859",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods) \\ G.1.3 Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues \\ G.1.3 Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix
inversion",
subject-dates = "Eduard Stiefel (21 April 1909--25 November 1978);
Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
}
@Article{Comon:1990:TFE,
author = "Pierre Comon and Gene H. Golub",
title = "Tracking a Few Extreme Singular Values and Vectors in
Signal Processing",
journal = j-PROC-IEEE,
volume = "78",
number = "8",
pages = "1327--1343",
month = aug,
year = "1990",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1109/5.58320",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Mon Sep 9 11:37:15 MDT 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=58320",
abstract = "In various applications it is necessary to keep track
of a low-rank approximation of a covariance matrix,
R(t), slowly varying with time. It is convenient to
track the left singular vectors associated with the
largest singular values of the triangular factor, L(t),
of its Cholesky factorization. These algorithms are
referred to as square-root. The drawback of the
eigenvalue decomposition (EVD) or the singular value
decompositions (SVD) is usually the volume of the
computations. Various numerical methods for carrying
out this task are surveyed, and it is shown why this
heavy computational burden is questionable in numerous
situations and should be revised. Indeed, the
complexity per eigenpair is generally a quadratic
function of the problem size, but there exist faster
algorithms with linear complexity. Finally, in order to
make a choice among the large and fuzzy set of
available techniques, comparisons based on computer
simulations in a relevant signal processing context are
made.",
acknowledgement = ack-nhfb,
affiliation = "Thomson-Sintra, Cagnes-sur-Mer, France",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290 (Numerical analysis); B6140 (Signal processing
and detection); C1260 (Information theory); C4100
(Numerical analysis)",
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "Adaptive algorithms; Cholesky factorization; Computer
simulations; Covariance matrix; Eigenvalue
decomposition; Extreme singular values; Extreme
singular vectors; Linear complexity; Low-rank
approximation; nla, signal processing, Lanczos
algorithm, rank determination; Numerical methods;
Signal processing; Singular value decompositions;
Square root algorithms; Tracking; Triangular factor",
thesaurus = "Computational complexity; Eigenvalues and
eigenfunctions; Matrix algebra; Numerical methods;
Signal processing",
}
@Article{Elman:1990:IMC,
author = "Howard C. Elman and Gene H. Golub",
title = "Iterative methods for cyclically reduced
non-self-adjoint linear systems",
journal = j-MATH-COMPUT,
volume = "54",
number = "190",
pages = "671--700",
month = apr,
year = "1990",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008506",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10 (65N22)",
MRnumber = "91b:65036",
MRreviewer = "Harry Yserentant",
bibdate = "Mon Sep 09 12:10:35 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/2008506",
abstract = "The authors study iterative methods for solving linear
systems of the type arising from two-cyclic
discretizations of non-self-adjoint two-dimensional
elliptic partial differential equations. A prototype is
the convection-diffusion equation. The methods consist
of applying one step of cyclic reduction, resulting in
a `reduced system' of half the order of the original
discrete problem, combined with a reordering and a
block iterative technique for solving the reduced
system. For constant-coefficient problems, they present
analytic bounds on the spectral radii of the iteration
matrices in terms of cell Reynolds numbers that show
the methods to be rapidly-convergent. In addition, they
describe numerical experiments that supplement the
analysis and that indicate that the methods compare
favourably with methods for solving the `unreduced'
system.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park,
MD, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290P (Differential equations); C4170 (Differential
equations)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Analytic bounds; Block iterative technique; Cell
Reynolds numbers; Convection-diffusion equation;
Cyclically reduced non-self-adjoint linear systems;
Elliptic partial differential equations; Iterative
methods; Linear systems; Numerical experiments;
Rapidly-convergent; Reordering; Spectral radii",
thesaurus = "Convergence of numerical methods; Iterative methods;
Partial differential equations",
}
@InProceedings{Elman:1990:IML,
author = "Howard C. Elman and Gene H. Golub",
title = "Block iterative methods for cyclically reduced
nonselfadjoint elliptic problems",
crossref = "Kincaid:1990:IML",
pages = "91--105",
year = "1990",
MRclass = "65F10",
MRnumber = "1 038 090",
bibdate = "Fri Dec 20 17:21:26 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Elman:1990:LIMa,
author = "Howard C. Elman and Gene H. Golub",
title = "Line Iterative Methods for Cyclically Reduced Discrete
Convection-Diffusion Problems",
type = "Technical Report",
number = "CS-TR-2403, UMIACS-TR-90-16",
institution = inst-U-MARYLAND-CS,
address = inst-U-MARYLAND-CS:adr,
pages = "29",
month = "????",
year = "1990",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "We perform an analytic and empirical study of line
iterative methods for solving the discrete
convection-diffusion equation. The methodology consists
of performing one step of the cyclic reduction method,
followed by iteration on the resulting cyclic reduction
method, followed by iteration on the resulting reduced
system using line orderings of the reduced grid. Two
classes of iterative methods are considered: block
stationary methods, such as the block Gauss--Seidel and
SOR methods, and preconditioned generalized minimum
residual methods with incomplete LU preconditioners.
New analysis extends convergence bounds for constant
coefficient problems to problems with separable
variable coefficients. In addition, analytic results
show that iterative methods based on incomplete LU
preconditioners have faster convergence rates on
incomplete LU preconditioners have faster convergence
rates than block Jacobi relaxation methods. Numerical
experiments examine additional properties of the two
classes of methods, including the effects of flow,
discretization, and grid ordering on performance.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "Iterative methods (Mathematics); Numerical analysis",
}
@InProceedings{Elman:1990:LIMb,
author = "Howard C. Elman and Gene H. Golub",
title = "Line iterative methods for cyclically reduced
nonselfadjoint elliptic problems",
crossref = "ARO:1990:TSA",
pages = "457--466",
year = "1990",
MRclass = "65F10 (65N20)",
MRnumber = "1 057 847",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Ferng:1990:ALM,
author = "W. R. Ferng and G. H. Golub and R. J. Plemmons",
title = "Adaptive {Lanczos} methods for recursive condition
estimation",
journal = j-PROC-SPIE,
volume = "1348",
pages = "326--337",
month = "????",
year = "1990",
CODEN = "PSISDG",
ISSN = "0277-786X (print), 1996-756X (electronic)",
ISSN-L = "0277-786X",
bibdate = "Mon Sep 9 11:37:15 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "This paper proposes an adaptive Lanczos Estimator
scheme for tracking the condition number of the
modified matrix over time. Applications to recursive
least squares computations using the covariance method
with sliding data windows are considered. Comparisons
are made with other adaptive and non-adaptive condition
estimators for recursive least squares problems.
Numerical experiments are reported.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290H (Linear algebra); B6140 (Signal processing
and detection); C1240 (Adaptive system theory); C1260
(Information theory); C4140 (Linear algebra)",
fjournal = "Proceedings of the SPIE --- The International Society
for Optical Engineering",
keywords = "Adaptive Lanczos Estimator; Covariance method;
Modified matrix; Recursive condition estimation;
Recursive least squares computations; RLS method;
Signal processing; Sliding data windows",
thesaurus = "Adaptive filters; Least squares approximations; Matrix
algebra; Parameter estimation; Signal processing;
Variational techniques",
}
@InProceedings{Gander:1990:SLE,
author = "Walter Gander and G. H. Golub and Dominik Gruntz",
title = "Solving linear equations by extrapolation",
crossref = "Kowalik:1990:SNA",
pages = "279--293",
year = "1990",
MRclass = "65F10",
MRnumber = "91j:65060",
MRreviewer = "R. P. Tewarson",
bibdate = "Sun Jan 14 09:09:38 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1990:DVK,
author = "Gene Golub and Bo K{\aa}gstr{\"o}m and Axel Ruhe and
Paul {Van Dooren}",
title = "Dedication to {Vera N. Kublanovskaya} on her 70th
Birthday",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "11",
number = "4",
pages = "vii--ix",
month = oct,
year = "1990",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0611033",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "01A70",
MRnumber = "91j:01043",
bibdate = "Fri Oct 17 06:15:04 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Golub:1990:IML,
author = "Gene H. Golub and John E. de Pillis",
title = "Toward an effective two-parameter {SOR} method",
crossref = "Kincaid:1990:IML",
pages = "107--119",
year = "1990",
MRclass = "65F10",
MRnumber = "038 091",
bibdate = "Sun Jan 14 10:13:28 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1990:MMI,
author = "Gene H. Golub and Martin H. Gutknecht",
title = "Modified Moments for Indefinite Weight Functions",
journal = j-NUM-MATH,
volume = "57",
number = "6\slash 7",
pages = "607--624",
month = jul,
year = "1990",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "30E05 (41A10 65F99)",
MRnumber = "91i:30034",
MRreviewer = "Jia Rong Yu",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Paper presented at the Conference on Approximation
Theory and Numerical Linear Algebra, 30 March -- 1
April, 1989, Kent, Ohio.",
abstract = "The problem of generating the recurrence coefficients
of orthogonal polynomials from the moments or from
modified moments of the weight function is well
understood for positive weight distributions. The
authors extend this theory and the basic algorithms to
the case of an indefinite weight function. While the
generic indefinite case is formally not much different
from the positive definite case, there exist nongeneric
degenerate situations, and these require a different
more complicated treatment. The understanding of these
degenerate situations makes it possible to construct a
stable approximate solution of an ill-conditioned
problem. The application to adaptive iterative methods
for linear systems of equations is anticipated.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C4140 (Linear algebra)",
corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "adaptive iterative methods; Adaptive iterative
methods; degenerate situations; Degenerate situations;
ill-conditioned problem; Ill-conditioned problem;
indefinite weight functions; Indefinite weight
functions; iterative methods; linear algebra; linear
systems; Linear systems; orthogonal polynomials;
Orthogonal polynomials; polynomials",
thesaurus = "Iterative methods; Linear algebra; Polynomials",
treatment = "T Theoretical or Mathematical",
}
@InCollection{Golub:1990:PRJ,
author = "Gene Golub",
title = "Prologue. Reflections on {Jim Wilkinson}",
crossref = "Cox:1990:RNC",
pages = "1--5",
year = "1990",
MRclass = "01A70",
MRnumber = "92b:01057a",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Berry:1991:ELS,
author = "Michael Berry and Gene Golub",
title = "Estimating the Largest Singular Values of Large Sparse
Matrices via Modified Moments",
journal = j-NUMER-ALGORITHMS,
volume = "1",
number = "4",
pages = "353--374 (or 353--373??)",
month = nov,
year = "1991",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F15 (65D32 65F50 65Y05)",
MRnumber = "93a:65046",
MRreviewer = "Cs. J. Heged{\H{u}}s",
bibdate = "Mon Sep 9 11:25:40 MDT 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
abstract = "The authors describe a procedure for determining a few
of the largest singular values of a large sparse
matrix. The method by Golub and Kent (1989) which uses
the method of modified moments for estimating the
eigenvalues of operators used in iterative methods for
the solution of linear systems of equations is
appropriately modified in order to generate a sequence
of bidiagonal matrices whose singular values
approximate those of the original sparse matrix. A
simple Lanczos recursion is proposed for determining
the corresponding left and right singular vectors. The
potential asynchronous computation of the bidiagonal
matrices using modified moments with the iterations of
an adapted Chebyshev semi-iterative (CSI) method is an
attractive feature for parallel computers. Comparisons
in efficiency and accuracy with an appropriate Lanczos
algorithm (with selective re-orthogonalization) are
presented on large sparse (rectangular) matrices
arising from applications such as information retrieval
and seismic reflection tomography. This procedure is
essentially motivated by the theory of moments and
Gauss quadrature.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); C4130 (Interpolation and
function approximation); C4140 (Linear algebra)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Adaptive Chebyshev semi-iterative method; Asynchronous
computation; Eigenvalues; Gauss quadrature; Information
retrieval; Iterative methods; Lanczos recursion; Large
sparse matrices; Largest singular values estimation;
Linear systems of equations; Modified moments; nla,
sparse, svd; Parallel computers; Seismic reflection
tomography; Singular vectors",
pubcountry = "Switzerland",
thesaurus = "Chebyshev approximation; Eigenvalues and
eigenfunctions; Iterative methods; Matrix algebra",
}
@InProceedings{Boley:1991:MNL,
author = "D. Boley and G. H. Golub",
title = "A modified non-symmetric {Lanczos} algorithm and
applications",
crossref = "Vaccaro:1991:SSP",
pages = "189--196",
month = "????",
year = "1991",
bibdate = "Mon Sep 9 11:37:15 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Gives a brief description of a non-symmetric Lanczos
algorithm that does not require strict bi-orthogonality
among the generated vectors. Several applications are
mentioned. For example, it is shown how the vectors
generated are algebraically related to `controllable
space' and `observable space' for a related linear
dynamical system. The algorithm described is
particularly appropriate for large sparse problems.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Minnesota, Univ., Minneapolis,
MN, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
keywords = "Controllable space; Large sparse problems; Linear
dynamical system; Matrix eigenvalue computation;
Modified nonsymmetric Lanczos algorithm; Observable
space",
thesaurus = "Eigenvalues and eigenfunctions; Matrix algebra",
}
@Article{Boley:1991:NLA,
author = "Daniel Boley and Gene Golub",
title = "The nonsymmetric {Lanczos} algorithm and
controllability",
journal = j-SYST-CONTROL-LETT,
volume = "16",
number = "2",
pages = "97--105",
month = feb,
year = "1991",
CODEN = "SCLEDC",
ISSN = "0167-6911 (print), 1872-7956 (electronic)",
ISSN-L = "0167-6911",
MRclass = "93B05 (93B40)",
MRnumber = "92e:93004",
MRreviewer = "Alexander N. Shoshitaishvili",
bibdate = "Fri Dec 20 17:23:54 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Gives a brief description of a nonsymmetric Lanczos
algorithm that does not require strict bi-orthogonality
among the generated vectors. The authors show how the
vectors generated are algebraically related to
reachable space and observable space for a related
linear dynamical system. The algorithm described is
particularly appropriate for large sparse systems.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Comput. Sci. Dept., Minnesota Univ., Minneapolis, MN,
USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C1110 (Algebra); C1120 (Analysis); C1310 (Analysis
and synthesis methods); C1320 (Stability)",
fjournal = "Systems and Control Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01676911",
keywords = "Controllability; Large sparse systems; Linear
dynamical system; Nonsymmetric Lanczos algorithm;
Observability; Observable space; Reachable space;
Vectors",
pubcountry = "Netherlands",
thesaurus = "Algebra; Controllability; Linear systems;
Observability; Vectors",
}
@Article{Boley:1991:NLF,
author = "Daniel L. Boley and Sylvan Elhay and Gene H. Golub and
Martin H. Gutknecht",
title = "Nonsymmetric {Lanczos} and finding orthogonal
polynomials associated with indefinite weights",
journal = j-NUMER-ALGORITHMS,
volume = "1",
number = "1",
pages = "21--43",
month = "????",
year = "1991",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F15 (65F30 65F50 65G05)",
MRnumber = "93f:65033",
MRreviewer = "Alexander S. Babanin",
bibdate = "Sun Jan 14 08:49:25 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "The nonsymmetric Lanczos algorithm reduces a general
matrix to tridiagonal by generating two sequences of
vectors which satisfy a mutual bi-orthogonality
property. The process can proceed as long as the two
vectors generated at each stage are not mutually
orthogonal, otherwise the process breaks down. The
authors propose a variant that does not break down by
grouping the vectors into clusters and enforcing the
bi-orthogonality property only between different
clusters, but relaxing the property within clusters.
They show how this variant of the matrix Lanczos
algorithm applies directly to a problem of computing a
set of orthogonal polynomials and associated indefinite
weights with respect to an indefinite inner product,
given the associated moments. The authors discuss the
close relationship between the modified Lanczos
algorithm and the modified Chebyshev algorithm. They
further show the connection between this last problem
and checksum-based error correction schemes for
fault-tolerant computing.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Minnesota Univ., Minneapolis,
MN, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290H (Linear algebra); B6120B (Codes); C4140
(Linear algebra)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Checksum-based error correction; Fault-tolerant
computing; Indefinite inner product; Indefinite
weights; Matrix Lanczos algorithm; Modified Chebyshev
algorithm; Modified Lanczos algorithm; Mutual
bi-orthogonality property; Nonsymmetric Lanczos
algorithm; Orthogonal polynomials; Tridiagonal matrix",
pubcountry = "Switzerland",
thesaurus = "Error correction codes; Matrix algebra; Polynomials",
}
@Article{DeMoor:1991:RSV,
author = "Bart L. R. {De Moor} and Gene H. Golub",
title = "The Restricted Singular Value Decomposition:
Properties and Applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "3",
pages = "401--425",
month = jul,
year = "1991",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0612029",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A09 (15A18 15A21 15A24 47A99)",
MRnumber = "92k:15012",
MRreviewer = "Zdzislaw W. Trzaska",
bibdate = "Sun Jan 14 08:07:16 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "nla, gsvd",
}
@InProceedings{Elhay:1991:UDOa,
author = "Sylvan Elhay and G. H. Golub and Jaroslav
Kautsk{\'y}",
title = "Updating and downdating of orthogonal polynomials with
data fitting applications",
crossref = "Golub:1991:NLA",
pages = "149--172",
year = "1991",
MRclass = "65D15 (65F30)",
MRnumber = "92j:65017",
bibdate = "Sun Jan 14 09:02:43 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Derives and assesses new methods for updating and
downdating least squares polynomial fits to discrete
data using polynomials orthogonal on all the data
points being used. Rather than fixing on one basis
throughout, the methods adaptively update and downdate
both the least squares fit and the polynomial basis.
This is achieved by performing similarity
transformations on the tridiagonal Jacobi matrices
representing the basis.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Adelaide Univ., SA, Australia",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B6140 (Signal processing and detection); C1260
(Information theory)",
keywords = "Data fitting applications; Data points; Downdating;
Least squares polynomial fits; Orthogonal polynomials;
Similarity transformations; Tridiagonal Jacobi
matrices; Updating",
thesaurus = "Data compression; Least squares approximations; Matrix
algebra; Polynomials",
}
@Article{Elhay:1991:UDOb,
author = "Sylvan Elhay and Gene H. Golub and Jaroslav
Kautsk{\'y}",
title = "Updating and downdating of orthogonal polynomials with
data fitting applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "2",
pages = "327--353",
month = apr,
year = "1991",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0612024",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65D20 (65F05)",
MRnumber = "91m:65054",
bibdate = "Sun Jan 14 09:07:02 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Elman:1991:IMC,
author = "Howard C. Elman and Gene H. Golub",
title = "Iterative methods for cyclically reduced
nonselfadjoint linear systems. {II}",
journal = j-MATH-COMPUT,
volume = "56",
number = "193",
pages = "215--242",
month = jan,
year = "1991",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008538",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10 (65N22)",
MRnumber = "91e:65051",
MRreviewer = "Harry Yserentant",
bibdate = "Sun Jan 14 09:10:54 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
abstract = "For pt.~I see ibid., vol.~54, p.~671--700 (1990). The
authors perform an analytic and experimental study of
line iterative methods for solving linear systems
arising from finite difference discretizations of
nonself-adjoint elliptic partial differential equations
on two-dimensional domains. The methods consist of
performing one step of cyclic reduction, followed by
solution of the resulting reduced system by line
relaxation. They augment previous analyses of one-line
methods, and derive a new convergence analysis for
two-line methods, showing that both classes of methods
are highly effective for solving the
convection-diffusion equation. In addition, they
compare the experimental performance of several
variants of these methods, and show that the methods
can be implemented efficiently on parallel
architectures.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park,
MD, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290P (Differential equations); C4170 (Differential
equations)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "2D domains; Convection-diffusion equation; Convergence
analysis; Finite difference discretizations; Line
iterative methods; Line relaxation; Linear systems;
Nonself-adjoint elliptic partial differential
equations; Parallel architectures",
thesaurus = "Convergence of numerical methods; Iterative methods;
Parallel algorithms; Partial differential equations",
}
@Article{Ferng:1991:ALM,
author = "William R. Ferng and Gene H. Golub and Robert J.
Plemmons",
title = "Adaptive {Lanczos} methods for recursive condition
estimation",
journal = j-NUMER-ALGORITHMS,
volume = "1",
number = "1",
pages = "1--20",
month = "????",
year = "1991",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F10 (65F20 65F35 93E10 94A12)",
MRnumber = "92h:65053",
MRreviewer = "De Hui Chen",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Estimates for the condition number of a matrix are
useful in many areas of scientific computing,
including: recursive least squares computations,
optimization, eigenanalysis, and general nonlinear
problems solved by linearization techniques where
matrix modification techniques are used. The purpose of
this paper is to propose an adaptive Lanczos estimator
scheme, which the authors call ale, for tracking the
condition number of the modified matrix over time.
Applications to recursive least squares (RLS)
computations using the covariance method with sliding
data windows are considered. ale is fast for relatively
small n-parameter problems arising in RLS methods in
control and signal processing, and is adaptive over
time, i.e., estimates at time t are used to produce
estimates at time t+1. Comparisons are made with other
adaptive and non-adaptive condition estimators for
recursive least squares problems. Numerical experiments
are reported indicating that ale yields a very accurate
recursive condition estimator.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); B6140 (Signal processing and
detection); C1260 (Information theory); C4130
(Interpolation and function approximation); C4140
(Linear algebra)",
corpsource = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Adaptive Lanczos estimator; adaptive Lanczos
estimator; Adaptive Lanczos methods; adaptive Lanczos
methods; Covariance method; covariance method; least
squares approximations; matrix algebra; Matrix
condition number; matrix condition number; Matrix
modification; matrix modification; numerical methods;
Recursive condition estimation; recursive condition
estimation; Recursive least squares computations;
recursive least squares computations; signal
processing; Sliding data windows; sliding data
windows",
pubcountry = "Switzerland",
thesaurus = "Least squares approximations; Matrix algebra;
Numerical methods; Signal processing",
treatment = "T Theoretical or Mathematical",
xxpages = "1--19",
}
@Article{Fischer:1991:GPW,
author = "Bernd Fischer and Gene H. Golub",
title = "On generating polynomials which are orthogonal over
several intervals",
journal = j-MATH-COMPUT,
volume = "56",
number = "194",
pages = "711--730",
month = apr,
year = "1991",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008403",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33C45",
MRnumber = "92d:33015",
MRreviewer = "J. Prasad",
bibdate = "Sun Jan 14 09:06:36 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/2008403",
abstract = "The authors consider the problem of generating the
recursion coefficients of orthogonal polynomials for a
given weight function. The weight function is assumed
to be the weighted sum of weight functions, each
supported on its own interval. Some of these intervals
may coincide, overlap or are contiguous. They discuss
three algorithms. Two of them are based on modified
moments, whereas the other is based on an explicit
expression for the desired coefficients. Several
examples, illustrating the numerical performance of the
various methods, are presented.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Inst. fur Angewandte Math., Hamburg Univ., Germany",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Explicit expression; Generating polynomials; Modified
moments; Numerical performance; Recursion coefficients;
Weight function; Weighted sum",
thesaurus = "Polynomials",
}
@TechReport{Freund:1991:ISLa,
author = "Roland W. Freund and Gene H. Golub and No{\"e}l M.
Nachtigal",
title = "Iterative Solution of Linear Systems",
type = "Technical Report",
number = "NA-91-05",
institution = "Computer Science Department, Stanford University",
address = "Stanford, CA, USA",
month = "????",
year = "1991",
bibdate = "Sun Jan 14 08:46:41 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InCollection{Gander:1991:CEP,
author = "Walter Gander and Gene H. Golub and Urs {von Matt}",
title = "A constrained eigenvalue problem",
crossref = "Golub:1991:NLA",
pages = "677--686",
year = "1991",
MRclass = "65F15",
MRnumber = "92k:65067",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1991:DJW,
author = "G. Golub and B. Parlett",
title = "Dedication to {J. Wallace Givens}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "1",
pages = "U1--U1",
month = jan,
year = "1991",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Golub:1991:HMN,
author = "Gene H. Golub",
title = "A history of modern numerical linear algebra",
journal = j-MITT-MATH-GES-HAMBURG,
volume = "12",
number = "4",
pages = "949--960",
year = "1991/1992",
CODEN = "MNGBAK",
ISSN = "0340-4358",
MRclass = "65-03 (01A60 65Fxx)",
MRnumber = "93c:65002",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Mathematische Wissenschaften gestern und heute. 300
Jahre Mathematische Gesellschaft in Hamburg, Teil 4
(Hamburg, 1990).",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mitteilungen der Mathematischen Gesellschaft in
Hamburg",
}
@InProceedings{Golub:1991:IMC,
author = "G. H. Golub and R. S. Tuminaro",
title = "Iterative Methods for Cyclically Reduced
Non-Self-Adjoint Linear Systems",
crossref = "Anonymous:1991:PIS",
pages = "7--8",
year = "1991",
bibdate = "Mon Aug 26 10:38:41 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1991:QCL,
author = "Gene H. Golub and Urs {von Matt}",
title = "Quadratically Constrained Least Squares and Quadratic
Problems",
journal = j-NUM-MATH,
volume = "59",
number = "6",
pages = "561--580",
month = sep,
year = "1991",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01385796",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F20 (65F50 65K10)",
MRnumber = "92f:65049",
MRreviewer = "R. P. Tewarson",
bibdate = "Sun Jan 14 09:05:23 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "The article considers the following problem: Compute a
vector x such that //Ax-b///sub 2/-min, subject to the
constraint //x///sub 2/= alpha. A new approach to this
problem based on Gauss quadrature is given. The method
is especially well suited when the dimensions of A are
large and the matrix is sparse. It is also possible to
extend this technique to a constrained quadratic form:
For a symmetric matrix A it considers the minimization
of x/sup T/Ax-2b/sup T/x subject to the constraint
//x///sub 2/= alpha. Some numerical examples are
given.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C1110 (Algebra); C1180 (Optimisation techniques);
C4140 (Linear algebra)",
corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "constraints; Gauss quadrature; lsq; matrix algebra;
minimisation; Minimization; minimization; nla; nllsq;
nlop; Quadratically constrained least squares problems;
quadratically constrained least squares problems;
Quadratically constrained quadratic problems;
quadratically constrained quadratic problems; Sparse
matrix; sparse matrix; Symmetric matrix; symmetric
matrix; Vector; vector",
thesaurus = "Matrix algebra; Minimisation",
treatment = "T Theoretical or Mathematical",
}
@Book{VanHuffel:1991:TLS,
author = "Sabine {Van Huffel} and Joos Vandewalle",
title = "The total least squares problem. Computational aspects
and analysis",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiv + 300",
year = "1991",
ISBN = "0-89871-275-0",
ISBN-13 = "978-0-89871-275-9",
LCCN = "QA275.H84 1991",
MRclass = "65-00 (00A69 65-01)",
MRnumber = "93b:65001",
MRreviewer = "R. P. Tewarson",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Foreword by Gene H. Golub.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Arbenz:1992:LAS,
author = "Peter Arbenz and Gene H. Golub",
title = "{$ Q R $}-Like Algorithms for Symmetric Arrow
Matrices",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "2",
pages = "655--658",
month = apr,
year = "1992",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0613039",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15",
MRnumber = "92k:65064",
bibdate = "Sun Jan 14 08:58:46 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "nla, arrowhead matrix, QR algorithm, eig",
}
@Article{Bojanczyk:1992:PSD,
author = "A. Bojanczyk and G. Golub and P. {Van Dooren}",
title = "The periodic {Schur} decomposition: algorithms and
applications",
journal = j-PROC-SPIE,
volume = "1770",
pages = "31--42",
month = "????",
year = "1992",
CODEN = "PSISDG",
ISSN = "0277-786X (print), 1996-756X (electronic)",
ISSN-L = "0277-786X",
bibdate = "Mon Sep 9 11:06:23 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "The authors derive a unitary eigendecomposition for a
sequence of matrices which they call the periodic Schur
decomposition. They prove its existence and discuss its
application to the solution of periodic difference
arising in control. It is shown how the classical QR
algorithm can be extended to provide a stable algorithm
for computing this generalized decomposition. The
decomposition is also applied to cyclic matrices and
two-point boundary value problems.",
acknowledgement = ack-nhfb,
affiliation = "Dept. Electr. Eng., Cornell Univ., Ithaca, NY, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C1110 (Algebra); C1120 (Analysis); C1340G
(Time-varying systems); C4140 (Linear algebra); C4170
(Differential equations)",
fjournal = "Proceedings of the SPIE --- The International Society
for Optical Engineering",
keywords = "Cyclic matrices; Matrix sequence; Periodic difference;
Periodic Schur decomposition; QR algorithm; Stable
algorithm; Time-varying control systems; Two-point
boundary value problems; Unitary eigendecomposition",
thesaurus = "Boundary-value problems; Difference equations;
Eigenvalues and eigenfunctions; Matrix algebra;
Time-varying systems",
}
@Article{Boley:1992:AFT,
author = "Daniel L. Boley and Richard P. Brent and Gene H. Golub
and Franklin T. Luk",
title = "Algorithmic Fault Tolerance Using the {Lanczos}
Method",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "312--332",
month = jan,
year = "1992",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0613023",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (94B05)",
MRnumber = "93f:65034",
MRreviewer = "Herbert J. Bernstein",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Carey:1992:NAS,
author = "Cheryl Carey and Hsin-Chu Chen and G. H. Golub and
Ahmed Sameh",
title = "A new approach for solving symmetric eigenvalue
problems",
journal = j-COMPUT-SYST-ENG,
volume = "3",
number = "6",
pages = "671--679",
month = dec,
year = "1992",
CODEN = "COSEEO",
ISSN = "0956-0521 (print), 1873-6211 (electronic)",
ISSN-L = "0956-0521",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Presents a new approach for the solution to a series
of slightly perturbed symmetric eigenvalue problems
(A+BS/sub i/B/sup T/)x= lambda x, 0<or=i<or=m, where
A=A/sup T/ in R/sup n*n/, B in R/sup n*p/, and S/sub
i/=S/sub i//sup T/ in R/sup p*p/, p<<n. The matrix B is
assumed to have full column rank. The main idea of the
approach lies in a specific choice of starting vectors
used in the block Lanczos algorithm so that the effect
of the perturbations is confined to lie in the first
diagonal block of the block tridiagonal matrix that is
produced by the block Lanczos algorithm. Subsequently,
for the perturbed eigenvalue problems under the
authors' consideration, the block Lanczos scheme needs
to be applied to the original (unperturbed) matrix only
once and then the first diagonal block updated for each
perturbation so that for low-rank perturbations, the
algorithm presented in the paper results in significant
savings. Numerical examples based on finite element
vibration analysis illustrate the advantages of this
approach.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "A0260 (Numerical approximation and analysis); A0320
(Classical mechanics of discrete systems: general
mathematical aspects); A0340K (Waves and wave
propagation: general mathematical aspects); C4140
(Linear algebra); C4185 (Finite element analysis)",
fjournal = "Computing systems in engineering: an international
journal",
keywords = "Block Lanczos algorithm; Block tridiagonal matrix;
Eigenvalues; Eigenvectors; Finite element vibration
analysis; Numerical algorithms; Perturbations;
Perturbed eigenvalue problems; Real symmetric matrices;
Symmetric eigenvalue problems",
pubcountry = "UK",
thesaurus = "Eigenvalues and eigenfunctions; Finite element
analysis; Matrix algebra; Vibrations",
}
@Article{Elhay:1992:JMS,
author = "Sylvan Elhay and Gene H. Golub and Jaroslav
Kautsk{\'y}",
title = "{Jacobi} matrices for sums of weight functions",
journal = j-BIT,
volume = "32",
number = "1",
pages = "143--166",
year = "1992",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01995114",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F30 (65D15)",
MRnumber = "93k:65036",
bibdate = "Fri Nov 13 07:00:34 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Orthogonal polynomials are conveniently represented by
the tridiagonal Jacobi matrix of coefficients of the
recurrence relation which they satisfy. Let J/sub 1/
and J/sub 2/ be finite Jacobi matrices for the weight
functions w/sub 1/ and w/sub 2/, resp. Is it possible
to determine a Jacobi matrix J, corresponding to the
weight functions w=w/sub 1/+w/sub 2/ using only J/sub
1/ and J/sub 2/ and if so, what can be said about its
dimension? Thus, it is important to clarify the
connection between a finite Jacobi matrix and its
corresponding weight function(s). This leads to the
need for stable numerical processes that evaluate such
matrices. Three new O(n/sup 2/) methods are derived
that `merge' Jacobi matrices directly without using any
information about the corresponding weight functions.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Sci., Adelaide Univ., SA, Australia",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C1110 (Algebra); C4140 (Linear algebra)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Jacobi matrices; O(n/sup 2/) methods; Orthogonal
polynomials; Tridiagonal Jacobi matrix; Weight
functions",
pubcountry = "Denmark",
thesaurus = "Matrix algebra; Polynomials",
}
@Article{Elman:1992:LIM,
author = "Howard C. Elman and Gene H. Golub",
title = "Line Iterative Methods for Cyclically Reduced Discrete
Convection-Diffusion Problems",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "13",
number = "1",
pages = "339--363",
month = jan,
year = "1992",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0913018",
ISSN = "0196-5204",
MRclass = "76Rxx (65F10 65N22 76M25)",
MRnumber = "92j:76085",
bibdate = "Mon Sep 9 11:25:40 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "An analytic and empirical study of line iterative
methods for solving the discrete convection-diffusion
equation is performed. The methodology consists of
performing one step of the cyclic reduction method,
followed by iteration on the resulting reduced system
using line orderings of the reduced grid. Two classes
of iterative methods are considered: block stationary
methods, such as the block Gauss--Seidel and SOR
methods, and preconditioned generalized minimum
residual methods with incomplete LU preconditioners.
New analysis extends convergence bounds for constant
coefficient problems to problems with separable
variable coefficients. In addition, analytic results
show that iterative methods based on incomplete LU
preconditioners have faster convergence rates than
block Jacobi relaxation methods. Numerical experiments
examine additional properties of the two classes of
methods, including the effects of direction of flow,
discretization, and grid ordering on performance.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Inst. for Adv. Comput. Studies,
Maryland Univ., College Park, MD, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "A0230 (Function theory, analysis); A0260 (Numerical
approximation and analysis); A4725Q (Convection and
heat transfer); C4130 (Interpolation and function
approximation); C4170 (Differential equations); C7320
(Physics and Chemistry)",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "Block Gauss--Seidel; Block stationary methods;
Constant coefficient problems; Convergence bounds;
Convergence rates; Cyclic reduction method; Discrete
convection-diffusion equation; Incomplete LU
preconditioners; Line iterative methods; Line
orderings; Preconditioned generalized minimum residual
methods; Separable variable coefficients; SOR methods",
thesaurus = "Convection; Convergence of numerical methods;
Diffusion; Iterative methods; Partial differential
equations; Physics computing",
}
@Article{Fischer:1992:HGU,
author = "Bernd Fischer and Gene H. Golub",
title = "How to generate unknown orthogonal polynomials out of
known orthogonal polynomials",
journal = j-J-COMPUT-APPL-MATH,
volume = "43",
number = "1--2",
pages = "99--115",
day = "25",
month = nov,
year = "1992",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(92)90261-U",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "42C05 (65D15)",
MRnumber = "93m:42011",
MRreviewer = "Zhong De Wang",
bibdate = "Sun Jan 14 08:44:03 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Considers the problem of generating the three-term
recursion coefficients of orthogonal polynomials for a
weight function nu (t)=r(t)w(t), obtained by modifying
a given weight function w by a rational function r.
Algorithms for the construction of the orthogonal
polynomials for the new weight nu in terms of those for
the old weight w are presented. All the methods are
based on modified moments. As applications the paper
presents Gaussian quadrature rules for integrals in
which the integrand has singularities close to the
interval of integration, and the generation of
orthogonal polynomials for the finite Hermite weight
e(-t/sup 2/), supported on a finite interval (-b, b).",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Inst. of Appl. Math., Hamburg Univ., Germany",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C4130 (Interpolation and function approximation);
C4160 (Numerical integration and differentiation);
C4180 (Integral equations)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "Finite Hermite weight; Gaussian quadrature rules;
Integrals; Integrand; Integration interval; Known
orthogonal polynomials; Modified moments; Rational
function; Singularities; Three-term recursion
coefficients; Unknown orthogonal polynomials; Weight
function",
pubcountry = "Netherlands",
thesaurus = "Chebyshev approximation; Integral equations;
Integration; Polynomials",
}
@Article{Freund:1992:ISL,
author = "Roland W. Freund and Gene H. Golub and No{\"e}l M.
Nachtigal",
title = "Iterative Solution of Linear Systems",
journal = j-ACTA-NUMERICA,
volume = "1",
pages = "57--100",
year = "1992",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492900002245",
ISBN = "0-521-41026-6",
ISBN-13 = "978-0-521-41026-7",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
bibdate = "Sat Sep 24 10:23:30 MDT 2011",
bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/habook.bib;
ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
abstract = "Recent advances in the field of iterative methods for
solving large linear systems are reviewed. The main
focus is on developments in the area of conjugate
gradient-type algorithms and Krylov subspace methods
for nonHermitian matrices.",
acknowledgement = ack-nhfb # " and " # ack-sf,
ajournal = "Acta Numer.",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "07 November 2008",
xxnote = "Cited in \cite{bjor:96}.",
}
@TechReport{Golub:1992:CCM,
author = "Gene H. Golub and Hongyuan Zha",
title = "The canonical correlations of matrix pairs and their
numerical computation",
type = "Technical Report",
number = "CS-92-21",
institution = "Pennsylvania State University, Dept. of Computer
Science",
address = "University Park, PA, USA",
pages = "21",
month = "????",
year = "1992",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "This paper is concerned with the analysis of canonical
correlations of matrix pairs and their numerical
computation. We first develop a decomposition theorem
for matrix pairs having the same number of rows which
explicitly exhibits the canonical correlations. We then
present a perturbation analysis of the correlations. We
then present a perturbation analysis of the canonical
correlations, which compares favorably with the
classical first order perturbation analysis. Then we
propose several numerical algorithms for computing the
canonical correlations of general matrix pairs;
emphasis is placed on the case of large sparse or
structured matrices.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1992:DBT,
author = "G. H. Golub and B. K{\aa}gstr{\"o}m and Paul {Van
Dooren}",
title = "Direct Block Tridiagonalization of Single-Input
Single-Output Systems",
journal = j-SYST-CONTROL-LETT,
volume = "18",
number = "2",
pages = "109--120",
month = feb,
year = "1992",
CODEN = "SCLEDC",
DOI = "https://doi.org/10.1016/0167-6911(92)90015-K",
ISSN = "0167-6911 (print), 1872-7956 (electronic)",
ISSN-L = "0167-6911",
MRclass = "93B10 (15A23 93B40 93B55)",
MRnumber = "93b:93021",
MRreviewer = "M. M. Konstantinov",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Derives a direct method for block tridiagonalizing a
single-input single-output system triple (A, b, c). The
method is connected to the nonsymmetric Lanczos
procedure and also leads to canonical representations
of such triples.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C1110 (Algebra); C1310 (Analysis and synthesis
methods)",
fjournal = "Systems and Control Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01676911",
keywords = "Block tridiagonalizing; Canonical representations;
nla, control, tridiagonal matrix, nonsymmetric matrix,
Lanczos algorithm; Nonsymmetric Lanczos procedure;
Single-input single-output systems",
pubcountry = "Netherlands",
thesaurus = "Control system analysis; Eigenvalues and
eigenfunctions; Matrix algebra",
}
@Book{Golub:1992:SCD,
author = "Gene H. Golub and James M. Ortega",
title = "Scientific Computing and Differential Equations: An
Introduction to Numerical Methods",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
edition = "Second",
pages = "xi + 337",
year = "1992",
ISBN = "0-12-289255-0",
ISBN-13 = "978-0-12-289255-4",
LCCN = "QA371 .G62 1992",
MRclass = "65Lxx, 00A06, 65-01, 65Fxx, 65Hxx, 65Mxx, 65Nxx",
MRnumber = "92f:65002",
bibdate = "Tue Dec 14 23:00:48 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
note = prep-latex,
ZMnumber = "0749.65041",
acknowledgement = ack-gg,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "na, book",
remark = "Several library catalogs identify this entry and entry
Golub:1996:SCD as `editions': however, the ISBN remains
unchanged, and no trace of first or third editions has
been found in library catalogs, so it may be that these
are just printings, possibly with corrections.",
tableofcontents = "The World of Scientific Computing \\
Letting It Fly \\
Initial Value Problems \\
Pinning It Down: Boundary Value Problems \\
More on Linear Systems of Equations \\
Life Is Really Nonlinear \\
Is There More Than Finite Differences? N Important
Numbers \\
Space and Time \\
The Curse of Dimensionality \\
Appendixes: Analysis of Differential Equations \\
Linear Algebra \\
Bibliography \\
Index",
}
@Article{Manteuffel:1992:ISS,
author = "Thomas A. Manteuffel and Gene H. Golub",
title = "Introduction to the Special Section on Iterative
Methods in Numerical Linear Algebra",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "3",
pages = "765--766",
month = jul,
year = "1992",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0613intro1",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Apr 09 15:38:52 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Calvetti:1993:GQA,
author = "D. Calvetti and G. H. Golub and L. Reichel",
title = "{Gaussian} quadrature applied to adaptive {Chebyshev}
iteration",
crossref = "Golub:1993:RAI",
pages = "??--??",
year = "1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Chan:1993:XHS,
author = "T. F. Chan and G. H. Golub",
title = "The {XII Householder} Symposium on Numerical Algebra:
{Submitted} Abstracts",
type = "CAM Report",
number = "9--12",
institution = "Department of Mathematics, University of California,
Los Angeles",
address = "Los Angeles, CA, USA",
month = "????",
year = "1993",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "Householder Symposium",
}
@InProceedings{Fischer:1993:ECP,
author = "Bernd Fischer and G. H. Golub",
title = "On the error computation for polynomial based
iteration methods",
crossref = "Golub:1993:RAI",
pages = "59--67",
year = "1993",
MRclass = "65F10",
MRnumber = "1 332 743",
bibdate = "Sun Jan 14 08:20:59 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InCollection{Freund:1993:RAL,
author = "Roland W. Freund and Gene H. Golub and No{\"e}l M.
Nachtigal",
title = "Recent advances in {Lanczos}-based iterative methods
for nonsymmetric linear systems",
crossref = "Hussaini:1993:ATC",
pages = "137--162",
year = "1993",
MRclass = "65F10",
MRnumber = "95f:65066",
MRreviewer = "L. W. Ehrlich",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Golub:1993:PAC,
author = "G. H. Golub and H. Zha",
title = "Perturbation Analysis of the Canonical Correlations of
Matrix Pairs",
type = "Technical Report",
number = "CS-93-02",
institution = "Department of Computer Science, Pennsylvania State
University",
address = "??",
month = "????",
year = "1993",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, pert, canonical correlation, CS decomposition",
}
@Book{Golub:1993:SCI,
author = "Gene H. (Gene Howard) Golub and James M. Ortega",
title = "Scientific Computing: An Introduction with Parallel
Computing",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 442",
year = "1993",
ISBN = "0-12-289253-4",
ISBN-13 = "978-0-12-289253-0",
LCCN = "QA76.58 .G64 1993",
MRclass = "65-01 (65Y05)",
MRnumber = "94c:65003",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.jstor.org/stable/2153127;
http://www.loc.gov/catdir/description/els032/93009408.html;
http://www.loc.gov/catdir/toc/els032/93009408.html",
abstract = "This book introduces the basic concepts of parallel
and vector computing in the context of an introduction
to numerical methods. It contains chapters on parallel
and vector matrix multiplication and solution of linear
systems by direct and iterative methods. It is suitable
for advanced undergraduate and beginning graduate
courses in computer science, applied mathematics, and
engineering. Ideally, students will have access to a
parallel or Vector computer, but the material can be
studied profitably in any case.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "Parallel processing (Electronic computers); Parallel
programming; Vector processing (Computer science)",
remark = "See review by H. J. S, Mathematics of Computation,
Vol. 60, No. 202 (Apr., 1993), p. 849.",
shorttableofcontents = "1: The World of Scientific Computing \\
2: Linear Algebra \\
3: Parallel and Vector Computing \\
4: Polynomial Approximation \\
5: Continuous Problems Solved Discretely \\
6: Direct Solution of Linear Equations \\
7: Parallel Direct Methods \\
8: Iterative Methods \\
9: Conjugate Gradient-Type Methods \\
Bibliography \\
Author Index \\
Subject Index",
subject = "Parallel processing (Electronic computers); Vector
processing (Computer science)",
tableofcontents = "Preface / ix \\
1: The World of Scientific Computing / 1 \\
1.1 What Is Scientific Computing? / 1 \\
1.2 Mathematical Modeling / 3 \\
1.3 The Process of Numerical Solution / 6 \\
1.4 The Computational Environment / 11 \\
2: Linear Algebra / 15 \\
2.1 Matrices and Vectors / 15 \\
2.2 Eigenvalues and Canonical Forms / 28 \\
2.3 Norms / 39 \\
3: Parallel and Vector Computing / 49 \\
3.1 Parallel and Vector Computers / 49 \\
3.2 Basic Concepts of Parallel Computing / 62 \\
3.3 Matrix Multiplication / 71 \\
4: Polynomial Approximation / 91 \\
4.1 Taylor Series, Interpolation and Splines / 91 \\
4.2 Least Squares Approximation / 106 \\
4.3 Application to Root-Finding / 117 \\
5: Continuous Problems Solved Discretely / 137 \\
5.1 Numerical Integration / 137 \\
5.2 Initial Value Problems / 150 \\
5.3 Boundary Value Problems / 173 \\
5.4 Space and Time / 191 \\
5.5 The Curse of Dimensionality / 202 \\
6: Direct Solution of Linear Equations / 215 \\
6.1 Gaussian Elimination / 215 \\
6.2 Errors in Gaussian Elimination / 236 \\
6.3 Other Factorizations / 257 \\
7: Parallel Direct Methods / 275 \\
7.1 Basic Methods / 275 \\
7.2 Other Organizations of Factorization / 294 \\
7.3 Banded and Tridiagonal Systems / 302 \\
8: Iterative Methods / 321 \\
8.1 Relaxation-Type Methods / 321 \\
8.2 Parallel and Vector Implementations / 333 \\
8.3 The Multigrid Method / 353 \\
9: Conjugate Gradient-Type Methods / 371 \\
9.1 The Conjugate Gradient Method / 371 \\
9.2 Preconditioning / 381 \\
9.3 Nonsymmetric and Nonlinear Problems / 397 \\
Bibliography / 413 \\
Author Index / 429 \\
Subject Index / 435",
}
@TechReport{Hu:1993:FAU,
author = "G. Hu and H. Zha and G. Golub and T. Kailath",
title = "Fast Algorithms for Updating Signal Subspaces",
type = "Technical Report",
number = "CS-93-01",
institution = "Department of Computer Science, Pennsylvania State
University",
address = "??",
month = "????",
year = "1993",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, signal processing, updating, Lanczos algorithm,
rank determination",
}
@InProceedings{Talwar:1993:RNA,
author = "S. Talwar and A. Paulraj and G. H. Golub",
title = "A robust numerical approach for array calibration",
crossref = "IEEE:1993:III",
pages = "316--319 (vol. 4)",
month = "????",
year = "1993",
DOI = "https://doi.org/10.1109/ICASSP.1993.319658",
bibdate = "Mon Sep 9 10:46:30 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=319658",
abstract = "The authors focus on the problem of sensor array
calibration in the presence of noise field
uncertainties. The objective is to compute a reliable
estimate of the array response vector given finite
sample estimates of the signal plus noise and noise
only array covariances. These covariances are computed
from data collected at the sensor array with a
calibration signal turned on and off. Numerical
difficulties are encountered in applying the usual
generalized eigenvalue technique when the noise field
is near singular or has changed significantly over the
two covariance measurements. A robust numerical
approach is presented for determining the response
vector in these situations. Results of computer
simulations to verify the proposed technique are also
presented.",
acknowledgement = ack-nhfb,
affiliation = "Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B6140 (Signal processing and detection); C1260
(Information theory)",
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=1051",
keywords = "Calibration signal; Covariances; Noise field
uncertainties; Response vector; Robust numerical
approach; Sensor array calibration",
thesaurus = "Array signal processing; Calibration; Numerical
analysis; Variational techniques",
}
@Article{Calvetti:1994:ACI,
author = "D. Calvetti and G. H. Golub and L. Reichel",
title = "An Adaptive {Chebyshev} Iterative Method for
Nonsymmetric Linear Systems Based on Modified Moments",
journal = j-NUM-MATH,
volume = "67",
number = "1",
pages = "21--40",
month = feb,
year = "1994",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s002110050016",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F10",
MRnumber = "95i:65047",
MRreviewer = "Alfonso Laratta",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://link.springer.de/link/service/journals/00211/bibs/4067001/40670021.htm;
http://science.springer.de/nmee/bibs/4067001/40670021.htm",
abstract = "Large, sparse nonsymmetric systems of linear equations
with a matrix whose eigenvalues lie in the right half
plane may be solved by an iterative method based on
Chebyshev polynomials for an interval in the complex
plane. Knowledge of the convex hull of the spectrum of
the matrix is required in order to choose parameters
upon which the iteration depends. Adaptive Chebyshev
algorithms, in which these parameters are determined by
using eigenvalue estimates computed by the power method
or modifications thereof, have been described by T. A.
Manteuffel (1978). This paper presents an adaptive
Chebyshev iterative method, in which eigenvalue
estimates are computed from modified moments determined
during the iterations. The computation of eigenvalue
estimates from modified moments requires less computer
storage than when eigenvalue estimates are computed by
a power method and yields faster convergence for many
problems.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Pure and Appl. Math., Stevens Inst. of
Technol., Hoboken, NJ, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); C4130 (Interpolation and
function approximation); C4140 (Linear algebra)",
corpsource = "Dept. of Pure and Appl. Math., Stevens Inst. of
Technol., Hoboken, NJ, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "adaptive Chebyshev iterative method; Adaptive
Chebyshev iterative method; Chebyshev approximation;
Chebyshev polynomials; convex hull; Convex hull;
eigenvalue estimates; Eigenvalue estimates;
eigenvalues; Eigenvalues; eigenvalues and
eigenfunctions; iterative methods; modified moments;
Modified moments; nonsymmetric linear systems;
Nonsymmetric linear systems; polynomials",
thesaurus = "Chebyshev approximation; Eigenvalues and
eigenfunctions; Iterative methods; Polynomials",
treatment = "T Theoretical or Mathematical",
}
@InCollection{Calvetti:1994:GQA,
author = "D. Calvetti and G. H. Golub and L. Reichel",
title = "{Gaussian} quadrature applied to adaptive {Chebyshev}
iteration",
crossref = "Golub:1994:RAI",
pages = "31--44",
year = "1994",
MRclass = "65F10",
MRnumber = "96c:65046",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Carey:1994:LBM,
author = "Cheryl M. M. Carey and Gene H. Golub and Kincho H.
Law",
title = "A {Lanczos}-based method for structural dynamic
reanalysis problems",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "37",
number = "16",
pages = "2857--2883",
day = "30",
month = aug,
year = "1994",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620371610",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
MRclass = "65F15 (15A18)",
MRnumber = "95d:65032",
bibdate = "Mon Jan 15 16:19:27 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "29 Jun 2005",
}
@Article{Dubrulle:1994:MQI,
author = "Augustin A. Dubrulle and G. H. Golub",
title = "A Multishift {$ {QR} $} iteration without computation
of the shifts",
journal = j-NUMER-ALGORITHMS,
volume = "7",
number = "2\slash 4",
pages = "173--181",
month = jul,
year = "1994",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F10",
MRnumber = "1 283 096",
bibdate = "Sun Jan 14 10:10:10 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Each iteration of the multishift QR algorithm of Bai
and Demmel (1989) requires the computation of a `shift
vector' defined by m shifts of the origin of the
spectrum that control the convergence of the process. A
common choice of shifts consists of the eigenvalues of
the trailing principal submatrix of order m, and
current practice includes the computation of these
eigenvalues in the determination of the shift vector.
In this paper, the authors describe an algorithm based
on the evaluation of the characteristic polynomial of a
Hessenberg matrix, which directly produces the shift
vector without computing eigenvalues. This algorithm is
stable, more accurate, faster, and simpler than the
current alternative. It also allows for a consistent
shift strategy with dynamic adjustment of the number of
shifts.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Hewlett--Packard Labs., Palo Alto, CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); C4130 (Interpolation and
function approximation); C4140 (Linear algebra)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Characteristic polynomial; Convergence; Hessenberg
matrix; Multishift QR iteration; Shift vector; Trailing
principal submatrix",
pubcountry = "Switzerland",
thesaurus = "Convergence of numerical methods; Matrix algebra;
Polynomials",
}
@Article{Elman:1994:CLI,
author = "Howard C. Elman and Gene H. Golub and Gerhard Starke",
title = "On the convergence of line iterative methods for
cyclically reduced non-symmetrizable linear systems",
journal = j-NUM-MATH,
volume = "67",
number = "2",
pages = "177--190",
month = mar,
year = "1994",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s002110050023",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F10 (65N06 65N22)",
MRnumber = "95b:65049",
MRreviewer = "G. Maess",
bibdate = "Sun Jan 14 08:41:07 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://link.springer.de/link/service/journals/00211/bibs/4067002/40670177.htm;
http://science.springer.de/nmee/bibs/4067002/40670177.htm",
abstract = "We derive analytic bounds on the convergence factors
associated with block relaxation methods for solving
the discrete two-dimensional convection-diffusion
equation. The analysis applies to the reduced systems
derived when one step of block Gaussian elimination is
performed on red-black ordered two-cyclic
discretizations. We consider the case where centered
finite difference discretization is used and one cell
Reynolds number is less than one in absolute value and
the other is greater than one. It is shown that line
ordered relaxation exhibits very fast rates of
convergence.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park,
MD, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "A0260 (Numerical approximation and analysis); A4710
(General theory, simulation and other computational
methods); A4725Q (Convection and heat transfer)",
corpsource = "Dept. of Comput. Sci., Maryland Univ., College Park,
MD, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Analytic bounds; analytic bounds; Block Gaussian
elimination; block Gaussian elimination; Block
relaxation methods; block relaxation methods;
convection; Convergence of line iterative methods;
convergence of line iterative methods; convergence of
numerical methods; Cyclically reduced nonsymmetrizable
linear systems; cyclically reduced nonsymmetrizable
linear systems; diffusion; Discrete 2D
convection-diffusion equation; discrete 2D
convection-diffusion equation; Finite difference
discretization; finite difference discretization;
finite difference methods; iterative methods; One cell
Reynolds number; one cell Reynolds number; Red-black
two-cyclic discretisation; red-black two-cyclic
discretisation",
thesaurus = "Convection; Convergence of numerical methods;
Diffusion; Finite difference methods; Iterative
methods",
treatment = "T Theoretical or Mathematical",
}
@Article{Elman:1994:IPU,
author = "Howard C. Elman and Gene H. Golub",
title = "Inexact and Preconditioned {Uzawa} Algorithms for
Saddle Point Problems",
journal = j-SIAM-J-NUMER-ANAL,
volume = "31",
number = "6",
pages = "1645--1661",
month = dec,
year = "1994",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0731085",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F10 (65F35 65N22 76M10)",
MRnumber = "95f:65065",
bibdate = "Fri Oct 23 11:51:33 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/2158371",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@InProceedings{Ernst:1994:DDA,
author = "Oliver Ernst and Gene H. Golub",
title = "A domain decomposition approach to solving the
{Helmholtz} equation with a radiation boundary
condition",
crossref = "Quarteroni:1994:DDM",
pages = "177--192",
year = "1994",
DOI = "https://doi.org/10.1090/conm/157/01417",
MRclass = "65N55 (65F10)",
MRnumber = "95c:65210",
MRreviewer = "Jan Mandel",
bibdate = "Sun Jan 14 08:39:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Fischer:1994:RAI,
author = "Bernd Fischer and Gene H. Golub",
title = "On the error computation for polynomial based
iteration methods",
crossref = "Golub:1994:RAI",
pages = "59--67",
year = "1994",
MRclass = "65F10",
MRnumber = "96a:65043",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Gander:1994:LCQ,
author = "Walter Gander and Gene H. Golub and Urs von Matt",
title = "Large Constrained Quadratic Problems",
crossref = "Brown:1994:PCL",
pages = "308--310",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Gander:1994:LSF,
author = "Walter Gander and Gene H. Golub and Rolf Strebel",
title = "Least-squares fitting of circles and ellipses",
journal = j-BIT,
volume = "34",
number = "4",
pages = "558--578",
month = dec,
year = "1994",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01934268",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65D10 (65F20 65H10)",
MRnumber = "97j:65020",
MRreviewer = "C. Ilioi",
bibdate = "Wed Jan 4 18:52:23 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=34&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.mai.liu.se/BIT/contents/bit34.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=34&issue=4&spage=558",
abstract = "Fitting circles and ellipses to given points in the
plane is a problem that arises in many application
areas, e.g. computer graphics, coordinate meteorology,
petroleum engineering, and statistics. In the past,
algorithms have been given which fit circles and
ellipses in some least-squares sense without minimizing
the geometric distance to the given points. In this
paper, we present several algorithms which compute the
ellipse for which the sum of the squares of the
distances to the given points is minimal. These
algorithms are compared with classical simple and
iterative methods. Circles and ellipses may be
represented algebraically, i.e., by an equation of the
form F(x)=0. If a point is on the curve, then its
coordinates x are a zero of the function F.
Alternatively, curves may be represented in parametric
form, which is well suited for minimizing the sum of
the squares of the distances.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Wissenschaftliches Rechnen, Eidgenossische
Tech. Hochschule, Zurich, Switzerland",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation); C4260
(Computational geometry)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "Algebraic representation; Circles; Computer graphics;
Coordinate meteorology; Coordinates; Curve fitting;
Ellipses; Geometric distance minimization; Iterative
methods; Least-squares fitting; Parametric form;
Petroleum engineering; Singular value decomposition;
Statistics",
pubcountry = "Denmark",
thesaurus = "Computational geometry; Curve fitting; Iterative
methods; Least squares approximations; Singular value
decomposition",
}
@InProceedings{Golub:1994:MMQ,
author = "G. H. Golub and G{\'e}rard Meurant",
title = "Matrices, moments and quadrature",
crossref = "Griffiths:1994:NAP",
pages = "105--156",
year = "1994",
MRclass = "65F05 (15A99 65D32)",
MRnumber = "95b:65042",
MRreviewer = "Stephen W. Brady",
bibdate = "Fri Dec 20 17:38:57 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1994:PAC,
author = "Gene H. Golub and Hong Yuan Zha",
title = "Perturbation analysis of the canonical correlations of
matrix pairs",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "210",
pages = "3--28",
year = "1994",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(94)90463-4",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F30 (65U05)",
MRnumber = "95f:65086",
MRreviewer = "Israel Koltracht",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Xu:1994:FAU,
author = "Guanghan Xu and Hongyuan Zha and Gene Golub and Thomas
Kailath",
title = "Fast algorithms for updating signal subspaces",
journal = j-IEEE-TRANS-CIRCUITS-SYST-2,
volume = "41",
number = "8",
pages = "537--549",
month = aug,
year = "1994",
CODEN = "ICSPE5",
DOI = "https://doi.org/10.1109/82.318942",
ISSN = "1057-7130 (print), 1558-125X (electronic)",
ISSN-L = "1057-7130",
bibdate = "Tue Mar 05 08:04:28 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=318942",
abstract = "In various real-time signal processing and
communication applications, it is often required to
track a low-dimensional signal subspace that slowly
varies with time. Conventional methods of updating the
signal subspace rely on eigendecomposition or singular
value decomposition, which is computationally expensive
and difficult to implement in parallel. Recently, Xu
and Kailath proposed fast and parallelizable
Lanczos-based algorithms for estimating the signal
subspace based on the data matrices or the covariance
matrices. In this paper, we shall extend these
algorithms to achieve fast tracking of the signal
subspace. The computational complexity of the new
methods is O(M/sup 2/d) per update, where M is the size
of the data vectors and d is the dimension of the
signal subspace. Unlike most tracking methods that
assume d is fixed and/or known a priori, the new
methods also update the signal subspace dimension. More
importantly, under certain stationarity conditions, we
can show that the Lanczos-based methods are
asymptotically equivalent to the more costly SVD or
eigendecomposition based methods and that the
estimation of d is strongly consistent. Knowledge of
the previous signal subspace estimate is incorporated
to achieve better numerical properties for the current
signal subspace estimate. Numerical simulations for
some signal scenarios are also presented.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Electr. and Comput. Eng., Texas Univ.,
Austin, TX, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290H (Linear algebra); B6140 (Signal processing
and detection); C1260 (Information theory); C4140
(Linear algebra)",
fjournal = "IEEE transactions on circuits and systems. 2, Analog
and digital signal processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
keywords = "Computational complexity; Covariance matrices; Data
matrices; Fast tracking; Lanczos-based algorithms;
Low-dimensional signal subspace; Numerical properties;
Real-time signal processing; Signal scenarios",
thesaurus = "Computational complexity; Matrix algebra; Signal
detection; Tracking",
xxauthor = "Guangban Xu and Hongyuan Zha and Gene H. Golub and
Thomaks Kailath",
}
@Article{Arbenz:1995:MSI,
author = "Peter Arbenz and Gene H. Golub",
title = "Matrix shapes invariant under the symmetric {$ {QR} $}
algorithm",
journal = j-NUM-LIN-ALG-APPL,
volume = "2",
number = "2",
pages = "87--93",
month = "????",
year = "1995",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.1680020203",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "65F15 (15A18 65F50)",
MRnumber = "95m:65060",
MRreviewer = "Zhenyue Zhang",
bibdate = "Sun Jan 14 08:22:24 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@Article{Boley:1995:FPF,
author = "Daniel L. Boley and Gene H. Golub and Samy R. Makar
and Nirmal R. Saxena and Elisabet J. {McCluskey, Jr.}",
title = "Floating point fault tolerance with backward error
assertions",
journal = j-IEEE-TRANS-COMPUT,
volume = "44",
number = "2",
pages = "302--311",
month = feb,
year = "1995",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/12.364541",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Sep 9 10:37:50 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=364541",
abstract = "The paper introduces an assertion scheme based on the
backward error analysis for error detection in
algorithms that solve dense systems of linear
equations, Ax=b. Unlike previous methods, this backward
error assertion model is specifically designed to
operate in an environment of floating point arithmetic
subject to round-off errors, and it can be easily
instrumented in a Watchdog processor environment. The
complexity of verifying assertions is O(n/sup 2/),
compared to the O(n/sup 3/) complexity of algorithms
solving Ax=b. Unlike other proposed error detection
methods, this assertion model does not require any
encoding of the matrix A. Experimental results under
various error models are presented to validate the
effectiveness of this assertion scheme.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Minnesota Univ., Minneapolis,
MN, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C4140 (Linear algebra); C4240C (Computational
complexity); C5230 (Digital arithmetic methods); C5470
(Performance evaluation and testing)",
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
keywords = "Assertion scheme; Backward error analysis; Backward
error assertions; Complexity; Dense systems; Error
detection; Error models; Floating point arithmetic;
Floating point fault tolerance; Linear equations;
Round-off errors; Watchdog processor environment",
thesaurus = "Computational complexity; Error analysis; Error
detection; Fault tolerant computing; Floating point
arithmetic; Linear algebra",
}
@Article{Chu:1995:ROR,
author = "Moody T. Chu and Robert E. Funderlic and Gene H.
Golub",
title = "A rank-one reduction formula and its applications to
matrix factorizations",
journal = j-SIAM-REVIEW,
volume = "37",
number = "4",
pages = "512--530",
month = dec,
year = "1995",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1037124",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "15A21 (15A23 65F30)",
MRnumber = "96j:15007",
MRreviewer = "George D. Poole",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/2132903",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Golub:1995:CCM,
author = "Gene H. Golub and Hong Yuan Zha",
title = "The canonical correlations of matrix pairs and their
numerical computation",
journal = j-IMA-VOL-MATH-APPL,
volume = "69",
number = "??",
pages = "27--49",
month = "????",
year = "1995",
MRclass = "65Fxx (15A18 15A21 62Hxx)",
MRnumber = "1 351 731",
MRreviewer = "Alan L. Andrew",
bibdate = "Sun Jan 14 08:16:07 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1995:EQF,
author = "Gene H. Golub and Zden{\v{e}}k Strako{\v{s}}",
title = "Estimates in quadratic formulas",
journal = j-NUMER-ALGORITHMS,
volume = "8",
number = "2-4",
pages = "241--268",
month = jan,
year = "1995",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F30",
MRnumber = "95j:65040",
MRreviewer = "W. Govaerts",
bibdate = "Tue Apr 29 08:56:05 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Let A be a real symmetric positive definite matrix. We
consider three particular questions, namely estimates
for the error in linear systems Ax=b, minimizing
quadratic functional min/sub x/(x/sup T/Ax-2b/sup T/x)
subject to the constraint //x//= alpha, alpha <//A/sup
-1/b//, and estimates for the entries of the matrix
inverse A/sup -1/. All of these questions can be
formulated as a problem of finding an estimate or an
upper and lower bound on u/sup T/F(A)u, where
F(A)=A/sup -1/ resp. F(A)=A/sup -2/, u is a real
vector. This problem can be considered in terms of
estimates in the Gauss-type quadrature formulas which
can be effectively computed exploiting the underlying
Lanczos process. Using this approach, we first recall
the exact arithmetic solution of the questions
formulated above and then analyze the effect of
rounding errors in the quadrature calculations. It is
proved that the basic relation between the accuracy of
Gauss quadrature for f( lambda )= lambda /sup -1/ and
the rate of convergence of the corresponding conjugate
gradient process holds true even for finite precision
computation. This allows us to explain experimental
results observed in quadrature calculations and in
physical chemistry and solid state physics computations
which are based on continued fraction recurrences.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290B (Error analysis in numerical methods); B0290H
(Linear algebra); B0290M (Numerical integration and
differentiation); C4110 (Error analysis in numerical
methods); C4140 (Linear algebra); C4160 (Numerical
integration and differentiation)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Conjugate gradient process; Estimates; Linear systems;
Matrix inverse; Quadratic formulas; Quadrature
formulas; Real symmetric positive definite matrix;
Rounding errors",
pubcountry = "Switzerland",
thesaurus = "Eigenvalues and eigenfunctions; Error analysis;
Integration; Linear algebra; Matrix inversion",
}
@InProceedings{Golub:1995:MCT,
author = "Gene H. Golub",
title = "Matrix computation and the theory of moments",
crossref = "Chatterji:1994:PIC",
pages = "1440--1448",
year = "1995",
MRclass = "65Fxx (44A60)",
MRnumber = "1 404 047",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Book{Golub:1995:WRD,
author = "Gene H. Golub and James M. Ortega",
title = "{Wissenschaftliches Rechnen und
Differentialgleichungen: Eine Einf{\"u}hrung in die
numerische Mathematik} ({German}) [{English}:
Scientific computing and differential equations: An
introduction to numerical methods]",
volume = "6",
publisher = "Heldermann Verlag",
address = "Berlin, Germany",
pages = "xii + 330",
year = "1995",
ISBN = "3-88538-106-0",
ISBN-13 = "978-3-88538-106-8",
LCCN = "????",
MRclass = "65-01",
MRnumber = "1307380 (95g:65002)",
bibdate = "Fri Dec 20 17:28:29 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
note = "Translated from the 1992 English original by Heinz
Dalkowski",
series = "Berliner Studienreihe zur Mathematik [Berlin Study
Series on Mathematics]",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
language = "German",
shorttableofcontents = "Vorwort / viii \\
Vorwort zur deutschen {\"U}bersetzung / xi \\
1: Die Welt des wissenschaftlichen / Rechnens \\
2: Packen wir's an: / Anfangswertprobleme \\
3: Nageln wir's fest: / Randwertprobleme \\
4: Mehr {\"u}ber lineare / Gleichungssysteme \\
5: Im wirklichen Leben geht's nichtlinear / zu \\
6: Gibt es noch etwas anderes als finite / Differenzen?
\\
7: Die Glorreichen / n \\
8: Raum und Zeit \\
9: Ausflug in h{\"o}here / Dimensionen \\
Anhang 1: Analysis und Differentialgleichungen / 307
\\
Anhang 2: Lineare Algebra / 311 \\
Literaturverzeichnis / 317 \\
Stichwortverzeichnis / 323",
tableofcontents = "Vorwort / viii \\
Vorwort zur deutschen {\"U}bersetzung / xi \\
1: Die Welt des wissenschaftlichen / Rechnens \\
1.1 Was ist wissenschaftliches Rechnen? / 1 \\
1.2 Mathematische Modellierung / 4 \\
1.3 Der numerische L{\"o}sungsproze{\ss} / 7 \\
1.4 Die EDV-Umgebung / 12 \\
2: Packen wir's an: / Anfangswertprobleme \\
2.1 Beispiele f{\"u}r Anfangswertprobleme / 17 \\
2.2 Einschritt-Verfahren / 22 \\
2.3 Polynom Interpolation / 40 \\
2.4 Mehr schrittverfahren / 47 \\
2.5 Stabilit{\"a}t, Instabilit{\"a}t und steife
Gleichungen / 57 \\
3: Nageln wir's fest: / Randwertprobleme \\
3.1 Die Methode finiter Differenzen f{\"u}r lineare
Probleme / 69 \\
3.2 Die L{\"o}sung des diskretisierten Problems / 82
\\
4: Mehr {\"u}ber lineare / Gleichungssysteme \\
4.1 Einf{\"u}hrung und Methoden kleinster Quadrate / 91
\\
4.2 Das Gau{\ss}sche Eliminationsverfahren / 102 \\
4.3 Austausch von Gleichungen / 113 \\
4.4 Schlechte Kondition und Fehleranalyse / 122 \\
4.5 Weitere Zerlegungen / 132 \\
5: Im wirklichen Leben geht's nichtlinear / zu \\
5.1 Nichtlineare Probleme und Schie{\ss}verfahren / 143
\\
5.2 Die L{\"o}sung einer einzelnen nichtlinearen
Gleichung / 147 \\
5.3 Systeme nichtlinearer Gleichungen / 164 \\
6: Gibt es noch etwas anderes als finite / Differenzen?
\\
6.1 Einf{\"u}hrung in Projektionsmethoden / 177 \\
6.2 Spline Approximation / 185 \\
6.3 Numerische Integration / 191 \\
6.4 Das diskrete Problem bei der Verwendung von
Splinefunktionen / 199 \\
7: Die Glorreichen / n \\
7.1 Eigenwertprobleme / 209 \\
7.2 Das QR-Verfahren / 221 \\
7.3 Weitere iterative Methoden / 231 \\
8: Raum und / Zeit \\
8.1 Partielle Differentialgleichungen / 245 \\
8.2 Explizite Verfahren und Stabilit{\"a}t / 251 \\
8.3 Implizite Verfahren / 260 \\
8.4 Halbdiskrete Verfahren / 264 \\
9: Ausflug in h{\"o}here / Dimensionen \\
9.1 Zwei und drei Raumdimensionen / 271 \\
9.2 Direkte Verfahren / 281 \\
9.3 Iterative Verfahren / 289 \\
Anhang 1: Analysis und Differentialgleichungen / 307
\\
Anhang 2: Lineare Algebra / 311 \\
Literaturverzeichnis / 317 \\
Stichwortverzeichnis / 323",
}
@Article{Lui:1995:HMN,
author = "S. H. Lui and G. H. Golub",
title = "Homotopy method for the numerical solution of the
eigenvalue problem of self-adjoint partial differential
operators",
journal = j-NUMER-ALGORITHMS,
volume = "10",
number = "3-4",
pages = "363--378",
month = oct,
year = "1995",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65N25",
MRnumber = "96g:65108",
MRreviewer = "S. F. McCormick",
bibdate = "Mon Sep 9 10:27:58 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Given A/sub 1/, the discrete approximation of a linear
self-adjoint partial differential operator, the
smallest few eigenvalues and eigenvectors of A/sub 1/
are computed by the homotopy (continuation) method. The
idea of the method is very simple. From some initial
operator A/sub 0/ with known eigenvalues and
eigenvectors, define the homotopy H(t)=(1-t)A/sub
0/+tA/sub 1/, 0<or=t<or=1. If the eigenvectors of
H(t/sub 0/) are known, then they are used to determine
the eigenpairs of H(t/sub 0/+dt) via the Rayleigh
quotient iteration, for some value of dt. This is
repeated until t becomes 1, when the solution to the
original problem is found. A fundamental problem is the
selection of the step size dt. A simple criterion to
select dt is given. It is shown that the iterative
solver used to find the eigenvector at each step can be
stabilized by applying a low-rank perturbation to the
relevant matrix. By carrying out a small part of the
calculation in higher precision, it is demonstrated
that eigenvectors corresponding to clustered
eigenvalues can be computed to high accuracy. Some
numerical results for the Schrodinger eigenvalue
problem are given. This algorithm will also be used to
compute the bifurcation point of a parametrized partial
differential equation.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Hong Kong Univ. of Sci. and Technol.,
Kowloon, Hong Kong",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); B0290P (Differential
equations); C4130 (Interpolation and function
approximation); C4140 (Linear algebra); C4170
(Differential equations)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Discrete approximation; Eigenvalue problem;
Eigenvectors; Homotopy method; Iterative solver;
Low-rank perturbation; Numerical solution; Rayleigh
quotient iteration; Schrodinger eigenvalue problem;
Self-adjoint partial differential operators",
pubcountry = "Switzerland",
thesaurus = "Eigenvalues and eigenfunctions; Iterative methods;
Partial differential equations",
}
@Article{Bai:1996:SLS,
author = "Zhaojun Bai and Mark Fahey and Gene Golub",
title = "Some large-scale matrix computation problems",
journal = j-J-COMPUT-APPL-MATH,
volume = "74",
number = "1--2",
pages = "71--89",
day = "5",
month = nov,
year = "1996",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(96)00018-0",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65F10",
MRnumber = "1 430 368",
bibdate = "Wed May 07 17:56:36 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0240G (Monte Carlo methods); B0290H (Linear
algebra); C1140G (Monte Carlo methods); C4140 (Linear
algebra)",
conflocation = "Austin, TX, USA; April 1995",
conftitle = "TICAM Symposium. Texas Institute for Computational and
Applied Mathematics",
corpsource = "Dept. of Math., Kentucky Univ., Lexington, KY, USA",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "bound entries; bound inverse trace; bounded bilinear
form; large sparse matrix determinant; large-scale
matrix computation problems; matrix multiplication;
matrix-vector multiplications; Monte Carlo method;
Monte Carlo methods; numerical algorithm; smooth
function; sparse matrices; spectrum; vectors",
pubcountry = "Netherlands",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Chan:1996:NPD,
author = "Tony F. Chan and Gene H. Golub and Pep Mulet",
booktitle = "{ICAOS '96} (Paris, 1996)",
title = "A nonlinear primal-dual method for total
variation-based image restoration",
volume = "219",
publisher = pub-SV,
address = pub-SV:adr,
pages = "241--252",
year = "1996",
MRclass = "",
MRnumber = "1 430 131",
bibdate = "Wed May 7 18:02:40 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Lecture Notes in Control and Inform. Sci.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Gander:1996:LSF,
author = "Walter Gander and Gene H. Golub and Rolf Strebel",
title = "Least-squares fitting of circles and ellipses.
Numerical analysis (Louvain-la-Neuve, 1995)",
journal = "Bull. Belg. Math. Soc. Simon Stevin",
volume = "3S",
pages = "63--84",
year = "1996",
MRclass = "65Dxx",
MRnumber = "1 431 316",
bibdate = "Wed May 7 18:02:40 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InCollection{Golub:1996:DDP,
author = "Gene Golub and David Silvester and Andy Wathen",
title = "Diagonal dominance and positive definiteness of upwind
approximations for advection diffusion problems",
crossref = "Griffiths:1996:NAR",
pages = "125--131",
year = "1996",
MRclass = "65M60 (65N30 76M20)",
MRnumber = "1 444 618",
bibdate = "Fri Oct 17 06:24:57 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Book{Golub:1996:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
edition = "Third",
pages = "xxvii + 694",
year = "1996",
ISBN = "0-8018-5413-X (hardcover), 0-8018-5414-8 (paperback)",
ISBN-13 = "978-0-8018-5413-2 (hardcover), 978-0-8018-5414-9
(paperback)",
LCCN = "QA188 .G65 1996",
MRclass = "65-02 (65Fxx)",
MRnumber = "1417720 (97g:65006)",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
series = "Johns Hopkins Studies in the Mathematical Sciences",
URL = "http://www.loc.gov/catdir/bios/jhu052/96014291.html;
http://www.loc.gov/catdir/description/jhu051/96014291.html",
acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
tableofcontents = "Preface to the Third Edition / xi \\
Software / xiii \\
Selected References / xv \\
1: Matrix Multiplication Problems \\
1.1 Basic Algorithms and Notation / 2 \\
1.2 Exploiting Structure / 16 \\
1.3 Block Matrices and Algorithms / 24 \\
1.4 Vectorization and Re-Use Issues / 34 \\
2: Matrix Analysis 48 V 2.1 Basic Ideas from Linear
Algebra / 48 \\
2.2 Vector Norms / 52 \\
2.3 Matrix Norms / 54 \\
2.4 Finite Precision Matrix Computations / 59 \\
2.5 Orthogonality and the SVD / 69 \\
2.6 Projections and the $CS$ Decomposition / 75 \\
2.7 The Sensitivity of Square Linear Systems / 80 \\
3: General Linear Systems / 87 \\
3.1 Triangular Systems / 88 \\
3.2 The $L U$ Factorization / 94 \\
3.3 Roundoff Analysis of Gaussian Elimination / 104 \\
3.4 Pivoting / 109 \\
3.5 Improving and Estimating Accuracy / 123 \\
4: Special Linear Systems / 133 \\
4.1 The $L D M^T$ and $L D L^T$ Factorizations / 135
\\
4.2 Positive Definite Systems / 140 \\
4.3 Banded Systems / 152 \\
4.4 Symmetric Indefinite Systems / 161 \\
4.5 Block Systems / 174 \\
4.6 Vandermonde Systems and the FFT / 183 \\
4.7 Toeplitz and Related Systems / 193 \\
5: Orthogonalization and Least Squares / 206 \\
5.1 Householder and Givens Matrices / 208 \\
5.2 The $Q R$ Factorization / 223 \\
5.3 The Full Rank LS Problem / 236 \\
5.4 Other Orthogonal Factorizations / 248 \\
5.5 The Rank Deficient LS Problem / 256 \\
5.6 Weighting and Iterative Improvement / 264 \\
5.7 Square and Underdetermined Systems / 270 \\
6: Parallel Matrix Computations / 275 \\
6.1 Basic Concepts / 276 \\
6.2 Matrix Multiplication / 292 \\
6.3 Factorizations / 300 \\
7: The Unsymmetric Eigenvalue Problem / 308 \\
7.1 Properties and Decompositions / 310 \\
7.2 Perturbation Theory / 320 \\
7.3 Power Iterations / 330 \\
7.4 The Hessenberg and Real Schur Forms / 341 \\
7.5 The Practical $Q R$ Algorithm / 352 \\
7.6 Invariant Subspace Computations / 362 \\
7.7 The $Q Z$ Method for $A x = \lambda B x$ / 375 \\
8: The Symmetric Eigenvalue Problem / 391 \\
8.1 Properties and Decompositions / 393 \\
8.2 Power Iterations / 405 \\
8.3 The Symmetric $Q R$ Algorithm / 414 \\
8.4 Jacobi Methods / 426 \\
8.5 Tridiagonal Methods / 439 \\
8.6 Computing the SVD / 448 \\
8.7 Some Generalized Eigenvalue Problems / 461 \\
9: Lanczos Methods / 470 \\
9.1 Derivation and Convergence Properties / 471 \\
9.2 Practical Lanczos Procedures / 479 \\
9.3 Applications to $A x = b$ and Least Squares / 490
\\
9.4 Arnoldi and Unsymmetric Lanczos / 499 \\
10: Iterative Methods for Linear Systems / 508 \\
10.1 The Standard Iterations / 509 \\
10.2 The Conjugate Gradient Method / 520 \\
10.3 Preconditioned Conjugate Gradients / 532 \\
10.4 Other Krylov Subspace Methods / 544 \\
11: Functions of Matrices / 555 \\
11.1 Eigenvalue Methods / 556 \\
11.2 Approximation Methods / 562 \\
11.3 The Matrix Exponential / 572 \\
12: Special Topics / 579 \\
12.1 Constrained Least Squares / 580 \\
12.2 Subset Selection Using the SVD / 590 \\
12.3 Total Least Squares / 595 \\
12.4 Computing Subspaces with the SVD / 601 \\
12.5 Updating Matrix Factorizations / 606 \\
12.6 Modified/Structured Eigenproblems / 621 \\
Bibliography / 637 \\
Index / 687",
}
@Article{Golub:1996:MCT,
author = "Gene H. Golub",
title = "Matrix computation and the theory of moments.
Numerical analysis (Louvain-la-Neuve, 1995)",
journal = "Bull. Belg. Math. Soc. Simon Stevin",
volume = "3S",
pages = "1--9",
month = dec,
year = "1996",
MRclass = "65F30 (44A60)",
MRnumber = "1 431 311",
bibdate = "Wed May 7 18:02:40 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.emis.de/journals/BBMS/Bulletin/sup962/golub.pdf;
http://www.ulb.ac.be/assoc/bms/bbmstocpv.html",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Bulletin of the Belgian Mathematical Society",
}
@Book{Golub:1996:SC,
author = "Gene Golub and James M. Ortega",
title = "Scientific computing: {Eine Einf{\"u}hrung in das
wissenschaftliche Rechnen und Parallele Numerik}
({German}) [{An} introduction to scientific computing
and parallel numerics]",
publisher = pub-TEUBNER,
address = pub-TEUBNER:adr,
pages = "534",
year = "1996",
DOI = "https://doi.org/10.1007/978-3-322-82981-8",
ISBN = "3-519-02969-3",
ISBN-13 = "978-3-519-02969-4",
MRclass = "65-01",
MRnumber = "97c:65002",
bibdate = "Fri Oct 17 06:10:36 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
note = "Translated from the 1993 English original
\cite{Golub:1993:SCI} and with a foreword by Rolf
Dieter Grigorieff and Hartmut Schwandt.",
URL = "http://link.springer.com/openurl?genre=book\%26isbn=978-3-519-02969-4",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
language = "German",
shorttableofcontents = "1: Die Welt des Wissenschaftlichen Rechnens /
11 \\
2: Lineare Algebra / 28 \\
3: Parallel- und Vektorrechnen / 69 \\
4: Approximation mit Polynomen / 119 \\
5: Kontinuierliche Probleme, diskretisiert gel{\"o}st /
172 \\
6: Direkte L{\"o}sung linearer Gleichungen / 265 7:
Direkte parallele Verfahren / 337 \\
8: Iterative Verfahren / 392 \\
9: Verfahren der konjugierten Gradienten / 451
Literaturverzeichnis / 503 \\
Stichwortverzeichnis / 521 \\
Autorenverzeichnis / 531",
tableofcontents = "1: Die Welt des Wissenschaftlichen Rechnens / 11
\\
1.1 Was ist Wissenschaftliches Rechnen? / 11 \\
1.2 Mathematische Modellierung / 13 \\
1.3 Der numerische L{\"o}sungsproze{\ss} / 17 \\
1.4 Die EDV-Umgebung / 23 \\
2: Lineare Algebra / 28 \\
2.1 Matrizen und Vektoren / 28 \\
2.2 Eigenwerte und Normalform / 43 \\
2.3 Normen / 57 \\
3: Parallel- und Vektorrechnen / 69 \\
3.1 Parallel- und Vektorrechner / 69 \\
3.2 Grundlegende Konzepte des Parallelen Rechnens / 85
\\
3.3 Matrixmultiplikation / 96 \\
4: Approximation mit Polynomen / 119 \\
4.1 Taylorreihe, Interpolation und Splines / 119 \\
4.2 Methode der kleinsten Quadrate / 137 \\
4.3 Anwendung auf die Nullstellenbestimmung / 150 \\
5: Kontinuierliche Probleme, diskretisiert gel{\"o}st /
172 \\
5.1 Numerische Integration / 172 \\
5.2 Anfangswertaufgaben / 187 \\
5.3 Randwertprobleme / 215 \\
5.4 Raum und Zeit / 237 \\
5.5 Der Fluch der Dimension / 251 \\
6: Direkte L{\"o}sung linearer Gleichungen / 265 \\
6.1 Gau{\ss}sche Elimination / 265 \\
6.2 Fehlerverhalten beim Gau{\ss}schen
Eliminationsverfahren / 290 \\
6.3 Andere Zerlegungen / 315 \\
7: Direkte parallele Verfahren / 337 \\
7.1 Basisverfahren / 337 \\
7.2 Weitere Formen der Organisation von
Faktorisierungen / 361 \\
7.3 Band- und Tridiagonalsysteme / 369 \\
8: Iterative Verfahren / 392 \\
8.1 Relaxationsverfahren / 392 \\
8.2 Parallel- und Vektorimplementierungen / 406 \\
8.3 Das Mehrgitterverfahren / 431 \\
9: Verfahren der konjugierten Gradienten / 451 \\
9.1 Das Verfahren der konjugierten Gradienten / 451 \\
9.2 Pr{\"a}konditionierung / 463 \\
9.3 Nichtsymmetrische und nichtlineare Probleme / 482
\\
Literaturverzeichnis / 503 \\
Stichwortverzeichnis / 521 \\
Autorenverzeichnis / 531",
}
@Book{Golub:1996:SCD,
author = "Gene Howard Golub and James M. Ortega",
title = "Scientific Computing and Differential Equations: an
Introduction to Numerical Methods",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
edition = "Fourth",
pages = "xi + 337",
year = "1996",
ISBN = "0-12-289255-0",
ISBN-13 = "978-0-12-289255-4",
LCCN = "QA371 1996",
bibdate = "Fri Nov 16 09:01:26 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
z3950.gbv.de:20011/gvk",
URL = "http://www.gbv.de/dms/bowker/toc/9780122892554.pdf",
abstract = "\booktitle{Scientific Computing and Differential
Equations: An Introduction to Numerical Methods}, is an
excellent complement to Introduction to Numerical
Methods by Ortega and Poole. The book emphasizes the
importance of solving differential equations on a
computer, which comprises a large part of what has come
to be called scientific computing. It reviews modern
scientific computing, outlines its applications, and
places the subject in a larger context.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
remark = "Several library catalogs identify this entry and entry
Golub:1992:SCD as `editions': however, the ISBN remains
unchanged, and no trace of first or third editions has
been found in library catalogs, so it may be that these
are just printings, possibly with corrections.",
tableofcontents = "Preface / ix \\
1: The World of Scientific Computing / 1 \\
1.1 What is Scientific Computing? / 1 \\
1.2 Mathematical Modeling / 3 \\
1.3 The Process of Numerical Solution / 6 \\
1.4 The Computational Environment / 11 \\
2: Letting It Fly: Initial Value Problems / 15 \\
2.1 Examples of Initial Value Problems / 15 \\
2.2 One-Step Methods / 20 \\
2.3 Polynomial Interpolation / 37 \\
2.4 Multistep Methods / 45 \\
2.5 Stability, Instability, and Stiff Equations / 55
\\
3: Pinning It Down: Boundary Value Problems / 67 \\
3.1 The Finite Difference Method for Linear Problems /
67 \\
3.2 Solution of the Discretized Problem / 80 \\
4: More on Linear Systems of Equations / 89 \\
4.1 Introduction and Least Squares Problems / 89 \\
4.2 Gaussian Elimination / 101 \\
4.3 Interchanges / 112 \\
4.4 Ill-conditioning and Error Analysis / 122 \\
4.5 Other Factorizations / 133 \\
5: Life Is Really Nonlinear / 145 \\
5.1 Nonlinear Problems and Shooting / 145 \\
5.2 Solution of a Single Nonlinear Equation / 149 \\
5.3 Systems of Nonlinear Equations / 166 \\
6: Is There More Than Finite Differences? / 179 \\
6.1 Introduction to Projection Methods / 179 \\
6.2 Spline Approximation / 187 \\
6.3 Numerical Integration / 193 \\
6.4 The Discrete Problem Using Splines / 202 \\
7: $N$ Important Numbers / 211 \\
7.1 Eigenvalue Problems / 211 \\
7.2 The QR Method / 224 \\
7.3 Other Iterative Methods / 234 \\
8: Space and Time / 247 \\
8.1 Partial Differential Equations / 247 \\
8.2 Explicit Methods and Stability / 253 \\
8.3 Implicit Methods / 262 \\
8.4 Semidiscrete Methods / 267 \\
9: The Curse of Dimensionality / 273 \\
9.1 Two and Three Space Dimensions / 273 \\
9.2 Direct Methods / 283 \\
9.3 Iterative Methods / 292 \\
Appendix 1: Analysis and Differential Equations / 309
\\
Appendix 2: Linear Algebra / 315 \\
Bibliography / 321 \\
Author Index / 329 \\
Subject Index / 333",
}
@InProceedings{Taubin:1996:OSS,
author = "G. Taubin and T. Zhang and G. Golub",
title = "Optimal surface smoothing as filter design",
crossref = "Buxton:1996:CVE",
pages = "283--292 (vol. 1)",
year = "1996",
bibdate = "Wed May 7 11:56:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0250 (Combinatorial mathematics); B6140 (Signal
processing and detection); C1160 (Combinatorial
mathematics); C5260 (Digital signal processing)",
conftitle = "Proceedings of Fourth European Conference on Computer
Vision. ECCV `96",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
keywords = "approximation algorithms; directed graph; directed
graphs; discrete graph signals; filter design; Fourier
series; low-pass filtering; low-pass filters; optimal
surface smoothing; optimisation; parameter estimation;
polyhedral surfaces; power spectrum estimation; signal
processing; smoothing methods; stability; stability
properties; surface smoothing filters",
sponsororg = "Eur. Vision Soc.; British Machine Vision Assoc",
treatment = "T Theoretical or Mathematical",
}
@Article{Varadhan:1996:ADS,
author = "Sowmini Varadhan and Michael W. Berry and Gene H.
Golub",
title = "Approximating dominant singular triplets of large
sparse matrices via modified moments",
journal = j-NUMER-ALGORITHMS,
volume = "13",
number = "1-2",
pages = "123--152",
month = "????",
year = "1996",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/BF02143130",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F50 (65F15 65Kxx)",
MRnumber = "1 417 686",
bibdate = "Tue Apr 29 08:56:05 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C4130 (Interpolation and function approximation);
C4140 (Linear algebra); C4240P (Parallel programming
and algorithm theory)",
corpsource = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
USA",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "256-processor Cray T3D; ANSI-C implementation;
Chebyshev approximation; Chebyshev semi-iterative
method; deflation techniques; dominant singular
triplets; eigenvalues and eigenfunctions; eigenvectors;
equivalent eigensystems; equivalent sparse
eigensystems; large sparse matrices; modified moments;
parallel algorithms; parallel implementations; singular
value decomposition; sparse matrices; UNIX workstation
network",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Article{Bai:1997:BTI,
author = "Zhaojun Bai and Gene H. Golub",
title = "Bounds for the trace of the inverse and the
determinant of symmetric positive matrices. The
heritage of {P. L. Chebyshev}: a {Festschrift} in honor
of the 70th birthday of {T. J. Rivlin}",
journal = j-ANN-NUM-MATH,
volume = "4",
number = "1-4",
pages = "29--38",
year = "1997",
ISSN = "1021-2655",
MRclass = "65F10 (15-XX)",
MRnumber = "1 422 668",
bibdate = "Wed May 7 18:02:40 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Annals of Numerical Mathematics",
}
@Book{Bellman:1997:IMA,
author = "Richard Bellman",
title = "Introduction to matrix analysis",
volume = "19",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxviii + 403",
year = "1997",
ISBN = "0-89871-399-4",
ISBN-13 = "978-0-89871-399-2",
LCCN = "QA188 .B445 1997",
MRclass = "01A75 (15-01 26-01 65-01 93-01)",
MRnumber = "98a:01021",
bibdate = "Fri Oct 17 06:07:51 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Reprint of the second (1970) edition, with a foreword
by Gene Golub.",
series = "Classics in Applied Mathematics",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Chandrasekaran:1997:BFP,
author = "S. Chandrasekaran and Gene H. Golub and Ming Gu and
Ali H. Sayed",
booktitle = "{Proceedings of the 1997 American Control Conference,
1997}",
title = "Best-fit parameter estimation for a bounded
errors-in-variables model",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "166--170",
year = "1997",
DOI = "https://doi.org/10.1109/ACC.1997.611778",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=611778",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4827",
}
@InCollection{Chandrasekaran:1997:EAL,
author = "Shivkumar Chandrasekaran and Ming Gu and Gene H. Golub
and Ali H. Sayed",
title = "Efficient Algorithms for Least Squares Type Problems
with Bounded Uncertainties",
crossref = "VanHuffel:1997:RAT",
pages = "171--180",
year = "1997",
MRclass = "65F20",
MRnumber = "1447474",
bibdate = "Tue May 8 11:35:55 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-do # "\slash " # ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Chandrasekaran:1997:PEP,
author = "Shivkumar Chandrasekaran and Gene H. Golub and Ming Gu
and Ali H. Sayed",
title = "Parameter estimation in the presence of bounded
modeling errors",
journal = j-IEEE-SIGNAL-PROCESS-LETT,
volume = "4",
number = "7",
pages = "195--197",
month = "????",
year = "1997",
CODEN = "ISPLEM",
DOI = "https://doi.org/10.1109/97.596884",
ISSN = "1070-9908 (print), 1558-2361 (electronic)",
ISSN-L = "1070-9908",
bibdate = "Tue Mar 06 11:19:40 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=596884",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IEEE signal processing letters",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
}
@InProceedings{Chandrasekaran:1997:WCP,
author = "S. Chandrasekaran and Gene H. Golub and Ming Gu and
Ali H. Sayed",
editor = "Naim A. Kheir",
booktitle = "{Proceedings of the 1997 American Control Conference,
1997. Albuquerque Convention Center, Albuquerque, New
Mexico, June 4--June 6, 1997}",
title = "Worst-case parameter estimation with bounded model
uncertainties",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "171--175 (vol. 1)",
year = "1997",
DOI = "https://doi.org/10.1109/ACC.1997.611779",
ISBN = "0-7803-3832-4 (softcover), 0-7803-3833-2 (hardcover),
0-7803-3834-0 (microfiche), 0-7803-3835-9 (CD-ROM)",
ISBN-13 = "978-0-7803-3832-6 (softcover), 978-0-7803-3833-3
(hardcover), 978-0-7803-3834-0 (microfiche),
978-0-7803-3835-7 (CD-ROM)",
bibdate = "Tue Mar 06 11:14:21 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=611779",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4827",
}
@Article{Chu:1997:VFG,
author = "Moody T. Chu and Robert E. Funderlic and Gene H.
Golub",
title = "On a Variational Formulation of the Generalized
Singular Value Decomposition",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "18",
number = "4",
pages = "1082--1092",
month = oct,
year = "1997",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479895287079",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65Fxx (15A18)",
MRnumber = "1 472 010",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/18/4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/28707",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Fierro:1997:RTT,
author = "R. D. Fierro and G. H. Golub and P. C. Hansen and D.
P. O'Leary",
title = "Regularization by Truncated Total Least Squares",
journal = j-SIAM-J-SCI-COMP,
volume = "18",
number = "4",
pages = "1223--1241",
month = "????",
year = "1997",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827594263837",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F20 (65F30)",
MRnumber = "98d:65051; 1 453 566",
MRreviewer = "Frederick N. Fritsch",
bibdate = "Thu Apr 9 08:17:18 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InProceedings{Golub:1997:CSI,
author = "Gene H. Golub and Henk A. van der Vorst",
title = "Closer to the Solution: Iterative Linear Solvers",
crossref = "Duff:1997:SAN",
volume = "63",
pages = "63--92",
year = "1997",
MRclass = "65F10 (15A06)",
MRnumber = "MR1628342 (99b:65034)",
bibdate = "Sat Dec 31 06:28:14 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
MathSciNet database",
series = "Inst. Math. Appl. Conf. Ser. New Ser.",
acknowledgement = ack-nhfb,
annote = "Based on papers presented at the conference",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "IMA; mathematics; numerical analysis",
}
@Article{Golub:1997:GCV,
author = "Gene H. Golub and Urs von Matt",
title = "Generalized Cross-Validation for Large-Scale
Problems",
journal = j-J-COMPUT-GRAPH-STAT,
volume = "6",
number = "1",
pages = "1--34",
month = mar,
year = "1997",
CODEN = "????",
DOI = "https://doi.org/10.2307/1390722",
ISSN = "1061-8600 (print), 1537-2715 (electronic)",
ISSN-L = "1061-8600",
MRclass = "62J05",
MRnumber = "98j:62052",
MRreviewer = "Girdhar G. Agarwal",
bibdate = "Sat Jan 2 17:33:21 MST 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/1390722",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Computational and Graphical Statistics",
journal-URL = "http://www.tandfonline.com/loi/ucgs20",
}
@InProceedings{Golub:1997:MMQa,
author = "Gene H. Golub",
title = "Matrices, moments and quadrature",
crossref = "Chan:1997:IMS",
pages = "45--57",
year = "1997",
MRclass = "65F30 (15A45 65D32)",
MRnumber = "1661959",
bibdate = "Tue May 08 12:03:21 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Article{Golub:1997:MMQb,
author = "G. H. Golub and G. Meurant",
title = "Matrices, moments and quadrature. {II}. {How} to
compute the norm of the error in iterative methods",
journal = j-BIT-NUM-MATH,
volume = "37",
number = "3",
pages = "687--705",
month = sep,
year = "1997",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF02510247",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F05 (15A99 65D32)",
MRnumber = "1 483 681",
bibdate = "Fri Nov 13 07:00:34 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Direct methods, linear algebra in optimization,
iterative methods (Toulouse, 1995/1996).",
URL = "http://www.mai.liu.se/BIT/contents/bit37.html;
http://www.springerlink.com/content/r44380210547348h/",
abstract = "In this paper, we study the numerical computation of
the errors in linear systems when using iterative
methods. This is done by using methods to obtain bounds
or approximations of quadratic forms {$ u^T A^{-1} u $}
where {$A$} is a symmetric positive definite matrix and
$u$ is a given vector. Numerical examples are given for
the Gauss--Seidel algorithm. Moreover, we show that
using a formula for the {$A$}-norm of the error from
Dahlquist, Golub and Nash [1978] very good bounds of
the error can be computed almost for free during the
iterations of the conjugate gradient method leading to
a reliable stopping criterion.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Golub:1997:TRL,
author = "Gene H. Golub and Urs von Matt",
title = "{Tikhonov} regularization for large scale problems",
crossref = "Golub:1997:PWS",
pages = "3--26",
year = "1997",
bibdate = "Sun Apr 13 08:44:29 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www-sccm.stanford.edu/pub/sccm/sccm97-03.ps.gz",
abstract = "Tikhonov regularization is a powerful tool for the
solution of ill-posed linear systems and linear least
squares problems. The choice of the regularization
parameter is a crucial step, and many methods have been
proposed for this purpose. However, efficient and
reliable methods for large scale problems are still
missing. In this paper approximation techniques based
on the Lanczos algorithm and the theory of Gauss
quadrature are proposed to reduce the computational
complexity for large scale.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Petzold:1997:DCW,
author = "L. R. Petzold and R. D. Skeel and U. Ascher and K.
Burrage and S. L. Campbell and G. H. Golub and E.
Hairer and J. M. Hyman and C. Lubich and R. D. Russell
and J. M. SanzSerna and A. Stuart",
title = "Dedication to {C. William Gear} on the occasion of his
60th birthday",
journal = j-SIAM-J-SCI-COMP,
volume = "18",
number = "1",
pages = "vii--ix",
month = jan,
year = "1997",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InProceedings{VanderVorst:1997:YOS,
author = "Henk A. van der Vorst and Gene H. Golub",
title = "150 Years Old and Still Alive: Eigenproblems",
crossref = "Duff:1997:SAN",
volume = "63",
pages = "93--120",
year = "1997",
MRclass = "65F15 (15A18)",
MRnumber = "MR1628343 (99b:65051)",
bibdate = "Sat Dec 31 06:28:14 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
MathSciNet database",
series = "Inst. Math. Appl. Conf. Ser. New Ser.",
acknowledgement = ack-nhfb,
annote = "Based on papers presented at the conference",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "IMA; mathematics; numerical analysis",
xxpages = "93--119",
}
@Article{Andersson:1998:SBE,
author = "Lars-Erik Andersson and Tommy Elfving and Gene H.
Golub",
title = "Solution of Biharmonic Equations with Application to
Radar Imaging",
journal = j-J-COMPUT-APPL-MATH,
volume = "94",
number = "2",
pages = "153--180",
day = "3",
month = aug,
year = "1998",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(98)00079-X",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:36:10 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704279800079X",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Baglama:1998:APG,
author = "J. Baglama and D. Calvetti and G. H. Golub and L.
Reichel",
title = "Adaptively Preconditioned {GMRES} Algorithms",
journal = j-SIAM-J-SCI-COMP,
volume = "20",
number = "1",
pages = "243--269",
month = jan,
year = "1998",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827596305258",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Dec 4 14:47:53 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/20/1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30525",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Chandrasekaran:1998:PEP,
author = "S. Chandrasekaran and G. H. Golub and M. Gu and A. H.
Sayed",
title = "Parameter Estimation in the Presence of Bounded Data
Uncertainties",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "19",
number = "1",
pages = "235--252",
month = jan,
year = "1998",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479896301674",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "93E10 (65U05 93E24)",
MRnumber = "99a:93094",
MRreviewer = "George Yin",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30167",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Chu:1998:RMS,
author = "M. T. Chu and R. E. Funderlic and G. H. Golub",
title = "Rank modifications of semidefinite matrices associated
with a secant update formula",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "20",
number = "2",
pages = "428--436",
month = oct,
year = "1998",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Giladi:1998:IOI,
author = "Eldar Giladi and Gene H. Golub and Joseph B. Keller",
title = "Inner and Outer Iterations for the {Chebyshev}
Algorithm",
journal = j-SIAM-J-NUMER-ANAL,
volume = "35",
number = "1",
pages = "300--319",
month = feb,
year = "1998",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/S0036142995293742",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Thu Apr 16 15:12:46 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib",
URL = "http://epubs.siam.org:80/sam-bin/dbq/toclist/SINUM/35/1;
http://www.jstor.org/stable/2587104",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Misc{Golub:1998:EDN,
author = "Gene H. Golub",
title = "Early Days of Numerical Computing at {Illinois} on the
{ILLIAC}",
howpublished = "Talk at conference \booktitle{Numerical Analysis and
Computers---50 Years of Progress}.",
day = "16",
month = jun,
year = "1998",
bibdate = "Wed Sep 09 08:53:21 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "https://www.siam.org/news/news.php?id=868",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1998:FPS,
author = "Gene H. Golub and Lan Chieh Huang and Horst Simon and
Wei-Pai Tang",
title = "A Fast {Poisson} Solver for the Finite Difference
Solution of the Incompressible {Navier--Stokes}
Equations",
journal = j-SIAM-J-SCI-COMP,
volume = "19",
number = "5",
pages = "1606--1624",
month = sep,
year = "1998",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827595285299",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Dec 4 14:47:53 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/19/5;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/28529",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Golub:1998:IIS,
author = "Gene H. Golub and Andrew J. Wathen",
title = "An Iteration for Indefinite Systems and Its
Application to the {Navier--Stokes} Equations",
journal = j-SIAM-J-SCI-COMP,
volume = "19",
number = "2",
pages = "530--539",
month = mar,
year = "1998",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S106482759529382X",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Tue Mar 06 11:20:14 2018",
bibsource = "http://epubs.siam.org/toc/sjoce3/19/2;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/29382",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Zhang:1998:EPG,
author = "T. Zhang and G. H. Golub and K. H. Law",
title = "Eigenvalue perturbation and generalized {Krylov}
subspace method",
journal = j-APPL-NUM-MATH,
volume = "27",
number = "2",
pages = "185--202",
year = "1998",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/S0168-9274(98)00002-6",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65F15 (65F30)",
MRnumber = "99i:65044",
MRreviewer = "J. Segethov{\'a}",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Applied Numerical Mathematics. An IMACS Journal",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Zhang:1998:HMP,
author = "T. Zhang and K. H. Law and G. H. Golub",
title = "On the Homotopy Method for Perturbed Symmetric
Generalized Eigenvalue Problems",
journal = j-SIAM-J-SCI-COMP,
volume = "19",
number = "5",
pages = "1625--1645",
month = sep,
year = "1998",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827596299755",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15 (15A18 65F50)",
MRnumber = "99e:65065",
MRreviewer = "Heike Fa{\ss}bender",
bibdate = "Fri Dec 4 14:47:53 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/19/5;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/29975",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Bai:1999:SUE,
author = "Z. Bai and G. H. Golub",
editor = "J. M. L. Palma and J. Dongarra and V. Hernandez",
booktitle = "Vector and Parallel Processing --- {VECPAR'98}",
title = "Some Unusual Eigenvalue Problems (Invited Talk)",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1573",
pages = "4--19",
year = "1999",
CODEN = "LNCSD9",
ISBN = "3-540-66228-6",
ISBN-13 = "978-3-540-66228-0",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
MRclass = "65F15",
MRnumber = "1 721 276",
bibdate = "Tue Sep 14 06:09:05 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "OPORTO, PORTUGAL",
conference-date = "JUN 21-23, 1998",
conference-name = "3rd International Conference on Vector And Parallel
Processing (VECPAR 98)",
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
keywords = "parallel processing; VECPAR; vector processing",
}
@Article{Benzi:1999:BEM,
author = "Michele Benzi and Gene H. Golub",
title = "Bounds for the entries of matrix functions with
applications to preconditioning",
journal = j-BIT-NUM-MATH,
volume = "39",
number = "3",
pages = "417--438",
month = sep,
year = "1999",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1022362401426",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F10 (15A12 65F30)",
MRnumber = "2000h:65047",
MRreviewer = "George D. Poole",
bibdate = "Wed Jan 4 15:06:03 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=39&issue=3;
http://www.mai.liu.se/BIT/contents/bit39.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
OCLC Article1st database",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=39&issue=3&spage=417",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Calvetti:1999:CEB,
author = "D. Calvetti and G. H. Golub and L. Reichel",
title = "A computable error bound for matrix functionals",
journal = j-J-COMPUT-APPL-MATH,
volume = "103",
number = "2",
pages = "301--306",
day = "31",
month = mar,
year = "1999",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(98)00267-2",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:39:43 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042798002672",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Calvetti:1999:ECL,
author = "D. Calvetti and G. H. Golub and L. Reichel",
title = "Estimation of the {$L$}-curve via {Lanczos}
bidiagonalization",
journal = j-BIT-NUM-MATH,
volume = "39",
number = "4",
pages = "603--619",
month = dec,
year = "1999",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1022383005969",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:03 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=39&issue=4;
http://www.mai.liu.se/BIT/contents/bit39.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib; OCLC
Article1st database",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=39&issue=4&spage=603",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Chan:1999:NPD,
author = "Tony F. Chan and Gene H. Golub and Pep Mulet",
title = "A Nonlinear Primal-Dual Method for Total
Variation-Based Image Restoration",
journal = j-SIAM-J-SCI-COMP,
volume = "20",
number = "6",
pages = "1964--1977",
month = nov,
year = "1999",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827596299767",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F30",
MRnumber = "2000c:65038",
bibdate = "Sat Jul 17 19:14:40 MDT 1999",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/20/6;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/29976",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Chandrasekaran:1999:EAB,
author = "S. Chandrasekaran and G. H. Golub and M. Gu and A. H.
Sayed",
title = "An Efficient Algorithm for a Bounded
Errors-in-Variables Model",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "20",
number = "4",
pages = "839--859",
month = oct,
year = "1999",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479896304678",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Sat Jan 22 14:39:14 MST 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30467",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Chu:1999:RMS,
author = "Moody T. Chu and R. E. Funderlic and Gene H. Golub",
title = "Rank Modifications of Semidefinite Matrices Associated
with a Secant Update Formula",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "20",
number = "2",
pages = "428--436",
month = apr,
year = "1999",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "90C30 (65F30)",
MRnumber = "99g:90117",
MRreviewer = "Henry Wolkowicz",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/2;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30602",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Elhay:1999:SEE,
author = "S. Elhay and G. M. L. Gladwell and G. H. Golub and Y.
M. Ram",
title = "On Some Eigenvector-Eigenvalue Relations",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "20",
number = "3",
pages = "563--574",
month = jul,
year = "1999",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S089547989631072X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Sat Jul 17 19:07:35 MDT 1999",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/3;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31072",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Golub:1999:IPC,
author = "Gene H. Golub and Qiang Ye",
title = "Inexact Preconditioned Conjugate Gradient Method with
Inner-Outer Iteration",
journal = j-SIAM-J-SCI-COMP,
volume = "21",
number = "4",
pages = "1305--1320",
month = jul,
year = "1999",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827597323415",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Oct 27 13:32:22 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/32341",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InProceedings{Golub:1999:LSS,
author = "Gene H. Golub and Zhenyue Zhang and Hongyuan Zha",
booktitle = "Advances in numerical mathematics: Proceedings of the
Fourth Japan-China Joint Seminar on Numerical
Mathematics (Chiba, 1998)",
title = "Large sparse symmetric eigenvalue problems with
homogeneous linear constraints: the {Lanczos} process
with inner-outer iterations",
volume = "12",
publisher = "Gakk{\=o}tosho",
address = "Tokyo, Japan",
pages = "21--34",
year = "1999",
MRclass = "65F15 (65F30 65F50)",
MRnumber = "1 763 339",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "GAKUTO Internat. Ser. Math. Sci. Appl.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1999:SNM,
author = "Gene H. Golub and Peyman Milanfar and James Varah",
title = "A Stable Numerical Method for Inverting Shape from
Moments",
journal = j-SIAM-J-SCI-COMP,
volume = "21",
number = "4",
pages = "1222--1243",
month = jul,
year = "1999",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827597328315",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15 (65D32 65F35 86-08 86A20)",
MRnumber = "2000m:65048",
bibdate = "Fri Oct 27 13:32:22 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/32831",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Golub:1999:TRT,
author = "Gene H. Golub and Per Christian Hansen and Dianne P.
O'Leary",
title = "{Tikhonov} Regularization and Total Least Squares",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "21",
number = "1",
pages = "185--194",
year = "1999",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479897326432",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F22 (65J20)",
MRnumber = "2000h:65061",
MRreviewer = "Thorsten Hohage",
bibdate = "Sat Jan 22 14:39:17 MST 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/21/1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/32643",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Nguyen:1999:BRS,
author = "Nhat Nguyen and Gene H. Golub and Peyman Milanfar",
booktitle = "{Conference Record of the Thirty-Third Asilomar
Conference on Signals, Systems, and Computers, 1999}",
title = "Blind restoration\slash superresolution with
generalized cross-validation using {Gauss}-type
quadrature rules",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1257--1261",
year = "1999",
DOI = "https://doi.org/10.1109/ACSSC.1999.831908",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=831908",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6676",
}
@InProceedings{Nguyen:1999:PRI,
author = "Nhat Nguyen and Gene H. Golub and Peyman Milanfar",
booktitle = "{1999 IEEE International Conference on Acoustics,
Speech, and Signal Processing, 1999. Proceedings}",
title = "Preconditioners for regularized image
superresolution",
volume = "6",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "3249--3252",
year = "1999",
DOI = "https://doi.org/10.1109/ICASSP.1999.757534",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=757534",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6110",
}
@Article{Zhang:1999:SIM,
author = "T. Zhang and G. H. Golub and K. H. Law",
title = "Subspace iterative methods for eigenvalue problems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "294",
number = "1--3",
pages = "239--258",
day = "15",
month = jun,
year = "1999",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(99)00074-9",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Sep 1 08:51:18 MDT 1999",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.elsevier.com/cas/tree/store/laa/sub/1999/294/1-3/6421.pdf;
http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1999&volume=294&issue=1-3&aid=6421",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Calvetti:2000:CGK,
author = "D. Calvetti and G. H. Golub and W. B. Gragg and L.
Reichel",
title = "Computation of {Gauss--Kronrod} quadrature rules",
journal = j-MATH-COMPUT,
volume = "69",
number = "231",
pages = "1035--1052",
month = jul,
year = "2000",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-00-01174-1",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Nov 1 11:50:05 MST 2000",
bibsource = "http://www.ams.org/mcom/2000-69-231;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
URL = "http://www.ams.org/journal-getitem?pii=S0025-5718-00-01174-1;
http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01174-1/S0025-5718-00-01174-1.dvi;
http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01174-1/S0025-5718-00-01174-1.pdf;
http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01174-1/S0025-5718-00-01174-1.ps;
http://www.ams.org/mcom/2000-69-231/S0025-5718-00-01174-1/S0025-5718-00-01174-1.tex",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Golub:2000:CSG,
author = "G. Golub and K. Solna and P. {Van Dooren}",
title = "Computing the {SVD} of a general matrix product\slash
quotient",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "1",
pages = "1--19",
month = jun,
year = "2000",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479897325578",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Golub:2000:ECC,
author = "Gene H. Golub and Henk A. van der Vorst",
title = "Eigenvalue computation in the 20th century",
journal = j-J-COMPUT-APPL-MATH,
volume = "123",
number = "1--2",
pages = "35--65",
day = "1",
month = nov,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00413-1",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65F15 (65-02)",
MRnumber = "MR1798518 (2001j:65064)",
bibdate = "Sat Feb 25 12:43:37 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib;
MathSciNet database",
note = "Numerical analysis 2000, Vol. III. Linear algebra.",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700004131",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Golub:2000:III,
author = "Gene H. Golub and Qiang Ye",
title = "Inexact inverse iteration for generalized eigenvalue
problems",
journal = j-BIT-NUM-MATH,
volume = "40",
number = "4",
pages = "671--684",
month = dec,
year = "2000",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1022388317839",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F15 (65F10)",
MRnumber = "2001j:65063",
MRreviewer = "Jesse L. Barlow",
bibdate = "Wed Jan 4 15:06:04 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=40&issue=4;
http://www.mai.liu.se/BIT/contents/bit40.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=40&issue=4&spage=671",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Golub:2000:LSS,
author = "Gene H. Golub and Zhenyue Zhang and Hongyuan Zha",
title = "Large sparse symmetric eigenvalue problems with
homogeneous linear constraints: the {Lanczos} process
with inner-outer iterations",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "309",
number = "1--3",
pages = "289--306",
day = "15",
month = apr,
year = "2000",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/S0024-3795(99)00204-9",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Oct 9 10:54:41 MDT 2000",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/39/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/126/25/39/article.pdf",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Golub:2000:PMS,
author = "Gene H. Golub and Denis Vanderstraeten",
title = "On the preconditioning of matrices with skew-symmetric
splittings",
journal = j-NUMER-ALGORITHMS,
volume = "25",
number = "1--4",
pages = "223--239",
year = "2000",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1023/A:1016637813615",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F35 (15A12 65F10)",
MRnumber = "1 827 156",
MRreviewer = "David R. Hill",
bibdate = "Wed Jul 25 07:43:10 MDT 2001",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
MathSciNet database",
note = "Mathematical journey through analysis, matrix theory
and scientific computation (Kent, OH, 1999).",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Murphy:2000:NPI,
author = "Malcolm F. Murphy and Gene H. Golub and Andrew J.
Wathen",
title = "A Note on Preconditioning for Indefinite Linear
Systems",
journal = j-SIAM-J-SCI-COMP,
volume = "21",
number = "6",
pages = "1969--1972",
month = nov,
year = "2000",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827599355153",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F35 (65F20)",
MRnumber = "2001a:65055",
bibdate = "Fri Oct 27 13:32:27 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/6;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/35515",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InCollection{Engquist:2001:NAC,
author = "Bj{\"o}rn Engquist and Gene Golub",
title = "From Numerical Analysis to Computational Science",
crossref = "Engquist:2001:MUB",
pages = "433--448",
year = "2001",
bibdate = "Mon Oct 31 14:18:51 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:2001:CSG,
author = "Gene Golub and Knut Solna and Paul {Van Dooren}",
title = "Computing the {SVD} of a General Matrix Product\slash
Quotient",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "1",
pages = "1--19",
month = jan,
year = "2001",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Oct 27 07:23:35 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/32557",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Golub:2001:PBS,
author = "Gene H. Golub and Ahmed H. Sameh and Vivek Sarin",
title = "A parallel balance scheme for banded linear systems",
journal = j-NUM-LIN-ALG-APPL,
volume = "8",
number = "5",
pages = "297--316",
month = "????",
year = "2001",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.241",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "65F05 (65F10 65Y05)",
MRnumber = "2002c:65045",
bibdate = "Mon Feb 25 14:09:06 MST 2002",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract/82004028/START;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=82004028&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@Article{Golub:2001:SAE,
author = "G. H. Golub and H. Melb{\"o}",
title = "A stochastic approach to error estimates for iterative
linear solvers: {Part} 1",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "5",
pages = "977--985",
month = dec,
year = "2001",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1021985111111",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:05 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=5;
http://www.mai.liu.se/BIT/contents/bit41.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=5&spage=977",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Golub:2001:SLM,
author = "Gene H. Golub and X. Wu and Jin-Yun Yuan",
title = "{SOR}-like Methods for Augmented Systems",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "1",
pages = "71--85",
month = jan,
year = "2001",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1021965717530",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F10",
MRnumber = "2002a:65055",
MRreviewer = "Jan Z{\'\i}tko",
bibdate = "Wed Jan 4 15:06:04 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=1;
http://www.mai.liu.se/BIT/contents/bit41.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=1&spage=71",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Nguyen:2001:CES,
author = "Nhat Nguyen and Peyman Milanfar and Gene H. Golub",
title = "A computationally efficient superresolution image
reconstruction algorithm",
journal = j-IEEE-TRANS-IMAGE-PROCESS,
volume = "10",
number = "4",
pages = "573--583",
month = "????",
year = "2001",
CODEN = "IIPRE4",
DOI = "https://doi.org/10.1109/83.913592",
ISSN = "1057-7149 (print), 1941-0042 (electronic)",
ISSN-L = "1057-7149",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=913592",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IEEE Transactions on Image Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=83",
}
@Article{Nguyen:2001:EGC,
author = "Nhat Nguyen and Peyman Milanfar and Gene H. Golub",
title = "Efficient generalized cross-validation with
applications to parametric image restoration and
resolution enhancement",
journal = j-IEEE-TRANS-IMAGE-PROCESS,
volume = "10",
number = "9",
pages = "1299--1308",
month = "????",
year = "2001",
CODEN = "IIPRE4",
DOI = "https://doi.org/10.1109/83.941854",
ISSN = "1057-7149 (print), 1941-0042 (electronic)",
ISSN-L = "1057-7149",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=941854",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IEEE Transactions on Image Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=83",
}
@Article{Zhang:2001:ROA,
author = "Tong Zhang and Gene H. Golub",
title = "Rank-One Approximation to High Order Tensors",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "23",
number = "2",
pages = "534--550",
year = "2001",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479899352045",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A69 (65F30)",
MRnumber = "2002j:15039",
MRreviewer = "C. S. Sharma",
bibdate = "Fri Feb 22 09:58:16 MST 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/2;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/35204",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Chu:2002:SIE,
author = "Moody T. Chu and Gene H. Golub",
title = "Structured inverse eigenvalue problems",
journal = j-ACTA-NUMERICA,
volume = "11",
pages = "1--71",
year = "2002",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492902000016",
ISBN = "0-521-81876-1",
ISBN-13 = "978-0-521-81876-6",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
MRclass = "65F18 (34A55 70J10)",
MRnumber = "2008966 (2005b:65040)",
MRreviewer = "Shu Fang Xu",
bibdate = "Sat Sep 24 11:37:17 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "15 July 2003",
}
@Article{Concus:2002:OOP,
author = "Paul Concus and Gene H. Golub and Yong Sun",
title = "Object-oriented parallel algorithms for computing
three-dimensional isopycnal flow",
journal = j-INT-J-NUMER-METHODS-FLUIDS,
volume = "39",
number = "7",
pages = "585--605",
year = "2002",
CODEN = "IJNFDW",
DOI = "https://doi.org/10.1002/fld.257",
ISSN = "0271-2091 (print), 1097-0363 (electronic)",
ISSN-L = "0271-2091",
MRclass = "76M25",
MRnumber = "2003d:76123",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "International Journal for Numerical Methods in
Fluids",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0363",
}
@InProceedings{Elad:2002:SMI,
author = "Michael Elad and Peyman Milanfar and Gene H. Golub",
booktitle = "{Conference Record of the Thirty-Sixth Asilomar
Conference on Signals, Systems and Computers, 2002}",
title = "Shape from moments as an inverse problem",
volume = "1",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "921--925",
year = "2002",
DOI = "https://doi.org/10.1109/ACSSC.2002.1197311",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1197311",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=8521",
}
@Article{Golub:2002:BOT,
author = "Gene H. Golub and Chen Greif and James M. Varah",
title = "Block orderings for tensor-product grids in two and
three dimensions",
journal = j-NUMER-ALGORITHMS,
volume = "30",
number = "2",
pages = "93--111",
year = "2002",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1023/A:1016030016985",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65N22 (65F10)",
MRnumber = "2003f:65182",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Golub:2002:IFP,
author = "Gene H. Golub and Qiang Ye",
title = "An inverse free preconditioned {Krylov} subspace
method for symmetric generalized eigenvalue problems",
journal = j-SIAM-J-SCI-COMP,
volume = "24",
number = "1",
pages = "312--334",
month = jan,
year = "2002",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827500382579",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15",
MRnumber = "2003h:65048",
MRreviewer = "E. Kreyszig",
bibdate = "Tue Oct 22 18:24:38 MDT 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/24/1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/38257",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Golub:2002:STD,
author = "Gene H. Golub and Jin-Yun Yuan",
title = "Symmetric-triangular decomposition and its
applications {Part I}: {Theorems} and algorithms",
journal = j-BIT-NUM-MATH,
volume = "42",
number = "4",
pages = "814--822",
month = dec,
year = "2002",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1021904604693",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F05 (15A23)",
MRnumber = "MR1944539 (2003k:65023)",
MRreviewer = "Ilse C. F. Ipsen",
bibdate = "Wed Jan 4 15:06:05 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=42&issue=4;
http://www.mai.liu.se/BIT/contents/bit42.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=42&issue=4&spage=814",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bai:2003:HSH,
author = "Zhong-Zhi Bai and Gene H. Golub and Michael K. Ng",
title = "Hermitian and skew-{Hermitian} splitting methods for
non-{Hermitian} positive definite linear systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "24",
number = "3",
pages = "603--626 (electronic)",
year = "2003",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479801395458",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10",
MRnumber = "1 972 670",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Benzi:2003:OHS,
author = "Michele Benzi and Martin J. Gander and Gene H. Golub",
title = "Optimization of the {Hermitian} and skew-{Hermitian}
splitting iteration for saddle-point problems",
journal = j-BIT-NUM-MATH,
volume = "43",
number = "5",
pages = "881--900",
month = dec,
year = "2003",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/B:BITN.0000014548.26616.65",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F10 (65N22)",
MRnumber = "MR2058873 (2005e:65032)",
MRreviewer = "Zden{\v{e}}k Dost{\'a}l",
bibdate = "Wed Jan 4 15:06:06 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=43&issue=5;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=43&issue=5&spage=881",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Elhay:2003:SML,
author = "S. Elhay and G. H. Golub and Y. M. Ram",
title = "The spectrum of a modified linear pencil",
journal = j-COMPUT-MATH-APPL,
volume = "46",
number = "8--9",
pages = "1413--1426",
month = oct # "\slash " # nov,
year = "2003",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/S0898-1221(03)00370-5",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "15A18 (15A21 15A48 70J10)",
MRnumber = "MR2020255 (2004j:15014)",
bibdate = "Wed Mar 1 21:49:33 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S089812210390229X",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@InCollection{Gander:2003:NOO,
author = "M. J. Gander and G. H. Golub",
booktitle = "Domain decomposition methods in science and
engineering",
title = "A non-overlapping optimized {Schwarz} method which
converges with arbitrarily weak dependence on $h$",
publisher = "Natl. Auton. Univ. Mex., M\'exico",
pages = "281--288 (electronic)",
year = "2003",
MRclass = "65N55",
MRnumber = "MR2099435",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:2003:SBS,
author = "Gene H. Golub and Chen Greif",
title = "On solving block-structured indefinite linear
systems",
journal = j-SIAM-J-SCI-COMP,
volume = "24",
number = "6",
pages = "2076--2092 (electronic)",
year = "2003",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827500375096",
ISSN = "1095-7197",
ISSN-L = "1064-8275",
MRclass = "65F10 (90C46)",
MRnumber = "MR2005622 (2004h:65030)",
MRreviewer = "Lars Eld{\'e}n",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Golub:2003:SNL,
author = "Gene Golub and Victor Pereyra",
title = "Separable nonlinear least squares: the variable
projection method and its applications",
journal = j-INVERSE-PROBLEMS,
volume = "19",
number = "2",
pages = "R1--R26",
year = "2003",
CODEN = "INPEEY",
DOI = "https://doi.org/10.1088/0266-5611/19/2/201",
ISSN = "0266-5611 (print), 1361-6420 (electronic)",
ISSN-L = "0266-5611",
MRclass = "65K10 (65D10)",
MRnumber = "MR1991786 (2004f:65082)",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Inverse Problems. An International Journal on the
Theory and Practice of Inverse Problems, Inverse
Methods and Computerized Inversion of Data",
journal-URL = "http://iopscience.iop.org/0266-5611/",
}
@TechReport{Kamvar:2003:EBS,
author = "S. Kamvar and T. Haveliwala and C. Manning and G.
Golub",
title = "Exploiting the block structure of the {Web} for
computing {PageRank}",
type = "Technical Report",
number = "2003-17",
institution = "Stanford InfoLab, Stanford University",
address = "Stanford, CA, USA",
year = "2003",
bibdate = "Fri Feb 19 15:17:26 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Kamvar:2003:EMA,
author = "Sepandar D. Kamvar and Taher H. Haveliwala and
Christopher D. Manning and Gene H. Golub",
editor = "ACM",
booktitle = "Proceedings of the Twelfth International Conference on
World Wide Web 2003, Budapest, Hungary, May 20--24,
2003",
title = "Extrapolation Methods for Accelerating {PageRank}
Computations",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "xx + 752",
pages = "261--270",
year = "2003",
DOI = "https://doi.org/10.1145/775152.775190",
ISBN = "1-58113-680-3",
ISBN-13 = "978-1-58113-680-7",
LCCN = "",
bibdate = "Wed Nov 10 16:22:54 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://dbpubs.stanford.edu:8090/pub/2003-16;
http://www.stanford.edu/~sdkamvar/papers/extrapolation.pdf",
abstract = "We present a novel algorithm for the fast computation
of PageRank, a hyperlink-based estimate of the
``importance'' of Web pages. The original PageRank
algorithm uses the Power Method to compute successive
iterates that converge to the principal eigenvector of
the Markov matrix representing the Web link graph. The
algorithm presented here, called Quadratic
Extrapolation, accelerates the convergence of the Power
Method by periodically subtracting off estimates of the
nonprincipal eigenvectors from the current iterate of
the Power Method. In Quadratic Extrapolation, we take
advantage of the fact that the first eigenvalue of a
Markov matrix is known to be 1 to compute the
nonprincipal eigenvectors using successive iterates of
the Power Method. Empirically, we show that using
Quadratic Extrapolation speeds up PageRank computation
by 25--300\% on a Web graph of 80 million nodes, with
minimal overhead. Our contribution is useful to the
PageRank community and the numerical linear algebra
community in general, as it is a fast method for
determining the dominant eigenvector of a matrix that
is too large for standard fast methods to be
practical.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "eigenvector computation; link analysis; PageRank",
}
@Article{Orchard:2003:SRA,
author = "Jeff Orchard and Chen Greif and Gene H. Golub and
Bruce Bjornson and M. Stella Atkins",
title = "Simultaneous registration and activation detection for
{fMRI}",
journal = j-IEEE-TRANS-MED-IMAG,
volume = "22",
number = "11",
pages = "1427--1435",
month = "????",
year = "2003",
CODEN = "ITMID4",
DOI = "https://doi.org/10.1109/TMI.2003.819294",
ISSN = "0278-0062 (print), 1558-254X (electronic)",
ISSN-L = "0278-0062",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1242345",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IEEE Transactions on Medical Imaging",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=42",
}
@InProceedings{Tsaig:2003:OFL,
author = "Yaakov Tsaig and Michael Elad and Gene H. Golub and
Peyman Milanfar",
booktitle = "{2003 International Conference on Image Processing,
2003. ICIP 2003. Proceedings}",
title = "Optimal framework for low bit-rate block coders",
volume = "2",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "II-219--II-222 (vol. 3)",
year = "2003",
DOI = "https://doi.org/10.1109/ICIP.2003.1246656",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/datacompression.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1246656",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=8824",
keywords = "data compression",
xxnote = "Resolve volume number conflict in IEEE Xplore data.",
}
@Article{Alter:2004:IAG,
author = "Orly Alter and Gene H. Golub",
title = "Integrative Analysis of Genome-Scale Data by Using
Pseudoinverse Projection Predicts Novel Correlation
between {DNA} Replication and {RNA} Transcription",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "101",
number = "47",
pages = "16577--16582",
day = "23",
month = nov,
year = "2004",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.0406767101",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Tue May 18 15:58:54 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.bme.utexas.edu/research/orly/pseudoinverse/;
http://www.jstor.org/stable/3373867",
abstract = "We describe an integrative data-driven mathematical
framework that formulates any number of genome-scale
molecular biological data sets in terms of one chosen
set of data samples, or of profiles extracted
mathematically from data samples, designated the
``basis'' set. By using pseudoinverse projection, the
molecular biological profiles of the data samples are
least-squares-approximated as superpositions of the
basis profiles. Reconstruction of the data in the basis
simulates experimental observation of only the cellular
states manifest in the data that correspond to those of
the basis. Classification of the data samples according
to their reconstruction in the basis, rather than their
overall measured profiles, maps the cellular states of
the data onto those of the basis and gives a global
picture of the correlations and possibly also causal
coordination of these two sets of states. We illustrate
this framework with an integration of yeast
genome-scale proteins' DNA-binding data with cell cycle
mRNA expression time course data. Novel correlation
between DNA replication initiation and RNA
transcription during the yeast cell cycle, which might
be due to a previously unknown mechanism of regulation,
is predicted.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
}
@InProceedings{Alter:2004:NGS,
author = "Orly Alter and Gene H. Golub and Patrick O. Brown and
David Botstein",
editor = "M. P. Deutscher and S. Black and P. E. Boehmer and G.
D'Urso and T. Fletcher and F. Huijing and A. Marshall
and B. Pulverer and B. Renault and J. D. Rosenblatt and
J. M. Slingerland and W. J. Whelan",
booktitle = "Proceedings of the 2004 Miami Nature Biotechnology
Winter Symposium on the Cell Cycle, Chromosomes and
Cancer",
title = "Novel Genome-Scale Correlation Between {DNA}
Replication and {RNA} Transcription During the Cell
Cycle in Yeast is Predicted by Data-Driven Models",
publisher = "Miller School of Medicine, University of Miami",
address = "Miami, FL, USA",
pages = "??--??",
year = "2004",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue May 18 16:22:50 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.med.miami.edu/mnbws/documents/Alter-.pdf",
abstract = "Recently we showed that singular value decomposition
(SVD) (1) and generalized SVD (GSVD) (2), applied to
genome-scale datasets of yeast RNA transcription during
the cell cycle (3), provide data-driven models, i.e.,
mathematical frameworks for the description of the
data, where the mathematical variables and operations
may represent biological reality. The variables of SVD,
``eigengenes'' and ``eigenarrays,'' and these of GSVD,
``genelets'' and ``arraylets,'' appear to represent
independent processes and corresponding cellular states
(such as observed genome-scale effects of cell cycle
regulators and measured samples in which these
regulators are overactive), respectively. Mathematical
reconstruction of gene and array expression in a subset
of eigengenes and eigenarrays, or that of genelets and
arraylets, appears to simulate experimental observation
of only the process and cellular state, respectively,
that these expression patterns represent. Now we
incorporate into these models genome-scale datasets of
yeast protein binding, including nine cell cycle
transcription factors (4), and four DNA replication
initiation proteins (5), across 2,928 ORFs.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
pagecount = "6",
}
@Article{Bai:2004:PHS,
author = "Zhong-Zhi Bai and Gene H. Golub and Jian-Yu Pan",
title = "Preconditioned {Hermitian} and skew-{Hermitian}
splitting methods for non-{Hermitian} positive
semidefinite linear systems",
journal = j-NUM-MATH,
volume = "98",
number = "1",
pages = "1--32",
month = jul,
year = "2004",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-004-0521-1",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F10",
MRnumber = "MR2076052",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Benzi:2004:PGS,
author = "Michele Benzi and Gene H. Golub",
title = "A preconditioner for generalized saddle point
problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "26",
number = "1",
pages = "20--41 (electronic)",
year = "2004",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479802417106",
ISSN = "1095-7162",
ISSN-L = "0895-4798",
MRclass = "65F10",
MRnumber = "MR2112850",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Elad:2004:SME,
author = "Michael Elad and Peyman Milanfar and Gene H. Golub",
title = "Shape from moments---an estimation theory
perspective",
journal = j-IEEE-TRANS-SIG-PROC,
volume = "52",
number = "7",
pages = "1814--1829",
year = "2004",
CODEN = "ITPRED",
DOI = "https://doi.org/10.1109/TSP.2004.828919",
ISSN = "1053-587X (print), 1941-0476 (electronic)",
ISSN-L = "1053-587X",
MRclass = "62H35 (62F10)",
MRnumber = "MR2087688",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1306639",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IEEE Transactions on Signal Processing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}
@Article{Holz:2004:SAM,
author = "U. B. Holz and G. H. Golub and K. H. Law",
title = "A subspace approximation method for the quadratic
eigenvalue problem",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "26",
number = "2",
pages = "498--521",
month = "????",
year = "2004",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479803423378",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Misc{Kamvar:2004:ACR,
author = "Sepandar D. Kamvar and Taher H. Haveliwala and Gene H.
Golub",
title = "Adaptive computation of ranking",
howpublished = "US Patent 7,028,029.",
day = "23",
month = aug,
year = "2004",
bibdate = "Wed Jun 01 18:43:31 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "A system and method is disclosed in which a ranking
function for a set of document rank values is
iteratively solved with respect to a set of linked
documents until a first stability condition is
satisfied. After such condition is satisfied, some of
the ranks will have converged. The ranking function is
modified to take into account these converged ranks so
as to reduce the ranking function's computation cost.
The modified ranking function is then solved until a
second stability condition is satisfied. After such
condition is satisfied more of the ranks will have
converged. The ranking function is again modified and
process continues until complete.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Kamvar:2004:AMC,
author = "Sepandar Kamvar and Taher Haveliwala and Gene Golub",
title = "Adaptive methods for the computation of {PageRank}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "386",
number = "1",
pages = "51--65",
day = "15",
month = jul,
year = "2004",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2003.12.008",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "60-04 (60G50 60J10)",
MRnumber = "MR2066607",
bibdate = "Tue Nov 9 07:02:36 MST 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "Google search engine; PageRank algorithm",
}
@InProceedings{Kim:2004:IMV,
author = "Hyunsoo Kim and Gene H. Golub and Haesun Park",
booktitle = "{2004 IEEE Computational Systems Bioinformatics
Conference, 2004. CSB 2004. Proceedings}",
title = "Imputation of missing values in {DNA} microarray gene
expression data",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "572--573",
year = "2004",
DOI = "https://doi.org/10.1109/CSB.2004.1332500",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1332500",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=9262",
}
@Article{Livne:2004:SB,
author = "Oren E. Livne and Gene H. Golub",
title = "Scaling by Binormalization",
journal = j-NUMER-ALGORITHMS,
volume = "35",
number = "1",
pages = "97--120",
month = jan,
year = "2004",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1023/B:NUMA.0000016606.32820.69",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F35",
MRnumber = "MR2041806 (2004m:65059)",
MRreviewer = "Yimin Wei",
bibdate = "Mon Dec 6 07:00:26 MST 2004",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/49/A/7/abstract.htm",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Sima:2004:RTL,
author = "Diana M. Sima and Sabine {Van Huffel} and Gene H.
Golub",
title = "Regularized total least squares based on quadratic
eigenvalue problem solvers",
journal = j-BIT,
volume = "44",
number = "4",
pages = "793--812",
year = "2004",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-004-6024-8",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F20 (65F15 65F30)",
MRnumber = "MR2211045 (2007e:65040)",
MRreviewer = "Dario Fasino",
bibdate = "Wed Jan 4 15:06:06 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Yuan:2004:SCD,
author = "J. Y. Yuan and G. H. Golub and R. J. Plemmons and W.
A. G. Cec{\'\i}lio",
title = "Semi-conjugate direction methods for real positive
definite systems",
journal = j-BIT,
volume = "44",
number = "1",
pages = "189--207",
year = "2004",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/B:BITN.0000025092.92213.da",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F10",
MRnumber = "MR2057370 (2005d:65052)",
MRreviewer = "Jan Z{\'\i}tko",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Alter:2005:RPC,
author = "Orly Alter and Gene H. Golub",
title = "Reconstructing the pathways of a cellular system from
genome-scale signals by using matrix and tensor
computations",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "102",
number = "49",
pages = "17559--17564",
day = "6",
month = dec,
year = "2005",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.0509033102",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Tue May 18 16:07:26 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.bme.utexas.edu/research/orly/network_decomposition/;
http://www.jstor.org/stable/4152766;
http://www.pnas.org/content/102/49/17559.full",
abstract = "We describe the use of the matrix eigenvalue
decomposition (EVD) and pseudoinverse projection and a
tensor higher-order EVD (HOEVD) in reconstructing the
pathways that compose a cellular system from
genome-scale nondirectional networks of correlations
among the genes of the system. The EVD formulates a
genes $ \times $ genes network as a linear
superposition of genes $ \times $ genes decorrelated
and decoupled rank-1 subnetworks, which can be
associated with functionally independent pathways. The
integrative pseudoinverse projection of a network
computed from a ``data'' signal onto a designated
``basis'' signal approximates the network as a linear
superposition of only the subnetworks that are common
to both signals and simulates observation of only the
pathways that are manifest in both experiments. We
define a comparative HOEVD that formulates a series of
networks as linear superpositions of decorrelated
rank-1 subnetworks and the rank-2 couplings among these
subnetworks, which can be associated with independent
pathways and the transitions among them common to all
networks in the series or exclusive to a subset of the
networks. Boolean functions of the discretized
subnetworks and couplings highlight differential, i.e.,
pathway-dependent, relations among genes. We illustrate
the EVD, pseudoinverse projection, and HOEVD of
genome-scale networks with analyses of yeast DNA
microarray data.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
}
@Article{Bai:2005:BTS,
author = "Zhong-Zhi Bai and Gene H. Golub and Lin-Zhang Lu and
Jun-Feng Yin",
title = "Block Triangular and Skew-{Hermitian} Splitting
Methods for Positive-Definite Linear Systems",
journal = j-SIAM-J-SCI-COMP,
volume = "26",
number = "3",
pages = "844--863",
month = may,
year = "2005",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827503428114",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F10 (65F50)",
MRnumber = "MR2126115 (2005m:65054)",
MRreviewer = "Stephen W. Brady",
bibdate = "Sat Apr 16 12:07:23 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/26/3;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/42811",
ZMnumber = "02138772",
abstract = "By further generalizing the concept of Hermitian (or
normal) and skew-Hermitian splitting for a
non-Hermitian and positive-definite matrix, we
introduce a new splitting, called positive-definite and
skew-Hermitian splitting (PSS), and then establish a
class of PSS methods similar to the Hermitian (or
normal) and skew-Hermitian splitting (HSS or NSS)
method for iteratively solving the positive-definite
systems of linear equations. Theoretical analysis shows
that the PSS method converges unconditionally to the
exact solution of the linear system, with the upper
bound of its convergence factor dependent only on the
spectrum of the positive-definite splitting matrix and
independent of the spectrum of the skew-Hermitian
splitting matrix as well as the eigenvectors of all
matrices involved. When we specialize the PSS to block
triangular (or triangular) and skew-Hermitian splitting
(BTSS or TSS), the PSS method naturally leads to a BTSS
or TSS iteration method, which may be more practical
and efficient than the HSS and NSS iteration methods.
Applications of the BTSS method to the linear systems
of block two-by-two structures are discussed in detail.
Numerical experiments further show the effectiveness of
our new methods.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classmath = "*65F10 Iterative methods for linear systems 65F15
Eigenvalues (numerical linear algebra) 65F50 Sparse
matrices",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
keywords = "block triangular matrix; Hermitian and skew-Hermitian
splitting; non-Hermitian matrix; positive-definite
matrix; splitting iteration method; triangular matrix",
}
@Article{Benzi:2005:NSS,
author = "Michele Benzi and Gene H. Golub and J{\"o}rg Liesen",
title = "Numerical solution of saddle point problems",
journal = j-ACTA-NUMERICA,
volume = "14",
pages = "1--137",
year = "2005",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S0962492904000212",
ISBN = "0-521-85807-0",
ISBN-13 = "978-0-521-85807-6",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
MRclass = "65F10 (76D07 90C47)",
MRnumber = "MR2168342 (2006m:65059)",
MRreviewer = "Timothy Nigel Phillips",
bibdate = "Sat Sep 24 10:35:17 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "19 April 2005",
}
@Article{Bertaccini:2005:PHM,
author = "Daniele Bertaccini and Gene H. Golub and Stefano Serra
Capizzano and Cristina Tablino Possio",
title = "Preconditioned {HSS} methods for the solution of
non-{Hermitian} positive definite linear systems and
applications to the discrete convection-diffusion
equation",
journal = j-NUM-MATH,
volume = "99",
number = "3",
pages = "441--484",
month = jan,
year = "2005",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-004-0574-1",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "76M20 (35J25 65F10 65N22)",
MRnumber = "MR2117735",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
ZMnumber = "02146845",
abstract = "This paper deals with the application of a
preconditioning step to the Hermitian skew-Hermitian
splitting (HSS) method. The result suggests that the
technique is effective for handling non Hermitian,
positive definite and ill conditioned problems with an
optimal convergence rate. Some numerical results for a
model problem (discretizing the convection-diffusion
problem by finite differences) are presented.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classmath = "*65F10 Iterative methods for linear systems 65N06
Finite difference methods (BVP of PDE) 65F35 Matrix
norms, etc. (numerical linear algebra) 35J25 Second
order elliptic equations, boundary value problems",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Hermitian skew; Hermitian splitting",
ZMreviewer = "Pavol Chocholat? (Bratislava)",
}
@Article{Boutry:2005:GEP,
author = "Gregory Boutry and Michael Elad and Gene H. Golub and
Peyman Milanfar",
title = "The Generalized Eigenvalue Problem for Nonsquare
Pencils Using a Minimal Perturbation Approach",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "27",
number = "2",
pages = "582--601",
month = apr,
year = "2005",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479803428795",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Dec 29 16:33:54 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/27/2;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/42879",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Book{Chu:2005:IEP,
author = "Moody T. Chu and Gene H. Golub",
title = "Inverse Eigenvalue Problems: Theory, Algorithms, and
Applications",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvii + 387",
year = "2005",
DOI = "https://doi.org/10.1093/acprof:oso/9780198566649.001.0001",
ISBN = "0-19-856664-6 (hardcover), 0-19-152422-0 (e-book),
0-19-171802-5",
ISBN-13 = "978-0-19-856664-9 (hardcover), 978-0-19-152422-6
(e-book), 978-0-19-171802-1",
LCCN = "QA193 .C48 2005",
MRclass = "65-02 (65F18)",
MRnumber = "MR2263317 (2007i:65001)",
MRreviewer = "Heike Fa{\ss}bender",
bibdate = "Sat Apr 07 10:19:58 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
series = "Numerical Mathematics and Scientific Computation",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
shorttableofcontents = "List of Acronyms / xiv \\
List of Figures / xv \\
List of Tables / xvii \\
1: Introduction / 1 \\
2: Applications / 10 \\
3: Parameterized inverse eigenvalue problems / 29 \\
4: Structured inverse eigenvalue problems / 71 \\
5: Partially described inverse eigenvalue problems /
146 \\
6: Least squares inverse eigenvalue problems / 192 \\
7: Spectrally constrained approximation / 212 \\
8: Structured low rank approximation / 246 \\
9: Group orbitally constrained approximation / 339 \\
References / 359 \\
Index / 381",
tableofcontents = "List of Acronyms / xiv \\
List of Figures / xv \\
List of Tables / xvii \\
1: Introduction / 1 \\
1.1 Direct problem / 2 \\
1.2 Inverse problem / 4 \\
1.2.1 Constraints / 4 \\
1.2.2 Fundamental issues / 5 \\
1.3 Nomenclature / 6 \\
1.4 Summary / 9 \\
2: Applications / 10 \\
2.1 Overview / 10 \\
2.2 Pole assignment problem / 11 \\
2.2.1 State feedback control / 11 \\
2.2.2 Output feedback control / 12 \\
2.3 Applied mechanics / 13 \\
2.3.1 A string with beads / 13 \\
2.3.2 Quadratic eigenvalue problem / 15 \\
2.3.3 Engineering applications / 17 \\
2.4 Inverse Sturm--Liouville problem / 18 \\
2.5 Applied physics / 19 \\
2.5.1 Quantum mechanics / 19 \\
2.5.2 Neuron transport theory / 20 \\
2.6 Numerical analysis / 21 \\
2.6.1 Preconditioning / 21 \\
2.6.2 Numerical ODEs / 22 \\
2.6.3 Quadrature rules / 23 \\
2.7 Signal and data processing / 25 \\
2.7.1 Signal processing / 25 \\
2.7.2 Computer algebra / 25 \\
2.7.3 Molecular structure modelling / 27 \\
2.7.4 Principal component analysis, data mining and
others / 27 \\
2.8 Summary / 28 \\
3: Parameterized inverse eigenvalue problems / 29 \\
3.1 Overview / 29 \\
3.1.1 Generic form / 30 \\
3.1.2 Variations / 31 \\
3.2 General results for linear PIEP / 34 \\
3.2.1 Existence theory / 34 \\
3.2.2 Sensitivity analysis / 39 \\
3.2.3 Ideas of computation / 45 \\
3.2.4 Newton's method (for LiPIEP2) / 47 \\
3.2.5 Projected gradient method (for LiPIEP2) / 52 \\
3.3 Additive inverse eigenvalue problems / 54 \\
3.3.1 Solvability / 56 \\
3.3.2 Sensitivity and stability (for AIEP2) / 59 \\
3.3.3 Numerical methods / 60 \\
3.4 Multiplicative inverse eigenvalue problems / 63 \\
3.4.1 Solvability / 65 \\
3.4.2 Sensitivity (for MIEP2) / 67 \\
3.4.3 Numerical methods / 68 \\
3.5 Summary / 70 \\
4: Structured inverse eigenvalue problems / 71 \\
4.1 Overview / 71 \\
4.2 Jacobi inverse eigenvalue problems / 72 \\
4.2.1 Variations / 73 \\
4.2.2 Physical interpretations / 77 \\
4.2.3 Existence theory / 79 \\
4.2.4 Sensitivity issues / 81 \\
4.2.5 Numerical methods / 82 \\
4.3 Toeplitz inverse eigenvalue problems / 85 \\
4.3.1 Symmetry and parity / 87 \\
4.3.2 Existence / 89 \\
4.3.3 Numerical methods / 89 \\
4.4 Nonnegative inverse eigenvalue problems / 93 \\
4.4.1 Some existence results / 94 \\
4.4.2 Symmetric nonnegative inverse eigenvalue problem
/ 95 \\
4.4.3 Minimum realizable spectral radius / 97 \\
4.5 Stochastic inverse eigenvalue problems / 103 \\
4.5.1 Existence / 104 \\
4.5.2 Numerical method / 106 \\
4.6 Unitary Hessenberg inverse eigenvalue problems /
110 \\
4.7 Inverse eigenvalue problems with prescribed entries
/ 112 \\
4.7.1 Prescribed entries along the diagonal / 112 \\
4.7.2 Prescribed entries at arbitrary locations / 116
\\
4.7 .3 Additive inverse eigenvalue problem revisit /
117 \\
4.7.4 Cardinality and locations / 118 \\
4.7.5 Numerical methods / 119 \\
4.8 Inverse singular value problems / 128 \\
4.8.1 Distinct singular values / 129 \\
4.8.2 Multiple singular values / 132 \\
4.8.3 Rank deficiency / 134 \\
4.9 Inverse singular/ eigenvalue problems / 134 \\
4.9.1 The 2 x 2 building block / 136 \\
4.9.2 Divide and conquer / 136 \\
4.9.3 A symbolic example / 141 \\
4.9.4 A numerical example / 142 \\
4.10 Equality constrained inverse eigenvalue problems /
144 \\
4.10.1 Existence and equivalence to PAPs / 144 \\
4.11 Summary / 145 \\
5: Partially described inverse eigenvalue problems /
146 \\
5.1 Overview / 146 \\
5.2 PDIEP for Toeplitz matrices / 147 \\
5.2.1 An example / 149 \\
5.2.2 General consideration / 150 \\
5.3 PDIEP for quadratic pencils / 160 \\
5.3.1 Recipe of construction / 164 \\
5.3.2 Eigenstructure of Q(A) / 167 \\
5.3.3 Numerical experiment / 173 \\
5.4 Monic quadratic inverse eigenvalue problem / 178
\\
5.4.1 Real linearly dependent eigenvectors / 179 \\
5.4.2 Complex linearly dependent eigenvectors / 181 \\
5.4.3 Numerical examples / 185 \\
5.5 Summary / 189 \\
6: Least squares inverse eigenvalue problems / 192 \\
6.1 Overview / 192 \\
6.2 An example of MIEP / 193 \\
6.3 Least Squares LiPIEP2 / 194 \\
6.3.1 Formulation / 195 \\
6.3.2 Equivalence / 197 \\
6.3.3 Lift and projection / 199 \\
6.3.4 The Newton method / 201 \\
6.3.5 Numerical experiment / 203 \\
6.4 Least squares PDIEP / 209 \\
6.5 Summary / 211 \\
7: Spectrally constrained approximation / 212 \\
7.1 Overview / 212 \\
7.1.1 Spectral constraint / 212 \\
7.1.2 Singular value constraint / 215 \\
7.1.3 Constrained optimization / 216 \\
7.2 Central framework / 217 \\
7.2.1 Projected gradient / 219 \\
7.2.2 Projected Hessian / 220 \\
7.3 Applications / 220 \\
7.3.1 Approximation with fixed spectrum / 221 \\
7.3.2 Toeplitz inverse eigenvalue problem revisit / 223
\\
7.3.3 Jacobi-type eigenvalue computation / 225 \\
7.4 Extensions / 226 \\
7.4.1 Approximation with fixed singular values / 226
\\
7.4.2 Jacobi-type singular value computation / 229 \\
7.5 Simultaneous reduction / 229 \\
7.5.1 Background review / 230 \\
7.5.2 Orthogonal similarity transformation / 234 \\
7.5.3 A nearest commuting pair problem / 238 \\
7.5.4 Orthogonal equivalence transformation / 239 \\
7.6 Closest normal matrix problem / 241 \\
7.6.1 First-order optimality condition / 242 \\
7.6.2 Second-order optimality condition / 243 \\
7.6.3 Numerical methods / 244 \\
7.7 Summary / 245 \\
8: Structured low rank approximation / 246 \\
8.1 Overview / 246 \\
8.2 Low rank Toeplitz approximation / 248 \\
8.2.1 Theoretical considerations / 248 \\
8.2.2 Tracking structured low rank matrices / 254 \\
8.2.3 Numerical methods / 257 \\
8.2.4 Summary / 263 \\
8.3 Low rank circulant approximation / 264 \\
8.3.1 Preliminaries / 264 \\
8.3.2 Basic spectral properties / 266 \\
8.3.3 Conjugate-even approximation / 267 \\
8.3.4 Algorithm / 273 \\
8.3.5 Numerical experiment / 275 \\
8.3.6 An application to image reconstruction / 278 \\
8.3.7 Summary / 279 \\
8.4 Low rank covariance approximation / 279 \\
8.4.1 Low dimensional random variable approximation /
280 \\
8.4.2 Truncated SVD / 285 \\
8.4.3 Summary / 286 \\
8.5 Euclidean distance matrix approximation / 286 \\
8.5.1 Preliminaries / 287 \\
8.5.2 Basic formulation / 291 \\
8.5.3 Analytic gradient and Hessian / 291 \\
8.5.4 Modification / 294 \\
8.5.5 Numerical examples / 295 \\
8.5.6 Summary / 300 \\
8.6 Low rank approximation on unit sphere / 300 \\
8.6.1 Linear model / 302 \\
8.6.2 Fidelity of low rank approximation / 306 \\
8.6.3 Compact form and Stiefel manifold / 313 \\
8.6.4 Numerical examples / 315 \\
8.6.5 Summary / 320 \\
8.7 Low rank nonnegative factorization / 320 \\
8.7.1 First-order optimality condition / 322 \\
8.7.2 Numerical methods / 324 \\
8.7.3 An air pollution and emission example / 332 \\
8.7.4 Summary / 337 \\
9: Group orbitally constrained approximation / 339 \\
9.1 Overview / 339 \\
9.2 A case study / 341 \\
9.2.1 Discreteness versus continuousness / 341 \\
9.2.2 Generalization / 343 \\
9.3 General Framework / 344 \\
9.3.1 Matrix group and actions / 344 \\
9.3.2 Tangent space and projection / 347 \\
9.4 Canonical form / 350 \\
9.5 Objective functions / 352 \\
9.5.1 Least squares and projected gradient / 352 \\
9.5.2 Systems for other objectives / 354 \\
9.6 Generalization to non-group structures / 356 \\
9.7 Summary / 358 \\
References / 359 \\
Index / 381",
}
@Article{Cuyt:2005:MII,
author = "Annie Cuyt and Gene Golub and Peyman Milanfar and
Brigitte Verdonk",
title = "Multidimensional integral inversion, with applications
in shape reconstruction",
journal = j-SIAM-J-SCI-COMP,
volume = "27",
number = "3",
pages = "1058--1070",
month = may,
year = "2005",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/030601703",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65R10 (41A63 44A12)",
MRnumber = "MR2199920 (2006i:65230)",
bibdate = "Tue Jun 27 09:33:32 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Golub:2005:AAB,
author = "Gene H. Golub and Chen Greif and James M. Varah",
title = "An algebraic analysis of block diagonal preconditioner
for saddle point systems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "27",
number = "3",
pages = "779--792",
month = jan,
year = "2005",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/04060679X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10",
MRnumber = "MR2208335 (2007c:65029)",
MRreviewer = "Joaqu{\'\i}m J. J{\'u}dice",
bibdate = "Tue May 18 22:32:04 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Holz:2005:SAM,
author = "U. B. Holz and G. H. Golub and K. H. Law",
title = "A Subspace Approximation Method for the Quadratic
Eigenvalue Problem",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "26",
number = "2",
pages = "498--521",
month = apr,
year = "2005",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479803423378",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15A18)",
MRnumber = "MR2124401 (2005m:65080)",
MRreviewer = "Christian Mehl",
bibdate = "Sat Apr 16 10:32:39 MDT 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/26/2;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/42337",
ZMnumber = "02135332",
abstract = "Quadratic eigenvalue problems involving large matrices
arise frequently in areas such as the vibration
analysis of structures, micro-electro-mechanical
systems (MEMS) simulation, and the solution of
quadratically constrained least squares problems. The
typical approach is to solve the quadratic eigenvalue
problem using a mathematically equivalent linearized
formulation, resulting in a doubled dimension and, in
many cases, a lack of backward stability. \par
This paper introduces an approach to solving the
quadratic eigenvalue problem directly without
linearizing it. Perturbation subspaces for block
eigenvector matrices are used to reduce the modified
problem to a sequence of problems of smaller dimension.
These perturbation subspaces are shown to be contained
in certain generalized Krylov subspaces of the
$n$-dimensional space, where $n$ is the undoubled
dimension of the matrices in the quadratic problem. The
method converges at least as fast as the corresponding
Taylor series, and the convergence can be accelerated
further by applying a block generalization of the
quadratically convergent Rayleigh quotient iteration.
Numerical examples are presented to illustrate the
applicability of the method.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classmath = "*15A18 Eigenvalues of matrices, etc. 65F15 Eigenvalues
(numerical linear algebra)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "block Rayleigh quotient iteration; generalized Krylov
subspaces; quadratic eigenvalue problems; subspace
approximation method",
}
@Article{Kim:2005:MVE,
author = "Hyunsoo Kim and Gene H. Golub and Haesun Park",
title = "Missing value estimation for {DNA} microarray gene
expression data: local least squares imputation",
journal = j-BIOINFORMATICS,
volume = "21",
number = "2",
pages = "187--198",
year = "2005",
CODEN = "BOINFP",
DOI = "https://doi.org/10.1093/bioinformatics/bth499",
ISSN = "1367-4803 (print), 1367-4811 (electronic)",
ISSN-L = "1367-4803",
bibdate = "Tue May 18 16:11:36 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "See correction \cite{Kim:2006:CMV}.",
URL = "http://bioinformatics.oxfordjournals.org/cgi/content/abstract/21/2/187;
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.3.9835&rep=rep1&type=pdf",
abstract = "Gene expression data often contain missing expression
values. Effective missing value estimation methods are
needed since many algorithms for gene expression data
analysis require a complete matrix of gene array
values. In this paper, imputation methods based on the
least squares formulation are proposed to estimate
missing values in the gene expression data, which
exploit local similarity structures in the data as well
as least squares optimization process.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Bioinformatics",
journal-URL = "http://bioinformatics.oxfordjournals.org/",
remark = "Published online 2004.08.27.",
}
@Article{Serra-Capizzano:2005:HDP,
author = "Stefano Serra-Capizzano and Daniele Bertaccini and
Gene H. Golub",
title = "How to Deduce a Proper Eigenvalue Cluster from a
Proper Singular Value Cluster in the Nonnormal Case",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "27",
number = "1",
pages = "82--86",
month = jan,
year = "2005",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/040608027",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Dec 29 16:33:52 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/27/1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/60802",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Tsaig:2005:VPN,
author = "Y. Tsaig and M. Elad and P. Milanfar and G. H. Golub",
title = "Variable projection for near-optimal filtering in low
bit-rate block coders",
journal = j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH,
volume = "15",
number = "1",
pages = "154--160",
month = "????",
year = "2005",
CODEN = "ITCTEM",
DOI = "https://doi.org/10.1109/TCSVT.2004.839980",
ISSN = "1051-8215 (print), 1558-2205 (electronic)",
ISSN-L = "1051-8215",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IEEE Transactions on Circuits and Systems for Video
Technology",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=76",
onlinedate = "JAN-2005",
}
@Article{Vandebril:2005:BSM,
author = "R. Vandebril and M. {Van Barel} and G. Golub and N.
Mastronardi",
title = "A bibliography on semiseparable matrices",
journal = j-CALCOLO,
volume = "42",
number = "3-4",
pages = "249--270",
year = "2005",
CODEN = "CALOBK",
DOI = "https://doi.org/10.1007/s10092-005-0107-z",
ISSN = "0008-0624 (print), 1126-5434 (electronic)",
ISSN-L = "0008-0624",
MRclass = "15A99",
MRnumber = "MR2191201",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Calcolo. A Quarterly on Numerical Analysis and Theory
of Computation",
journal-URL = "http://link.springer.com/journal/10092",
}
@Article{Alter:2006:SVD,
author = "Orly Alter and Gene H. Golub",
title = "Singular value decomposition of genome-scale {mRNA}
lengths distribution reveals asymmetry in {RNA} gel
electrophoresis band broadening",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "103",
number = "32",
pages = "11828--11833",
day = "8",
month = aug,
year = "2006",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.0604756103",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Tue May 18 16:14:48 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/30051625;
http://www.pnas.org/content/103/32/11828.abstract",
abstract = "We describe the singular value decomposition (SVD) of
yeast genome-scale mRNA lengths distribution data
measured by DNA microarrays. SVD uncovers in the mRNA
abundance levels data matrix of genes $ \times $
arrays, i.e., electrophoretic gel migration lengths or
mRNA lengths, mathematically unique decorrelated and
decoupled ``eigengenes.'' The eigengenes are the
eigenvectors of the arrays $ \times $ arrays
correlation matrix, with the corresponding series of
eigenvalues proportional to the series of the
``fractions of eigen abundance.'' Each fraction of
eigen abundance indicates the significance of the
corresponding eigengene relative to all others. We show
that the eigengenes fit ``asymmetric Hermite
functions,'' a generalization of the eigenfunctions of
the quantum harmonic oscillator and the integral
transform which kernel is a generalized coherent state.
The fractions of eigen abundance fit a geometric series
as do the eigenvalues of the integral transform which
kernel is a generalized coherent state. The
``asymmetric generalized coherent state'' models the
measured data, where the profiles of mRNA abundance
levels of most genes as well as the distribution of the
peaks of these profiles fit asymmetric Gaussians. We
hypothesize that the asymmetry in the distribution of
the peaks of the profiles is due to two competing
evolutionary forces. We show that the asymmetry in the
profiles of the genes might be due to a previously
unknown asymmetry in the gel electrophoresis thermal
broadening of a moving, rather than a stationary, band
of RNA molecules.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
}
@Article{Bai:2006:CPP,
author = "Zhong-Zhi Bai and Gene H. Golub and Chi-Kwong Li",
title = "Convergence properties of preconditioned {Hermitian}
and skew-{Hermitian} splitting methods for
non-{Hermitian} positive semidefinite matrices",
journal = j-MATH-COMPUT,
volume = "76",
number = "257",
pages = "287--298",
month = "????",
year = "2006",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Bai:2006:OPH,
author = "Zhong-Zhi Bai and Gene H. Golub and Chi-Kwong Li",
title = "Optimal parameter in {Hermitian} and skew-{Hermitian}
splitting method for certain two-by-two block
matrices",
journal = j-SIAM-J-SCI-COMP,
volume = "28",
number = "2",
pages = "583--603",
month = mar,
year = "2006",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/050623644",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F10 (65F50)",
MRnumber = "MR2231722 (2007a:65037)",
MRreviewer = "Thomas K. Huckle",
bibdate = "Tue Jun 27 09:24:33 MDT 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Bartels:2006:SOL,
author = "R. H. Bartels and G. H. Golub and F. F. Samavati",
title = "Some observations on local least squares",
journal = j-BIT-NUM-MATH,
volume = "46",
number = "3",
pages = "455--477",
month = sep,
year = "2006",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-006-0075-y",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Oct 31 11:37:27 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Botchev:2006:CNP,
author = "Mike A. Botchev and Gene H. Golub",
title = "A class of nonsymmetric preconditioners for saddle
point problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "27",
number = "4",
pages = "1125--1149",
year = "2006",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/040618680",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10 (65F22 65F35 65K10 65N22)",
MRnumber = "MR2205616 (2006k:65078)",
MRreviewer = "Marc Van Barel",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Chu:2006:GEP,
author = "Delin Chu and Gene H. Golub",
title = "On a generalized eigenvalue problem for nonsquare
pencils",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "28",
number = "3",
pages = "770--787",
year = "2006",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/050628258",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A18 (65F15)",
MRnumber = "MR2262980 (2007h:15012)",
MRreviewer = "Heinrich Voss",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Comon:2006:GRD,
author = "Pierre Comon and Bernard Mourrain and Lek-Heng H. Lim
and Gene H. Golub",
booktitle = "{2006 IEEE International Conference on Acoustics,
Speech and Signal Processing, 2006. ICASSP 2006
Proceedings}",
title = "Genericity and Rank Deficiency of High Order Symmetric
Tensors",
volume = "3",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "III-125--III-128",
year = "2006",
DOI = "https://doi.org/10.1109/ICASSP.2006.1660606",
bibdate = "Tue Mar 5 07:53:18 MST 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1660606",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=11024",
}
@Article{Golub:2006:ATA,
author = "G. H. Golub and C. Greif",
title = "An {Arnoldi}-type algorithm for computing page rank",
journal = j-BIT-NUM-MATH,
volume = "46",
number = "4",
pages = "759--771",
month = dec,
year = "2006",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-006-0091-y",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Oct 31 11:37:27 MDT 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Golub:2006:CME,
author = "Gene H. Golub and Li-Zhi Liao",
title = "Continuous methods for extreme and interior eigenvalue
problems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "415",
number = "1",
pages = "31--51",
day = "1",
month = may,
year = "2006",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2005.01.009",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Mar 29 10:29:33 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
remark = "Special issue on large scale linear and nonlinear
eigenvalue problems.",
}
@Article{Kim:2006:CMV,
author = "Hyunsoo Kim and Gene H. Golub and Haesun Park",
title = "Correction: Missing value estimation for {DNA}
microarray gene expression data: local least squares
imputation",
journal = j-BIOINFORMATICS,
volume = "22",
number = "11",
pages = "1410--1411",
day = "1",
month = jun,
year = "2006",
CODEN = "BOINFP",
DOI = "https://doi.org/10.1093/bioinformatics/btk053",
ISSN = "1367-4803 (print), 1367-4811 (electronic)",
ISSN-L = "1367-4803",
bibdate = "Thu Aug 25 10:08:04 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "See \cite{Kim:2005:MVE}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Bioinformatics",
journal-URL = "http://bioinformatics.oxfordjournals.org/",
}
@Article{Vandebril:2006:SNS,
author = "Raf Vandebril and Gene Golub and Marc {Van Barel}",
title = "A small note on the scaling of symmetric positive
definite semiseparable matrices",
journal = j-NUMER-ALGORITHMS,
volume = "41",
number = "3",
pages = "319--326",
year = "2006",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-006-9014-x",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F35 (15A12)",
MRnumber = "MR2222252 (2006m:65086)",
MRreviewer = "Heike Fa{\ss}bender",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Bai:2007:AHS,
author = "Zhong-Zhi Bai and Gene H. Golub",
title = "Accelerated {Hermitian} and skew-{Hermitian} splitting
iteration methods for saddle-point problems",
journal = j-IMA-J-NUMER-ANAL,
volume = "27",
number = "1",
pages = "1--23",
year = "2007",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drl017",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F10",
MRnumber = "MR2289269 (2007k:65053)",
MRreviewer = "Timothy Nigel Phillips",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Bai:2007:CPP,
author = "Zhong-Zhi Bai and Gene H. Golub and Chi-Kwong Li",
title = "Convergence properties of preconditioned {Hermitian}
and skew-{Hermitian} splitting methods for
non-{Hermitian} positive semidefinite matrices",
journal = j-MATH-COMPUT,
volume = "76",
number = "257",
pages = "287--298",
year = "2007",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.1090/S0025-5718-06-01892-8",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10",
MRnumber = "MR2261022",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Bai:2007:SOA,
author = "Zhong-Zhi Bai and Gene H. Golub and Michael K. Ng",
title = "On successive-overrelaxation acceleration of the
{Hermitian} and skew-{Hermitian} splitting iterations",
journal = j-NUM-LIN-ALG-APPL,
volume = "14",
number = "4",
pages = "319--335",
year = "2007",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.517",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "65F10",
MRnumber = "MR2310394",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
}
@Article{Beckermann:2007:NCG,
author = "B. Beckermann and G. H. Golub and G. Labahn",
title = "On the numerical condition of a generalized {Hankel}
eigenvalue problem",
journal = j-NUM-MATH,
volume = "106",
number = "1",
pages = "41--68",
month = mar,
year = "2007",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-006-0054-x",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F15 (30E10)",
MRnumber = "MR2286006",
bibdate = "Tue Jul 8 10:28:23 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Bertaccini:2007:SAP,
author = "Daniele Bertaccini and Gene H. Golub and Stefano
Serra-Capizzano",
title = "Spectral analysis of a preconditioned iterative method
for the convection-diffusion equation",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "1",
pages = "260--278",
year = "2007",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/050627381",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10 (15A18 65N22 76M25)",
MRnumber = "MR2288025 (2008f:65055)",
MRreviewer = "Timothy Nigel Phillips",
bibdate = "Tue May 18 22:32:16 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InBook{Gleich:2007:TRP,
author = "David Gleich and Peter Glynn and Gene Golub and Chen
Greif",
title = "Three results on the {PageRank} vector:
eigenstructure, sensitivity, and the derivative",
publisher = "International Begegnungs- und Forschungszentrum
f{\"u}r Informatik",
address = "Wadern, Germany",
pages = "????",
year = "2007",
LCCN = "????",
bibdate = "Fri Jun 3 10:03:23 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Dagstuhl seminar proceedings 07071",
URL = "http://drops.dagstuhl.de/opus/volltexte/2007/1061/pdf/07071.GleichDavid.Paper.1061",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:2007:HAC,
author = "Gene H. Golub and Daniel Ruiz and Ahmed Touhami",
title = "A hybrid approach combining {Chebyshev} filter and
conjugate gradient for solving linear systems with
multiple right-hand sides",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "3",
pages = "774--795",
year = "2007",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/060649458",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10",
MRnumber = "MR2338462",
bibdate = "Mon Mar 10 17:02:18 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Book{Golub:2007:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
volume = "43",
publisher = "Hindustan Book Agency",
address = "New Delhi, India",
edition = "Third",
pages = "xxvii + 3 + 694",
year = "2007",
ISBN = "81-85931-72-0",
ISBN-13 = "978-81-85931-72-2",
MRclass = "65Fxx (Numerical linear algebra); 65-01 (Textbooks
(numerical analysis)); 65Y05 (Parallel computation
(numerical methods)); 15A18 (Eigenvalues of matrices,
etc.); 15A60 (Appl. of functional analysis to matrix
theory)",
bibdate = "Wed Oct 31 12:42:00 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Texts and Readings in Mathematics",
ZMnumber = "1118.65316",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Golub:2007:WOR,
author = "Gene H. Golub",
title = "Welcome and opening remarks",
crossref = "Du:2007:SSA",
pages = "??--??",
year = "2007",
bibdate = "Sat Apr 07 09:08:50 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Lee:2007:TSA,
author = "Chris P. Lee and Gene H. Golub and Stefanos A.
Zenios",
title = "A two-stage algorithm for computing {PageRank} and
multistage generalizations",
journal = j-INTERNET-MATH,
volume = "4",
number = "4",
pages = "299--327",
year = "2007",
CODEN = "????",
ISSN = "1542-7951 (print), 1944-9488 (electronic)",
ISSN-L = "1542-7951",
MRclass = "68M11",
MRnumber = "MR2522947",
bibdate = "Wed May 5 19:28:06 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://projecteuclid.org/getRecord?id=euclid.im/1243430809",
abstract = "The PageRank model pioneered by Google is the most
common approach for generating web search results. We
present a two-stage algorithm for computing the
PageRank vector where the algorithm exploits the
lumpability of the underlying Markov chain. We make
three contributions. First, the algorithm speeds up the
PageRank calculation significantly. With web graphs
having millions of webpages, the speed-up is typically
in the two- to three-fold range. The algorithm can also
embed other acceleration methods such as quadratic
extrapolation, the Gauss-Seidel method, or the
Biconjugate gradient stable method for an even greater
speed-up; cumulative speed-up is as high as 7 to 14
times. The second contribution relates to the handling
of dangling nodes. Conventionally, dangling nodes are
included only towards the end of the computation. While
this approach works reasonably well, it can fail in
extreme cases involving aggressive personalization. We
prove that our algorithm is the generally correct way
of handling dangling nodes using probabilistic
arguments. We also discuss variants of our algorithm,
including a multistage extension for calculating a
generalized version of the PageRank model where
different personalization vectors are used for webpages
of different classes. The ability to form class
associations may be useful for building more refined
models of web traffic.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Internet Mathematics",
journal-URL = "http://projecteuclid.org/info/euclid.im",
}
@Article{Mastronardi:2007:NLA,
author = "Nicola Mastronardi and Gene H. Golub and Shivkumar
Chandrasekaran and Marc Moonen and Paul {Van Dooren}
and Sabine {Van Huffel}",
title = "Numerical linear algebra in signal processing
applications",
journal = j-EURASIP-J-ADV-SIGNAL-PROCESS,
pages = "Art. ID 26914, 3",
year = "2007",
DOI = "https://doi.org/10.1155/2007/26914",
ISSN = "1687-6172 (print), 1687-6180 (electronic)",
ISSN-L = "1687-6172",
MRclass = "94A12 (15A24)",
MRnumber = "MR2366747",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "EURASIP Journal on Advances in Signal Processing",
journal-URL = "http://asp.eurasipjournals.springeropen.com/",
}
@Article{Omberg:2007:THO,
author = "Larsson Omberg and Gene H. Golub and Orly Alter",
title = "A tensor higher-order singular value decomposition for
integrative analysis of {DNA} microarray data from
different studies",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "104",
number = "47",
pages = "18371--18376",
day = "20",
month = nov,
year = "2007",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.0709146104",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Tue May 18 16:04:13 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/25450431;
http://www.pnas.org/content/104/47/18371.full",
abstract = "We describe the use of a higher-order singular value
decomposition (HOSVD) in transforming a data tensor of
genes $ \times $ ``x-settings,'' that is, different
settings of the experimental variable $ x \times $
``y-settings,'' which tabulates DNA microarray data
from different studies, to a ``core tensor'' of
``eigenarrays'' $ \times $ ``x-eigengenes'' $ \times $
``y-eigengenes.'' Reformulating this multilinear HOSVD
such that it decomposes the data tensor into a linear
superposition of all outer products of an eigenarray,
an x- and a y-eigengene, that is, rank-1
``subtensors,'' we define the significance of each
subtensor in terms of the fraction of the overall
information in the data tensor that it captures. We
illustrate this HOSVD with an integration of
genome-scale mRNA expression data from three yeast cell
cycle time courses, two of which are under exposure to
either hydrogen peroxide or menadione. We find that
significant subtensors represent independent biological
programs or experimental phenomena. The picture that
emerges suggests that the conserved genes YKU70, MRE11,
AIF1, and ZWF1, and the processes of
retrotransposition, apoptosis, and the oxidative
pentose phosphate pathway that these genes are involved
in, may play significant, yet previously unrecognized,
roles in the differential effects of hydrogen peroxide
and menadione on cell cycle progression. A genome-scale
correlation between DNA replication initiation and RNA
transcription, which is equivalent to a recently
discovered correlation and might be due to a previously
unknown mechanism of regulation, is independently
uncovered.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
}
@Article{Bai:2008:IHS,
author = "Zhong-Zhi Bai and Gene H. Golub and Michael K. Ng",
title = "On inexact {Hermitian} and skew-{Hermitian} splitting
methods for non-{Hermitian} positive definite linear
systems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "428",
number = "2--3",
pages = "413--440",
year = "2008",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2007.02.018",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F10 (65F50)",
MRnumber = "MR2374557 (2008m:65084)",
MRreviewer = "Valeria Simoncini",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Chang:2008:TBP,
author = "X.-W. Chang and G. H. Golub and C. C. Paige",
title = "Towards a Backward Perturbation Analysis for Data
Least Squares Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "4",
pages = "1281--1301",
month = "????",
year = "2008",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/060668626",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Comon:2008:STS,
author = "Pierre Comon and Gene Golub and Lek-Heng Lim and
Bernard Mourrain",
title = "Symmetric tensors and symmetric tensor rank",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "3",
pages = "1254--1279",
year = "2008",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/060661569",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A69 (15A03 15A72)",
MRnumber = "MR2447451 (2009i:15039)",
MRreviewer = "Gustavo Adolfo Mu{\~n}oz-Fern{\'a}ndez",
bibdate = "Tue May 18 22:32:29 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Dongarra:2008:NNB,
author = "Jack Dongarra and Gene H. Golub and Eric Grosse and
Cleve Moler and Keith Moore",
title = "{Netlib} and {NA-Net}: Building a Scientific Computing
Community",
journal = j-IEEE-ANN-HIST-COMPUT,
volume = "30",
number = "2",
pages = "30--41",
month = apr # "\slash " # jun,
year = "2008",
CODEN = "IAHCEX",
DOI = "https://doi.org/10.1109/MAHC.2008.29",
ISSN = "1058-6180 (print), 1934-1547 (electronic)",
ISSN-L = "1058-6180",
MRclass = "Database Expansion Item",
MRnumber = "MR2432392",
bibdate = "Thu Jul 3 10:46:12 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4544554",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IEEE Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
remark = "Gene H. Golub, (Deceased 16 November 2007).",
}
@Article{Gao:2008:CMS,
author = "Xing-Bao Gao and Gene H. Golub and Li-Zhi Liao",
title = "Continuous methods for symmetric generalized
eigenvalue problems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "428",
number = "2--3",
pages = "676--696",
year = "2008",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2007.08.034",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (65K10 65L15 65M12)",
MRnumber = "MR2374572 (2008k:65073)",
MRreviewer = "Raffaella Pavani",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Golub:2008:ASA,
author = "Gene H. Golub and Martin Stoll and Andy Wathen",
title = "Approximation of the scattering amplitude and linear
systems",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "31",
pages = "178--203",
year = "2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
MRclass = "65F10 (65F08)",
MRnumber = "MR2569600",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://etna.mcs.kent.edu/vol.31.2008/pp178-203.dir/pp178-203.pdf",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Wu:2008:STD,
author = "Xiaonan Wu and Gene H. Golub and Jos{\'e} A. Cuminato
and Jin Yun Yuan",
title = "Symmetric-triangular decomposition and its
applications. {II}. {Preconditioners} for indefinite
systems",
journal = j-BIT,
volume = "48",
number = "1",
pages = "139--162",
month = mar,
year = "2008",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-008-0160-5",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F10 (15A06 15A12 15A23 65F35)",
MRnumber = "MR2386119 (2009b:65090)",
MRreviewer = "Ilse C. F. Ipsen",
bibdate = "Wed Jul 9 09:02:44 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=48&issue=1&spage=139",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "indefinite system; nonsymmetric system; symmetric and
positive definite system; symmetric and triangular (ST)
decomposition; symmetric-positive-definite and
triangular decomposition; tridiagonal system",
}
@Article{Chang:2009:SEC,
author = "Xiao-Wen Chang and Gene H. Golub",
title = "Solving Ellipsoid-Constrained Integer Least Squares
Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "1071--1089",
month = "????",
year = "2009",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/060660680",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Chang:2009:TBP,
author = "X.-W. Chang and G. H. Golub and C. C. Paige",
title = "Towards a Backward Perturbation Analysis For Data
Least Squares Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "4",
pages = "1281--1301",
month = "????",
year = "2009",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/060668626",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F35 (15A06 65F20)",
MRnumber = "MR2448669 (2009g:65059)",
MRreviewer = "Ilse C. F. Ipsen",
bibdate = "Tue May 18 22:32:31 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Golub:2009:AYL,
author = "Gene Golub and Frank Uhlig",
title = "The {$ Q R $} algorithm: 50 years later: its genesis
by {John Francis} and {Vera Kublanovskaya} and
subsequent developments",
journal = j-IMA-J-NUMER-ANAL,
volume = "29",
number = "3",
pages = "467--485",
year = "2009",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drp012",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F15 (01A70 65-03)",
MRnumber = "MR2520155 (2010d:65089)",
MRreviewer = "David Scott Watkins",
bibdate = "Tue Mar 16 21:53:41 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@Article{Vandebril:2009:QSA,
author = "Raf Vandebril and Gene Golub and Marc {Van Barel}",
title = "A quasi-separable approach to solve the symmetric
definite tridiagonal generalized eigenvalue problem",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "1",
pages = "154--174",
year = "2009",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/070679491",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15B57)",
MRnumber = "MR2487055 (2010b:65087)",
MRreviewer = "Fabio Di Benedetto",
bibdate = "Tue May 18 22:32:33 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Chang:2010:SEC,
author = "Xiao-Wen Chang and Gene H. Golub",
title = "Solving Ellipsoid-Constrained Integer Least Squares
Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "3",
pages = "1071--1089",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/060660680",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65Kxx (65F20 90C10)",
MRnumber = "MR2538667",
bibdate = "Tue May 18 22:32:37 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Book{Golub:2010:MMQ,
author = "Gene H. Golub and G{\'e}rard Meurant",
title = "Matrices, Moments and Quadrature with Applications",
publisher = pub-PRINCETON,
address = pub-PRINCETON:adr,
pages = "xii + 363",
year = "2010",
ISBN = "0-691-14341-2",
ISBN-13 = "978-0-691-14341-5",
MRclass = "65-02 (65D30)",
MRnumber = "MR2582949",
bibdate = "Mon May 17 14:08:36 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Princeton Series in Applied Mathematics",
ZMnumber = "pre05661633; 1217.65056",
abstract = "This computationally oriented book describes and
explains the mathematical relationships among matrices,
moments, orthogonal polynomials, quadrature rules, and
the Lanczos and conjugate gradient algorithms. The book
bridges different mathematical areas to obtain
algorithms to estimate bilinear forms involving two
vectors and a function of the matrix. The first part of
the book provides the necessary mathematical background
and explains the theory. The second part describes the
applications and gives numerical examples of the
algorithms and techniques developed in the first part.
Applications addressed in the book include computing
elements of functions of matrices; obtaining estimates
of the error norm in iterative methods for solving
linear systems and computing parameters in least
squares and total least squares; and solving ill-posed
problems using Tikhonov regularization. This book will
interest researchers in numerical linear algebra and
matrix computations, as well as scientists and
engineers working on problems involving computation of
bilinear forms.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
shorttableofcontents = "Preface / xi \\
Part 1. Theory / 1 \\
1: Introduction / 3 \\
2: Orthogonal Polynomials / 8 \\
3: Properties of Tridiagonal Matrices / 24 \\
4: The Lanczos and Conjugate Gradient Algorithms / 39
\\
5: Computation of the Jacobi Matrices / 55 \\
6: Gauss Quadrature / 84 \\
7: Bounds for Bilinear Forms $u^T f(A) v$ / 112 \\
8: Extensions to Nonsymmetric Matrices / 117 \\
9: Solving Secular Equations / 122 \\
10: Examples of Gauss Quadrature Rules / 139 \\
11: Bounds and Estimates for Elements of Functions of
Matrices / 162 \\
12: Estimates of Norms of Errors in the Conjugate
Gradient Algorithm / 200 \\
13: Least Squares Problems / 227 \\
14: Total Least Squares / 256 \\
15: Discrete Ill-Posed Problems / 280 \\
Bibliography / 335 \\
Index / 361",
tableofcontents = "Preface / xi \\
Part 1. Theory / 1 \\
1: Introduction / 3 \\
2: Orthogonal Polynomials / 8 \\
2.1 Definition of Orthogonal Polynomials / 8 \\
2.2 Three-Term Recurrences / 10 \\
2.3 Properties of Zeros / 14 \\
2.4 Historical Remarks / 15 \\
2.5 Examples of Orthogonal Polynomials / 15 \\
2.6 Variable-Signed Weight Functions / 20 \\
2.7 Matrix Orthogonal Polynomials / 21 \\
3: Properties of Tridiagonal Matrices / 24 \\
3.1 Similarity / 24 \\
3.2 Cholesky Factorizations of a Tridiagonal Matrix /
25 \\
3.3 Eigenvalues and Eigenvectors / 27 \\
3.4 Elements of the Inverse / 29 \\
3.5 The $Q D$ Algorithm / 32 \\
4: The Lanczos and Conjugate Gradient Algorithms / 39
\\
4.1 The Lanczos Algorithm / 39 \\
4.2 The Nonsymmetric Lanczos Algorithm / 43 \\
4.3 The Golub--Kahan Bidiagonalization Algorithms / 45
\\
4.4 The Block Lanczos Algorithm / 47 \\
4.5 The Conjugate Gradient Algorithm / 49 \\
5: Computation of the Jacobi Matrices / 55 \\
5.1 The Stieltjes Procedure / 55 \\
5.2 Computing the Coefficients from the Moments / 56
\\
5.3 The Modified Chebyshev Algorithm / 58 \\
5.4 The Modified Chebyshev Algorithm for Indefinite
Weight Functions / 61 \\
5.5 Relations between the Lanczos and Chebyshev
Semi-Iterative Algorithms / 62 \\
5.6 Inverse Eigenvalue Problems / 66 \\
5.7 Modifications of Weight Functions / 72 \\
6: Gauss Quadrature / 84 \\
6.1 Quadrature Rules / 84 \\
6.2 The Gauss Quadrature Rules / 86 \\
6.3 The Anti-Gauss Quadrature Rule / 92 \\
6.4 The Gauss-Kronrod Quadrature Rule / 95 \\
6.5 The Nonsymmetric Gauss Quadrature Rules / 99 \\
6.6 The Block Gauss Quadrature Rules / 102 \\
7: Bounds for Bilinear Forms $u^T f(A) v$ / 112 \\
7.1 Introduction / 112 \\
7.2 The Case $u = v$ / 113 \\
7.3 The Case $u \neq v$ / 114 \\
7.4 The Block Case / 115 \\
7.5 Other Algorithms for $u \neq v$ / 115 \\
8: Extensions to Nonsymmetric Matrices / 117 \\
8.1 Rules Based on the Nonsymmetric Lanczos Algorithm /
118 \\
8.2 Rules Based on the Arnoldi Algorithm / 119 \\
9: Solving Secular Equations / 122 \\
9.1 Examples of Secular Equations / 122 \\
9.2 Secular Equation Solvers / 129 \\
9.3 Numerical Experiments / 134 \\
Part 2. Applications / 137 \\
10: Examples of Gauss Quadrature Rules / 139 \\
10.1 The Golub and Welsch Approach / 139 \\
10.2 Comparisons with Tables / 140 \\
10.3 Using the Full $Q R$ Algorithm / 141 \\
10.4 Another Implementation of $Q R$ / 143 \\
10.5 Using the $Q L$ Algorithm / 144 \\
10.6 Gauss--Radau Quadrature Rules / 144 \\
10.7 Gauss--Lobatto Quadrature Rules / 146 \\
10.8 Anti-Gauss Quadrature Rule / 148 \\
10.9 Gauss--Kronrod Quadrature Rule / 148 \\
10.10 Computation of Integrals / 149 \\
10.11 Modification Algorithms / 155 \\
10.12 Inverse Eigenvalue Problems / 156 \\
11: Bounds and Estimates for Elements of Functions of
Matrices / 162 \\
11.1 Introduction / 162 \\
11.2 Analytic Bounds for the Elements of the Inverse /
163 \\
11.3 Analytic Bounds for Elements of Other Functions /
166 \\
11.4 Computing Bounds for Elements of $f(A)$ / 167 \\
11.5 Solving $A x = c$ and Looking at $d^T x$ / 167 \\
11.6 Estimates of $\tr(A^{-1})$ and $\det(A)$ / 168 \\
11.7 Krylov Subspace Spectral Methods / 172 \\
11.8 Numerical Experiments / 173 \\
12: Estimates of Norms of Errors in the Conjugate
Gradient Algorithm / 200 \\
12.1 Estimates of Norms of Errors in Solving Linear
Systems / 200 \\
12.2 Formulas for the $A$-Norm of the Error / 202 \\
12.3 Estimates of the $A$-Norm of the Error / 203 \\
12.4 Other Approaches / 209 \\
12.5 Formulas for the $\ell_2$ Norm of the Error / 210
\\
12.6 Estimates of the $\ell_2$ Norm of the Error / 211
\\
12.7 Relation to Finite Element Problems / 212 \\
12.8 Numerical Experiments / 214 \\
13: Least Squares Problems / 227 \\
13.1 Introduction to Least Squares / 227 \\
13.2 Least Squares Data Fitting / 230 \\
13.3 Numerical Experiments / 237 \\
13.4 Numerical Experiments for the Backward Error / 253
\\
14: Total Least Squares / 256 \\
14.1 Introduction to Total Least Squares / 256 \\
14.2 Scaled Total Least Squares / 259 \\
14.3 Total Least Squares Secular Equation Solvers / 261
\\
15: Discrete Ill-Posed Problems / 280 \\
15.1 Introduction to Ill-Posed Problems / 280 \\
15.2 Iterative Methods for Ill-Posed Problems / 295 \\
15.3 Test Problems / 298 \\
15.4 Study of the GCV Function / 300 \\
15.5 Optimization of Finding the GCV Minimum / 305 \\
15.6 Study of the $L$-Curve / 313 \\
15.7 Comparison of Methods for Computing the
Regularization Parameter / 325 \\
Bibliography / 335 \\
Index / 361",
}
@Book{Golub:2013:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
edition = "Fourth",
pages = "xxi + 756",
year = "2013",
ISBN = "1-4214-0794-9 (hardcover), 1-4214-0859-7 (e-book)",
ISBN-13 = "978-1-4214-0794-4 (hardcover), 978-1-4214-0859-0
(e-book)",
LCCN = "QA188 .G65 2013",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Johns Hopkins Studies in the Mathematical Sciences",
URL = "https://jhupbooks.press.jhu.edu/title/matrix-computations",
abstract = "This revised edition provides the mathematical
background and algorithmic skills required for the
production of numerical software. It includes rewritten
and clarified proofs and derivations, as well as new
topics such as Arnoldi iteration, and domain
decomposition methods.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
shorttableofcontents = "1: Matrix multiplication \\
2: Matrix analysis \\
3: General linear systems \\
4: Special linear systems \\
5: Orthogonalization and least squares \\
6: Modified least squares problems and methods \\
7: Unsymmetric eigenvalue problems \\
8: Symmetric eigenvalue problems \\
9: Functions of matrices \\
10: Large sparse eigenvalue problems \\
11: Large sparse linear system problems \\
12: Special topics",
subject = "Matrices; Data processing; Data processing.; Matrix.;
Matrizenrechnung.; Matrizentheorie.; Numerische
Mathematik.",
tableofcontents = "Preface \\
Global References \\
Other Books \\
Useful URLs \\
Common Notation \\
1: Matrix Multiplication \\
1.1 Basic Algorithms and Notation \\
1.2 Structure and Efficiency \\
1.3 Block Matrices and Algorithms \\
1.4 Fast Matrix--Vector Products \\
1.5 Vectorization and Locality \\
1.6 Parallel Matrix Multiplication \\
2: Matrix Analysis \\
2.1 Basic Ideas from Linear Algebra \\
2.2 Vector Norms \\
2.3 Matrix Norms \\
2.4 The Singular Value Decomposition \\
2.5 Subspace Metrics \\
2.6 The Sensitivity of Square Systems \\
2.7 Finite Precision Matrix Computations \\
3: General Linear Systems \\
3.1 Triangular Systems \\
3.2 The $L U$ Factorization \\
3.3 Roundoff Error in Gaussian Elimination \\
3.4 Pivoting \\
3.5 Improving and Estimating Accuracy \\
3.6 Parallel $L U$ \\
4: Special Linear Systems \\
4.1 Diagonal Dominance and Symmetry \\
4.2 Positive Definite Systems \\
4.3 Banded Systems \\
4.4 Symmetric Indefinite Systems \\
4.5 Block Tridiagonal Systems \\
4.6 Vandermonde Systems \\
4.7 Classical Methods for Toeplitz Systems \\
4.8 Circulant and Discrete Poisson Systems \\
5: Orthogonalization and Least Squares \\
5.1 Householder and Givens Transformations \\
5.2 The $Q R$ Factorization \\
5.3 The Full-Rank Least Squares Problem \\
5.4 Other Orthogonal Factorizations \\
5.5 The Rank-Deficient Least Squares Problem \\
5.6 Square and Underdetermined Systems \\
6: Modified Least Squares Problems and Methods \\
6.1 Weighting and Regularization \\
6.2 Constrained Least Squares \\
6.3 Total Least Squares \\
6.4 Subspace Computations with the SVD \\
6.5 Updating Matrix Factorizations \\
7: Unsymmetric Eigenvalue Problems \\
7.1 Properties and Decompositions \\
7.2 Perturbation Theory \\
7.3 Power Iterations \\
7.4 The Hessenberg and Real Schur Forms \\
7.5 The Practical $Q R$ Algorithm \\
7.6 Invariant Subspace Computations \\
7.7 The Generalized Eigenvalue Problem \\
7.8 Hamiltonian and Product Eigenvalue Problems \\
7.9 Pseudospectra \\
8: Symmetric Eigenvalue Problems \\
8.1 Properties and Decompositions \\
8.2 Power Iterations \\
8.3 The Symmetric $Q R$ Algorithm \\
8.4 More Methods for Tridiagonal Problems \\
8.5 Jacobi Methods \\
8.6 Computing the SVD \\
8.7 Generalized Eigenvalue Problems with Symmetry \\
9: Functions of Matrices \\
9.1 Eigenvalue Methods \\
9.2 Approximation Methods \\
9.3 The Matrix Exponential \\
9.4 The Sign, Square Root, and Log of a Matrix \\
10: Large Sparse Eigenvalue Problems \\
10.1 The Symmetric Lanczos Process \\
10.2 Lanczos, Quadrature, and Approximation \\
10.3 Practical Lanczos Procedures \\
10.4 Large Sparse SVD Frameworks \\
10.5 Krylov Methods for Unsymmetric Problems \\
10.6 Jacobi--Davidson and Related Methods \\
11: Large Sparse Linear System Problems \\
11.1 Direct Methods \\
11.2 The Classical Iterations \\
11.3 The Conjugate Gradient Method \\
11.4 Other Krylov Methods \\
11.5 Preconditioning \\
11.6 The Multigrid Framework \\
12: Special Topics \\
12.1 Linear Systems with Displacement Structure \\
12.2 Structured-Rank Problems \\
12.3 Kronecker Product Computations \\
12.4 Tensor Unfoldings and Contractions \\
12.5 Tensor Decompositions and Iterations \\
Index",
}
@Book{Golub:1980:NA,
editor = "Gene H. Golub and Joseph Oliger",
booktitle = "Numerical Analysis",
title = "Numerical Analysis",
volume = "22",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "viii + 135",
year = "1980",
DOI = "https://doi.org/10.1090/psapm/022",
ISBN = "0-8218-0122-8, 0-8218-9237-1 (e-book)",
ISBN-13 = "978-0-8218-0122-2, 978-0-8218-9237-4 (e-book)",
LCCN = "QA1 .S93 v.22",
MRclass = "65-06",
MRnumber = "80c:65007",
bibdate = "Sun Jan 14 09:43:24 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib",
series = "Proceedings of symposia in applied mathematics",
acknowledgement = ack-nhfb,
annote = "Reprinted with corrections, 1980. Lecture notes
prepared for the American Mathematical Society Short
Course on Numerical Analysis, held in Atlanta, Georgia,
January 3--4, 1978.",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "Numerical analysis.",
tableofcontents = "Preface / vii \\
Three research problems in numerical linear algebra /
Cleve B. Moler / 1 \\
A brief introduction to quasi-Newton methods / J. E.
Dennis / 19 \\
The approximation of functions and linear functionals:
Best vs. good approximation / Carl de Boor / 53 \\
Numerical methods for the solution of ordinary
differential equations / James M. Varah / 71 \\
Methods for time dependent partial differential
equations / Joseph E. Oliger / 87 \\
Variational methods for elliptic boundary value
problems / George J. Fix / 109",
}
@Article{Schryer:1969:CA,
author = "N. L. Schryer",
title = "Certification of {Algorithm 328 [F4]}: {``Chebyshev
Solution to an Overdetermined Linear System (Richard H.
Bartels and Gene H. Golub, Comm. ACM 11(6) 428
(1968))''}",
journal = j-CACM,
volume = "12",
number = "6",
pages = "326--326",
month = jun,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Jul 05 16:49:36 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
note = "See \cite{Bartels:1968:ACS}.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Spjotvoll:1972:NTF,
author = "Emil Spjotvoll",
title = "A Note on a Theorem of {Forsythe} and {Golub}",
journal = j-SIAM-J-APPL-MATH,
volume = "23",
number = "3",
pages = "307--311",
month = nov,
year = "1972",
CODEN = "SMJMAP",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Goldfarb:1977:BGD,
author = "D. Goldfarb",
title = "{Bartels--Golub} Decomposition for Linear-Programming
Bases",
journal = j-MATH-PROG,
volume = "13",
number = "3",
pages = "272--279",
month = "????",
year = "1977",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01584343",
ISSN = "0025-5610",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Reid:1982:SEV,
author = "J. K. Reid",
title = "A Sparsity-Exploiting Variant of the {Bartels--Golub}
Decomposition for Linear-Programming Bases",
journal = j-MATH-PROG,
volume = "24",
number = "1",
pages = "55--69",
month = "????",
year = "1982",
CODEN = "MHPGA4",
DOI = "https://doi.org/10.1007/BF01585094",
ISSN = "0025-5610",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Programming",
journal-URL = "http://link.springer.com/journal/10107",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Manneback:1985:MAG,
author = "P. E. Manneback and Ch. Murigande and Ph. L. Toint",
title = "A Modification of an Algorithm by {Golub} and
{Plemmons} for Large Linear Least-Squares in the
Context of {Doppler} Positioning",
journal = j-IMA-J-NUMER-ANAL,
volume = "5",
number = "2",
pages = "221--233",
month = "????",
year = "1985",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/5.2.221",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "86A30 (65F20)",
MRnumber = "86g:86004",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Moharir:1985:ESG,
author = "P. S. Moharir",
title = "Extending the Scope of {Golub}'s Method Beyond Complex
Multiplication",
journal = j-IEEE-TRANS-COMPUT,
volume = "C-34",
number = "5",
pages = "484--487",
month = may,
year = "1985",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.1985.1676590",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Sun Jul 10 08:32:33 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676590",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Powell:1987:EGB,
author = "M. J. D. Powell",
title = "On Error Growth in the {Bartels--Golub} and
{Fletcher--Matthews} Algorithms for Updating Matrix
Factorizations",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88--89",
number = "??",
pages = "597--621",
month = "????",
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90127-3",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F05 (65G05 65K05)",
MRnumber = "89c:65039",
MRreviewer = "Alfonso Laratta",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Sheng:1987:PGW,
author = "Rong Qin Sheng",
title = "Properties of the {Golub--Wilkinson} Algorithm",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "92",
number = "??",
pages = "75--80",
month = jul,
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90251-5",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15",
MRnumber = "88f:65063",
MRreviewer = "V. L. Makarov",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379587902515",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Stewart:1987:RBC,
author = "G. W. Stewart",
title = "Review of {{\booktitle{Matrix Computations}}, by Gene
H. Golub and Charles F. Van Loan}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "95",
number = "??",
pages = "211--215",
month = oct,
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90036-X",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Nov 30 13:50:37 MST 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/linala1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002437958790036X",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Demmel:1990:BRM,
author = "James W. Demmel",
title = "Book Review: {{\booktitle{Matrix Computations; Second
Edition}} (Gene Golub and Charles F. Van Loan)}",
journal = j-SIAM-REVIEW,
volume = "32",
number = "4",
pages = "690--691",
month = dec,
year = "1990",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1032141",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Tue Mar 06 11:46:00 2018",
bibsource = "http://epubs.siam.org/toc/siread/32/4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "December 1990",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Higham:1990:RGH,
author = "Nicholas J. Higham",
title = "Review of {``G. H. Golub and C. F. Van Loan, Matrix
Computations, Second Edition, Johns Hopkins University
Press, Baltimore, Maryland, 1989''}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "141",
pages = "289--292",
year = "1990",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-njh,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Kockler:1991:PIG,
author = "N. Kockler and M. Simons",
title = "Parallel Implementation of the {Golub--Reinsch} Method
on an Asynchronous Processor Array",
journal = j-Z-ANGE-MATH-MECH,
volume = "71",
number = "6",
pages = "T803--T806",
month = "????",
year = "1991",
CODEN = "ZAMMAX",
ISSN = "0044-2267 (print), 1521-4001 (electronic)",
ISSN-L = "0044-2267",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und
Mechanik}",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Higham:1992:IWP,
author = "Nicholas J. Higham",
title = "{IMA} Workshop Participants {F}{\^e}te {Golub} on 60th
Birthday",
journal = j-SIAM-NEWS,
volume = "25",
pages = "3--??",
month = may,
year = "1992",
ISSN = "0036-1437",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
acknowledgement = ack-njh,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Moler:1992:DGG,
author = "C. Moler",
title = "Dedication to {Gene H. Golub} on the Occasion of His
15th Birthday",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "U1--U2",
month = "????",
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Moler:1992:DGH,
author = "Cleve Moler",
title = "Dedication to {Gene H. Golub} on the occasion of his
15th birthday",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "vii--viii",
month = jan,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "01A70",
MRnumber = "MR1146646",
bibdate = "Tue Jan 28 14:03:35 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
remark = "Gene Golub's birthday is February 29, that is, every
fourth year, whence the curious title.",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
xxnote = "Gene Golub's birthday is February 29, that is, every
fourth year, whence the curious title.",
}
@Article{Young:1993:SCD,
author = "David M. Young",
title = "Scientific computing and differential equations --- An
introduction to numerical methods by {Gene H. Golub}
and {James M. Ortega}",
journal = j-BAMS-NS,
volume = "28",
number = "2",
pages = "397--397",
month = apr,
year = "1993",
ISSN = "0273-0979 (print), 1088-9485 (electronic)",
bibdate = "Thu Jan 18 19:35:06 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib",
acknowledgement = ack-nhfb,
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Gautschi:2002:IBC,
author = "Walter Gautschi",
title = "The interplay between classical analysis and
(numerical) linear algebra --- a tribute to {Gene H.
Golub}",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "13",
number = "??",
pages = "119--147",
month = "????",
year = "2002",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/etna.bib",
URL = "http://etna.mcs.kent.edu/vol.13.2002/pp119-147.dir/pp119-147.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Haigh:2005:IGG,
author = "Thomas Haigh",
title = "An interview with {Gene Golub}",
institution = "Computer History Museum",
address = "Mountain View, CA, USA",
pages = "75",
year = "2005",
bibdate = "Tue Jan 08 12:18:07 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Transcript recorded 22--23 October 2005.",
URL = "https://archive.computerhistory.org/resources/access/text/2013/12/102746795-05-01-acc.pdf",
acknowledgement = ack-do # "\slash " # ack-nhfb,
}
@Article{Higham:2006:RMC,
author = "Nicholas J. Higham",
title = "Review of {``Moody T. Chu and Gene H. Golub.
\booktitle{Inverse Eigenvalue Problems: Theory,
Algorithms, and Applications}''}",
journal = j-J-FLUID-MECH,
volume = "556",
pages = "442--443",
year = "2006",
CODEN = "JFLSA7",
ISSN = "0022-1120 (print), 1469-7645 (electronic)",
ISSN-L = "0022-1120",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
acknowledgement = ack-njh,
created = "2006.05.11",
fjournal = "Journal of Fluid Mechanics",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=FLM",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
updated = "2006.05.11",
}
@Article{Hnetynkova:2006:LTG,
author = "Iveta Hn{\v{e}}tynkov{\'a} and Martin Ple{\v{s}}inger
and Zden{\v{e}}k Strako{\v{s}}",
title = "{Lanczos} tridiagonalization, {Golub--Kahan}
bidiagonalization and coreproblem",
journal = j-PAMM,
volume = "6",
number = "1",
pages = "717--718",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1002/pamm.200610339",
ISSN = "1617-7061",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings in Applied Mathematics and Mechanics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1617-7061",
onlinedate = "23 Jan 2007",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Gutknecht:2007:PSV,
author = "Martin Gutknecht and Michael Overton and Lothar
Reichel and Daniel B. Szyld and Nick Trefethen and Paul
{Van Dooren} and Andy Wathen",
title = "Preface: {Special} volume dedicated to {Gene Golub} on
the occasion of his 75th birthday",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "28",
pages = "vii",
year = "2007\slash 2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
MRclass = "65-06 (01A70)",
MRnumber = "MR2455655",
bibdate = "Wed May 19 16:25:33 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
https://www.math.utah.edu/pub/tex/bib/etna.bib",
note = "Special volume for Gene Golub.",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Mantica:2007:QDE,
author = "Giorgio Mantica",
title = "Quantum Dynamical Entropy and an Algorithm by {Gene
Golub}",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "28",
number = "??",
pages = "190--205",
month = "????",
year = "2007\slash 2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/etna.bib",
note = "Special volume for Gene Golub.",
URL = "http://etna.mcs.kent.edu/vol.28.2007-2008/pp190-205.dir/pp190-205.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
report-number = "mantica, giorgio/B-7516-2012",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Heath:2008:GGR,
author = "Michael Heath",
title = "{Gene Golub} Remembered",
journal = j-SIAM-NEWS,
volume = "41",
number = "1",
pages = "??--??",
month = jan # "\slash " # feb,
year = "2008",
ISSN = "0036-1437",
bibdate = "Wed Sep 09 08:59:48 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "https://www.siam.org/news/news.php?id=1289",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Higham:2008:HOW,
author = "Nicholas J. Higham",
title = "In His Own Words [Interview with {Gene Golub}]",
journal = j-SIAM-NEWS,
volume = "41",
number = "1",
pages = "3",
month = jan # "/" # feb,
year = "2008",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Wed Sep 9 08:03:51 2015",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib",
URL = "https://www.siam.org/news/news.php?id=1290",
acknowledgement = ack-njh,
created = "2013.11.28",
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
updated = "2013.11.28",
xxnote = "Extracts from \cite{high08-ghg}.",
}
@Article{OLeary:2008:GHG,
author = "Dianne P. O'Leary",
title = "{Gene Howard Golub}, 1932--2007",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "428",
number = "11--12",
pages = "2405--2409",
day = "1",
month = jun,
year = "2008",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2008.01.014",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/linala2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Ruhe:2008:GHG,
author = "Axel Ruhe",
title = "{Gene Howard Golub} in memoriam",
journal = j-BIT-NUM-MATH,
volume = "48",
number = "1",
pages = "1--2",
month = "????",
year = "2008",
DOI = "https://doi.org/10.1007/s10543-008-0165-0",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Hnetynkova:2009:REG,
author = "Iveta Hn{\v{e}}tynkov{\'a} and Martin Ple{\v{s}}inger
and Zden{\v{e}}k Strako{\v{s}}",
title = "The regularizing effect of the {Golub--Kahan}
iterative bidiagonalization and revealing the noise
level in the data",
journal = j-BIT-NUM-MATH,
volume = "49",
number = "4",
pages = "669--696",
month = dec,
year = "2009",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-009-0239-7",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=49&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=49&issue=4&spage=669",
acknowledgement = ack-nhfb,
fjournal = "BIT. Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Ikramov:2009:CBG,
author = "Kh. D. Ikramov",
title = "On complex {Benzi--Golub} matrices",
journal = j-DOKL-MATH,
volume = "79",
number = "3",
pages = "342--344",
month = "????",
year = "2009",
DOI = "https://doi.org/10.1134/S1064562409030119",
ISSN = "1064-5624 (print), 1531-8362 (electronic)",
ISSN-L = "1064-5624",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
fjournal = "Doklady Mathematics",
journal-URL = "http://link.springer.com/journal/11472",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Meurant:2009:GHG,
author = "G{\'e}rard Meurant",
title = "{Gene H. Golub} 1932--2007",
journal = j-NUMER-ALGORITHMS,
volume = "51",
number = "1",
pages = "1--4",
month = may,
year = "2009",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-008-9245-0",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=51&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
note = "Tributes to Gene H. Golub, Part I--III appear in
volume 53 of this journal.",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=51&issue=1&spage=1",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Reichel:2011:RMM,
author = "Lothar Reichel",
title = "Review of {``Matrices, Moments and Quadrature with
Applications'' by G. H. Golub and G. Meurant, Princeton
University Press, 2010, xi + 363 pages}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "434",
number = "1",
pages = "379--380",
day = "1",
month = jan,
year = "2011",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Mar 30 23:04:12 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/linala2010.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Strakos:2011:GHG,
author = "Zden{\v{e}}k Strako{\v{s}}",
title = "{Gene H. Golub} and {Gerard Meurant}: Matrices,
Moments and Quadrature with Applications",
journal = j-FOUND-COMPUT-MATH,
volume = "11",
number = "2",
pages = "241--255",
month = "????",
year = "2011",
DOI = "https://doi.org/10.1007/s10208-010-9082-0",
ISSN = "1615-3375 (print), 1615-3383 (electronic)",
ISSN-L = "1615-3375",
bibdate = "Thu Jun 6 10:18:47 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
fjournal = "Foundations of Computational Mathematics. The Journal
of the Society for the Foundations of Computational
Mathematics",
journal-URL = "http://link.springer.com/journal/10208",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Gazzola:2016:LGK,
author = "Silvia Gazzola and Enyinda Onunwor and Lothar Reichel
and Giuseppe Rodriguez",
title = "On the {Lanczos} and {Golub--Kahan} reduction methods
applied to discrete ill-posed problems",
journal = j-NUM-LIN-ALG-APPL,
volume = "23",
number = "1",
pages = "187--204",
month = jan,
year = "2016",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.2020",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Tue Feb 9 06:31:34 MST 2016",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
http://www3.interscience.wiley.com/journalfinder.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/numlinaa.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "12 Oct 2015",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Meyer-Spasche:2016:PPO,
author = "Rita Meyer-Spasche and Rolf Tomas Nossum",
title = "Persecution and Patronage: {Oscar Buneman}'s years in
{Britain}",
journal = j-ALMAGEST,
volume = "7",
number = "2",
pages = "4--21",
year = "2016",
DOI = "https://doi.org/10.1484/J.ALMAGEST.5.112684",
ISSN = "1792-2593",
ISSN-L = "1792-2593",
bibdate = "Wed Sep 06 08:01:20 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/tex/bib/almagest.bib",
URL = "https://pure.mpg.de/rest/items/item_2403602/component/file_2403630/content;
https://www.brepolsonline.net/doi/10.1484/J.ALMAGEST.5.112684",
abstract = "The German student Oscar B{\"u}nemann, in trouble with
the Nazi authorities in the mid-1930s, chose to
emigrate to Britain and pursue a PhD there. After
emigration, his surname appears as Buneman. On the
verge of completing his degree in 1940, he was detained
as an enemy alien and spent almost a year in
internment. Upon release, he found work as an atomic
scientist in England, and went on to lead a post-war
career as a pioneering plasma physicist in the
USA.\par
We study forced migration of European scientists before
and during the Second World War, and scientific
patronage in the host countries. Buneman's case is
interesting from several points of view. Being a
non-Jewish, non-communist, anti-Nazi activist, he
belongs to a group not much investigated by historians.
His emigration from Germany was facilitated by his
family's business contacts in Britain. Being caught up
in the wave of detainments of enemy aliens in 1940, he
was assisted in pleading for release by the Society for
the Protection of Science and Learning, the archives of
which abound with information about refugee scientists
from Nazi Germany. We have also had access to material
not available to previous investigators, kindly
provided by Buneman's family.",
acknowledgement = ack-nhfb,
ajournal = "Almagest",
fjournal = "Almagest: International Journal for the History of
Scientific Ideas",
journal-URL = "https://www.brepolsonline.net/loi/almagest",
remark-1 = "The URL points to a slightly revised version of the
journal article.",
remark-2 = "From page 8: ``B{\"u}nemann's main contact persons
during the first years at Manchester University were
Professor Mordell, Professor Blackett (Nobel Prize in
Physics 1948) and Professor Hartree. He got his MSc
degree in 1938 with a thesis on stability theory for
ordinary dynamical systems (Bunemann 1938a). This
research resulted in two publications (Bunemann 1938b,
1938c).''",
remark-3 = "From page 8: ``Professor Hartree later wrote: `My
knowledge of him dates from Oct. 1935, when he entered
the University [\ldots{} ] I have known him not only in
his work as an undergraduate and post-graduate student,
but also in more informal ways, particularly in
connection with musical activities both in the
University and at home.'\,''",
remark-4 = "From page 16: ``Mathematically speaking, they computed
the paths of many charged particles (an electron beam)
in a given electro-magnetic field of a cavity
magnetron, taking into account that the moving charged
particles generate fields themselves. The resulting
field is called a self-consistent field. One of the
equations to be solved again and again was the Poisson
equation. By observing the particles timestep by
timestep, he discovered the `threshold' criterion for
magnetron operation, later on an important design tool.
\ldots{} In a cyclotron, charged particles move in
circles, the radii of which depend on isotopical mass;
different isotopes describe different paths. The work
at Berkeley entailed computing paths of charged
particles (ions) in their self-consistent fields.''",
remark-5 = "From page 18: ``In the 1960s he and his PhD student
Roger Willis Hockney were strongly involved in the
development of numerical methods closely related to the
Fast Fourier Transform, together with Gene Golub
(Hockney 1966a). Buneman became well-known among
numerical analysts for his Fast Poisson Solver, the
`Buneman algorithm' (Buneman 1969, Buzbee et al. 1970,
4, Henrici 1986, Stoer et al. 1983).",
remark-6 = "From page 19: ``His name is tied to the `Buneman
Instability', a property first introduced in his most
frequently cited paper (Buneman 1959), and the `Buneman
Algorithm' (Buneman 1969) which is still cited in
numerical analysis papers and used in plasma codes
(`Buneman trees' and the `Buneman-Levy algorithm' are
named in honor of his son Oscar Peter.) The dedication
of the first text book on computer simulation using
particles (Hockney et al. 1981) reads: `To Oscar,
Founder of the subject'.''",
subject-dates = "Oscar Buneman (28 September 1913--24 January 1993)",
}
@Article{Trogdon:2016:RHA,
author = "Thomas Trogdon and Sheehan Olver",
title = "A {Riemann--Hilbert} approach to {Jacobi} operators
and {Gaussian} quadrature",
journal = j-IMA-J-NUMER-ANAL,
volume = "36",
number = "1",
pages = "174--196",
month = jan,
year = "2016",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/dru061",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
bibdate = "Mon Jan 25 16:37:17 MST 2016",
bibsource = "http://imanum.oxfordjournals.org/content/36/1.toc;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
URL = "http://imajna.oxfordjournals.org/content/36/1/174",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
keywords = "Gaussian quadrature; Golub--Welsch algorithm; inverse
spectral problem; Jacobi operator; Riemann Hilbert
problems",
onlinedate = "January 18, 2015",
subject-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Book{OLeary:2018:BMG,
author = "Dianne P. O'Leary",
title = "Biographical Memoirs: {Gene H. Golub} 1932--2007",
publisher = "National Academy of Sciences",
address = "Washington, DC, USA",
pages = "23",
year = "2018",
bibdate = "Tue Oct 23 06:07:05 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/golub-gene.pdf",
acknowledgement = ack-nhfb,
}
@Article{Alqahtani:2019:GBA,
author = "Hessah Alqahtani and Lothar Reichel",
title = "Generalized block anti-{Gauss} quadrature rules",
journal = j-NUM-MATH,
volume = "143",
number = "3",
pages = "605--648",
month = nov,
year = "2019",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-019-01069-z",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 28 08:05:02 MDT 2019",
bibsource = "http://link.springer.com/journal/211/143/3;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
URL = "https://link.springer.com/article/10.1007/s00211-019-01069-z",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Gil:2019:FRU,
author = "Amparo Gil and Javier Segura and Nico M. Temme",
title = "Fast, reliable and unrestricted iterative computation
of {Gauss--Hermite} and {Gauss--Laguerre} quadratures",
journal = j-NUM-MATH,
volume = "143",
number = "3",
pages = "649--682",
month = nov,
year = "2019",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/s00211-019-01066-2",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Mon Oct 28 08:05:02 MDT 2019",
bibsource = "http://link.springer.com/journal/211/143/3;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
URL = "https://link.springer.com/article/10.1007/s00211-019-01066-2",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Goldenberg:2019:GKD,
author = "Steven Goldenberg and Andreas Stathopoulos and Eloy
Romero",
title = "A {Golub--Kahan Davidson} Method for Accurately
Computing a Few Singular Triplets of Large Sparse
Matrices",
journal = j-SIAM-J-SCI-COMP,
volume = "41",
number = "4",
pages = "A2172--A2192",
month = "????",
year = "2019",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/18M1222004",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Thu Oct 10 06:58:08 MDT 2019",
bibsource = "http://epubs.siam.org/toc/sjoce3/41/4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2019",
}
@Article{Asgari:2020:EBG,
author = "Z. Asgari and F. Toutounian and E. Babolian and E.
Tohidi",
title = "An extended block {Golub--Kahan} algorithm for large
algebraic and differential matrix {Riccati} equations",
journal = j-COMPUT-MATH-APPL,
volume = "79",
number = "8",
pages = "2447--2457",
day = "15",
month = apr,
year = "2020",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/j.camwa.2019.11.010",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Jul 8 08:11:13 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122119305437",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Bai:2021:GKV,
author = "Xianglan Bai and Alessandro Buccini and Lothar
Reichel",
title = "{Golub--Kahan} vs. {Monte Carlo}: a comparison of
bidiagonalization and a randomized {SVD} method for the
solution of linear discrete ill-posed problems",
journal = j-BIT-NUM-MATH,
volume = "61",
number = "4",
pages = "1093--1114",
month = dec,
year = "2021",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-021-00857-0",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Thu Feb 24 10:35:56 MST 2022",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "https://link.springer.com/article/10.1007/s10543-021-00857-0",
acknowledgement = ack-nhfb,
fjournal = "BIT Numerical Mathematics",
journal-URL = "http://link.springer.com/journal/10543",
}
@Misc{Moler:2022:CCC,
author = "Cleve Moler",
title = "{Cleve}'s Corner: {Christian Reinsch}, {Roland
Bulirsch}, and the {SVD}",
howpublished = "MathWorks Web site.",
day = "23",
month = oct,
year = "2022",
bibdate = "Thu Jun 27 14:42:19 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://feeds.feedburner.com/mathworks/moler",
acknowledgement = ack-nhfb,
subject-dates = "Roland Zden{\v{e}}k Bulirsch (10 November 1932--21
September 2022); Christian H. Reinsch (?? ?? 1932--8
October 2022)",
}
@Article{Bentbib:2023:GGK,
author = "A. H. Bentbib and M. {El Ghomari} and K. Jbilou and L.
Reichel",
title = "The global {Golub--Kahan} method and {Gauss}
quadrature for tensor function approximation",
journal = j-NUMER-ALGORITHMS,
volume = "92",
number = "1",
pages = "5--34",
month = jan,
year = "2023",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-022-01392-x",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Jan 30 12:22:09 MST 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-022-01392-x",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Laudadio:2023:CGQ,
author = "Teresa Laudadio and Nicola Mastronardi and Paul {Van
Dooren}",
title = "Computing {Gaussian} quadrature rules with high
relative accuracy",
journal = j-NUMER-ALGORITHMS,
volume = "92",
number = "1",
pages = "767--793",
month = jan,
year = "2023",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-022-01297-9",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Jan 30 12:22:09 MST 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-022-01297-9",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Reinsch:2023:SVD,
author = "Christian Reinsch and Mathias Richter",
title = "Singular value decomposition in extended double
precision arithmetic",
journal = j-NUMER-ALGORITHMS,
volume = "93",
number = "3",
pages = "1137--1155",
month = jul,
year = "2023",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-022-01459-9",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Thu Jun 8 10:00:53 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-022-01459-9",
abstract = "A well-known and successful algorithm to compute the
singular value decomposition (SVD) of a matrix was
published by Golub and Reinsch (Numer. Math.
14:403--420, 1970), together with an implementation in
Algol. We give an updated implementation in extended
double precision arithmetic in the C programming
language. Extended double precision is native for Intel
x86 processors and provides improved accuracy at full
hardware speed. The complete program for computing the
SVD is listed. Additionally, a comprehensive
explanation of the original algorithm of Golub and
Reinsch (Numer. Math. 14:403--420, 1970) is given at an
elementary level without referring to the more general
results of Francis (Comput. J. 4:265--271, 1961,
1962).",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Carson:2024:TUC,
author = "Erin Carson and J{\"o}rg Liesen and Zden{\v{e}}k
Strako{\v{s}}",
title = "Towards understanding {CG} and {GMRES} through
examples",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "692",
number = "??",
pages = "241--291",
day = "1",
month = jul,
year = "2024",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2024.04.003",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Apr 24 13:20:32 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/linala2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0024379524001381",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Book{Hansen:2013:LSD,
author = "Per Christian Hansen and V. (V{\'\i}ctor) Pereyra and
Godela Scherer",
title = "Least Squares Data Fitting with Applications",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
pages = "xv + 305",
year = "2013",
ISBN = "1-4214-0786-8 (hardcover), 1-4214-0858-9 (e-book)",
ISBN-13 = "978-1-4214-0786-9 (hardcover), 978-1-4214-0858-3
(e-book)",
LCCN = "QA275 .H26 2013",
MRclass = "65-01 (62J05 65Fxx)",
MRnumber = "3012616",
bibdate = "Sat Feb 2 09:11:29 MST 2019",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
prodorbis.library.yale.edu:7090/voyager;
z3950.loc.gov:7090/Voyager
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://muse.jhu.edu/books/9781421408583/",
abstract = "As one of the classical statistical regression
techniques, and often the first to be taught to new
students, least squares fitting can be a very effective
tool in data analysis. Given measured data, we
establish a relationship between independent and
dependent variables so that we can use the data
predictively. The main concern of Least Squares Data
Fitting with Applications is how to do this on a
computer with efficient and robust computational
methods for linear and nonlinear relationships. The
presentation also establishes a link between the
statistical setting and the computational issues. In a
number of applications, the accuracy and efficiency of
the least squares fit is central, and Per Christian
Hansen, V{\'i}ctor Pereyra, and Godela Scherer survey
modern computational methods and illustrate them in
fields ranging from engineering and environmental
sciences to geophysics. Anyone working with problems of
linear and nonlinear least squares fitting will find
this book invaluable as a hands-on guide, with
accessible text and carefully explained problems.",
acknowledgement = ack-nhfb,
remark = "In his interview \cite[page 44]{Haigh:2005:IGG}, Gene
Golub notes that he was working on a book with
V{\'\i}ctor Pereyra. This is the further development of
that book, as the preface reports on page xi: ``Prior
to his untimely death in November 2007, Professor Gene
Golub had been an integral part of the project team.
Although the book has changed significantly since then,
it has greatly benefitted from his insight and
knowledge. He was an aspiring mentor and great friend,
and we miss him dearly.''",
subject = "Least squares; Mathematical models; MATHEMATICS;
General.; Least squares.; Mathematical models.",
tableofcontents = "Preface / ix \\
Symbols and Acronyms / xiii \\
1 The Linear Data Fitting Problem / 1 \\
1.1 Parameter estimation, data approximation / 1 \\
1.2 Formulation of the data fitting problem / 4 \\
1.3 Maximum likelihood estimation / 9 \\
1.4 The residuals and their properties / 13 \\
1.5 Robust regression / 19 \\
2 The Linear Least Squares Problem / 25 \\
2.1 Linear least squares problem formulation / 25 \\
2.2 The QR factorization and its role / 33 \\
2.3 Permuted QR factorization / 39 \\
3 Analysis of Least Squares Problems / 47 \\
3.1 The pseudoinverse / 47 \\
3.2 The singular value decomposition / 50 \\
3.3 Generalized singular value decomposition / 54 \\
3.4 Condition number and column scaling / 55 \\
3.5 Perturbation analysis / 58 \\
4 Direct Methods for Full-Rank Problems / 65 \\
4.1 Normal equations / 65 \\
4.2 LU factorization / 68 \\
4.3 QR factorization / 70 \\
4.4 Modifying least squares problems / 80 \\
4.5 Iterative refinement / 85 \\
4.6 Stability and condition number estimation / 88 \\
4.7 Comparison of the methods / 89 \\
5 Direct Methods for Rank-Deficient Problems / 91 \\
5.1 Numerical rank / 92 \\
5.2 Peters-Wilkinson LU factorization / 93 \\
5.3 QR factorization with column permutations / 94 \\
5.4 UTV and VSV decompositions / 98 \\
5.5 Bidiagonalization / 99 \\
5.6 SVD computations / 101 \\
6 Methods for Large-Scale Problems / 105 \\
6.1 Iterative versus direct methods / 105 \\
6.2 Classical stationary methods / 107 \\
6.3 Non-stationary methods, Krylov methods / 108 \\
6.4 Practicalities: preconditioning and stopping
criteria / 114 \\
6.5 Block methods / 117 \\
7 Additional Topics in Least Squares / 121 \\
7.1 Constrained linear least squares problems / 121 \\
7.2 Missing data problems / 131 \\
7.3 Total least squares (TLS) / 136 \\
7.4 Convex optimization / 143 \\
7.5 Compressed sensing / 144 \\
8 Nonlinear Least Squares Problems / 147 \\
8.1 Introduction / 147 \\
8.2 Unconstrained problems / 150 \\
8.3 Optimality conditions for constrained problems /
156 \\
8.4 Separable nonlinear least squares problems / 158
\\
8.5 Multiobjective optimization / 160 \\
9 Algorithms for Solving Nonlinear LSQ Problems / 163
\\
9.1 Newton's method / 164 \\
9.2 The Gauss-Newton method / 166 \\
9.3 The Levenberg-Marquardt method / 170 \\
9.4 Additional considerations and software / 176 \\
9.5 Iteratively reweighted LSQ algorithms for robust
data fitting problems / 178 \\
9.6 Variable projection algorithm / 181 \\
9.7 Block methods for large-scale problems / 186 \\
10 Ill-Conditioned Problems / 191 \\
10.1 Characterization / 191 \\
10.2 Regularization methods / 192 \\
10.3 Parameter selection techniques / 195 \\
10.4 Extensions of Tikhonov regularization / 198 \\
10.5 Ill-conditioned NLLSQ problems / 201 \\
11 Linear Least Squares Applications / 203 \\
11.1 Splines in approximation / 203 \\
11.2 Global temperatures data fitting / 212 \\
11.3 Geological surface modeling / 221 \\
12 Nonlinear Least Squares Applications / 231 \\
12.1 Neural networks training / 231 \\
12.2 Response surfaces, surrogates or proxies / 238 \\
12.3 Optimal design of a supersonic aircraft / 241 \\
12.4 NMR spectroscopy / 248 \\
12.5 Piezoelectric crystal identification / 251 \\
12.6 Travel time inversion of seismic data / 258 \\
Appendix A Sensitivity Analysis / 263 \\
A.l Floating-point arithmetic / 263 \\
A.2 Stability, conditioning and accuracy / 264 \\
Appendix B Linear Algebra Background / 267 \\
B.l Norms / 267 \\
B.2 Condition number / 268 \\
B.3 Orthogonality / 269 \\
B.4 Some additional matrix properties / 270 \\
Appendix C Advanced Calculus Background / 271 \\
C.l Convergence rates / 271 \\
C.2 Multivariable calculus / 272 \\
Appendix D Statistics / 275 \\
D.l Definitions / 275 \\
D.2 Hypothesis testing / 280 \\
References / 281 \\
Index / 301",
}
@Proceedings{Kalenich:1965:IPP,
editor = "Wayne A. Kalenich",
booktitle = "Information Processing 1965: Proceedings of {IFIP}
Congress 65",
title = "Information Processing 1965: Proceedings of {IFIP}
Congress 65",
publisher = pub-SPARTAN,
address = pub-SPARTAN:adr,
pages = "xv + 648",
year = "1965",
LCCN = "QA76 .I575",
bibdate = "Sun Jan 14 10:24:53 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{Milton:1969:CSC,
editor = "Roy C. Milton and John A. Nelder",
booktitle = "Conference on Statistical Computation (1969:
University of Wisconsin) Statistical computation;
proceedings",
title = "Conference on Statistical Computation (1969:
University of Wisconsin) Statistical computation;
proceedings",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xii + 462",
year = "1969",
LCCN = "QA276.4 .C6 1969",
bibdate = "Mon Oct 24 09:07:27 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Abadie:1970:INP,
editor = "J. Abadie",
booktitle = "Integer and Nonlinear Programming",
title = "Integer and Nonlinear Programming",
publisher = pub-NH,
address = pub-NH:adr,
pages = "x + 544",
year = "1970",
ISBN = "0-444-10000-8",
ISBN-13 = "978-0-444-10000-9",
LCCN = "T57.7 .I57",
bibdate = "Mon Oct 24 09:12:37 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "A NATO Summer School held in Bandol, France.",
acknowledgement = ack-nhfb,
}
@Proceedings{Rosen:1970:SNP,
editor = "J. B. Rosen and O. L. Mangasarian and K. Ritter",
booktitle = "Symposium on Nonlinear Programming (1st: 1970:
Madison, {WI}, {USA})",
title = "Symposium on Nonlinear Programming (1st: 1970:
Madison, {WI}, {USA})",
number = "25",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xii + 490",
year = "1970",
ISBN = "0-12-597050-1",
ISBN-13 = "978-0-12-597050-1",
LCCN = "QA3 .U45 no. 25",
bibdate = "Mon Oct 24 09:10:04 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Publication of the Mathematics Research Center,
University of Wisconsin, Madison",
acknowledgement = ack-nhfb,
}
@Book{Morris:1971:STN,
editor = "John Ll. Morris",
booktitle = "Symposium on the Theory of Numerical Analysis, held in
{Dundee/Scotland}, September 15--23, 1970",
title = "Symposium on the Theory of Numerical Analysis, held in
{Dundee/Scotland}, September 15--23, 1970",
volume = "193",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vi + 152",
year = "1971",
ISBN = "0-387-05422-7",
ISBN-13 = "978-0-387-05422-3",
LCCN = "QA3 .L35 v.193",
MRclass = "65-06",
MRnumber = "51 \#2242",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Lecture Notes in Mathematics",
acknowledgement = ack-sf,
tableofcontents = "Direct methods for solving elliptic difference
equations \\
Matrix methods in mathematical programming \\
Topics in stability theory for partial difference
operators \\
Iteration parameters in the numerical solution of
elliptic problems \\
to finite difference approximations to initial value
problems for partial differential equations",
}
@Book{Wilkinson:1971:LA,
editor = "James H. Wilkinson and Christian Reinsch",
booktitle = "Linear Algebra",
title = "Linear Algebra",
volume = "II",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 439",
year = "1971",
ISBN = "0-387-05414-6, 3-540-05414-6",
ISBN-13 = "978-0-387-05414-8, 978-3-540-05414-6",
LCCN = "QA251 .W67",
bibdate = "Wed Dec 15 18:44:50 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/nummath.bib",
series = "Handbook for Automatic Computation, Editors: {F. L.
Bauer, A. S. Householder, F. W. J. Olver, H.
Rutishauser, K. Samelson and E. Stiefel}",
acknowledgement = ack-nhfb,
editor-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022);
James H. Wilkinson (27 September 1919--5 October
1986)",
tableofcontents = "Part I: Linear systems, least squares and linear
programming \\
J. H. Wilkinson / Introduction to Part I / 1--8 \\
1. Introduction \\
2. List of procedures \\
3. Positive definite symmetric matrices \\
4. Non-positive definite symmetric matrices \\
5. Non-Hermitian matrices \\
6. Least squares and related problems \\
7. The linear programming problem \\
R. S. Martin, G. Peters and J. H. Wilkinson / Symmetric
decomposition of a positive definite matrix / 9--30 \\
Martin, Peters and Wilkinson / Iterative refinement of
the solution of a positive definite system of equations
/ 31--44 \\
F. L. Bauer and C. Reinsch / Inversion of positive
definite matrices by the Gauss-Jordan method / 45--49
\\
Martin and Wilkinson / Symmetric decomposition of
positive definite band matrices / 50--56 \\
T. Ginsburg / The conjugate gradient method / 57--69
\\
Martin and Wilkinson / Solution of symmetric and
unsymmetric band equations and the calculation of
eigenvectors of band matrices / 70--92 \\
H. J. Bowdler, Martin, Peters and Wilkinson / Solution
of real and complex systems of linear equations /
93--110 \\
P. Businger and G. H. Golub / Linear least squares
solutions by Householder transformations / 111--118 \\
Bauer / Elimination with weighted row combinations for
solving linear equations and least squares problems /
119--133 \\
Golub and Reinsch / Singular value decomposition and
least squares solutions / 134--151 \\
R. H. Bartels, J. Stoer and Ch. Zenger / A realization
of the simplex method based on triangular
decompositions / 152--190 \\
Part II: The algebraic eigenvalue problem \\
Wilkinson / Introduction to Part II / 191--201 \\
1. Introduction \\
2. List of procedures \\
3. Real, dense, symmetric matrices \\
4. Symmetric band matrices \\
5. Simultaneous determination of dominant eigenvalues
and eigenvectors of a symmetric sparse matrix \\
6. The generalized symmetric eigenvalue problems $A x =
\lambda B x$ and $A B x = \lambda x$ \\
7. Hermitian matrices \\
8. Real dense unsymmetric matrices \\
9. Unsymmetric band matrices \\
10. Dense unsymmetric matrices with complex elements,
H. Rutishauser / The Jacobi method for real symmetric
matrices / 202--211 \\
Martin, Reinsch and Wilkinson / Householder's
tridiagonalization of a symmetric matrix / 212--226 \\
H. Bowdler, Martin, Reinsch and Wilkinson / The $QR$
and $QL$ algorithms for symmetric matrices / 227--240
\\
A. Dubrulle, Martin and Wilkinson / The implicit $QL$
algorithm / 241--248 \\
W. Barth, Martin, and Wilkinson / Calculation of the
eigenvalues of a symmetric tridiagonal matrix by the
method of bisection / 249--256 \\
Reinsch and Bauer / Rational $QR$ transformation with
Newton shift for symmetric tridiagonal matrices /
257--265 \\
Martin, Reinsch and Wilkinson / The $QR$ algorithm for
band symmetric matrices / 266--272 \\
H. R. Schwarz / Tridiagonalization of a symmetric band
matrix / 273--283 \\
Rutishauser / Simultaneous iteration method for
symmetric matrices / 284--302 \\
Martin and Wilkinson / Reduction of the symmetric
eigenproblem $A x = \lambda B x$ and related problems
to standard form / 303--314 \\
B. N. Parlett and Reinsch / Balancing a matrix for
calculation of eigenvalues and eigenvectors / 315--326
\\
P. J. Eberlein and J. Boothroyd / Solution to the
eigenproblem by a norm reducing Jacobi type method /
327--338 \\
Martin and Wilkinson / Similarity reduction of a
general matrix to Hessenberg form / 339--358 \\
Martin, Peters and Wilkinson / The $QR$ algorithm for
real Hessenberg matrices / 359--371 \\
Peters and Wilkinson / Eigenvectors of real and complex
matrices by $LR$ and $QR$ triangularizations / 372--395
\\
Martin and Wilkinson / The modified $LR$ algorithm for
complex Hessenberg matrices / 396--403 \\
Eberlein / Solution to the complex eigenproblem by a
norm reducing Jacobi type method / 404--417 \\
Peters and Wilkinson / The calculation of specified
eigenvectors by inverse iteration / 418--439",
}
@Proceedings{Hu:1973:MPP,
editor = "T. C. Hu and Stephen M. Robinson",
booktitle = "Mathematical Programming: Proceedings of an Advanced
Seminar",
title = "Mathematical Programming: Proceedings of an Advanced
Seminar",
number = "30",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 295",
year = "1973",
ISBN = "0-12-358350-0",
ISBN-13 = "978-0-12-358350-5",
LCCN = "QA3.U45 no. 30 T57.7",
bibdate = "Fri Dec 20 18:19:22 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Publication of the Mathematics Research Center, the
University of Wisconsin",
acknowledgement = ack-nhfb,
}
@Proceedings{Kabe:1973:MSI,
editor = "D. J. Kabe and R. P. Gupta",
booktitle = "Multivariate Statistical Inference; Proceedings of The
Research Seminar Dalhousie University, Halifax, March
23--25, 1972",
title = "Multivariate Statistical Inference; Proceedings of The
Research Seminar Dalhousie University, Halifax, March
23--25, 1972",
publisher = pub-NH,
address = pub-NH:adr,
pages = "x + 258",
year = "1973",
ISBN = "0-444-10532-8",
ISBN-13 = "978-0-444-10532-5",
LCCN = "QA278 .M861",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
}
@Proceedings{Kennedy:1973:PCS,
editor = "William Jo Kennedy",
booktitle = "Proceedings of the Computer Science and Statistics
Seventh Annual Symposium on the Interface, Ames, Iowa,
October 18--19, 1973",
title = "Proceedings of the Computer Science and Statistics
Seventh Annual Symposium on the Interface, Ames, Iowa,
October 18--19, 1973",
publisher = "Statistical Laboratory, Iowa State University",
address = "Ames, IA, USA",
pages = "x + 440",
year = "1973",
LCCN = "QA 276.4 C58 1973",
bibdate = "Sat Oct 29 16:02:11 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
xxISBN = "none",
}
@Proceedings{Miller:1973:TNA,
editor = "John J. H. Miller",
booktitle = "Topics in Numerical Analysis: Proceedings of the Royal
Irish Academy Conference on Numerical Analysis,
Dublin",
title = "Topics in Numerical Analysis: Proceedings of the Royal
Irish Academy Conference on Numerical Analysis,
Dublin",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xviii + 348",
year = "1973",
ISBN = "0-12-496950-X",
ISBN-13 = "978-0-12-496950-6",
LCCN = "QA297 .R691 1972",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
}
@Proceedings{Tarter:1973:PCS,
editor = "Michael E. Tarter",
booktitle = "Proceedings of the Computer Science and Statistics 6th
Annual Symposium on the Interface, held Oct. 16--17,
1972, on the Berkeley campus of the University of
California",
title = "Proceedings of the Computer Science and Statistics 6th
Annual Symposium on the Interface, held Oct. 16--17,
1972, on the Berkeley campus of the University of
California",
publisher = pub-WESTERN-PERIODICALS,
address = pub-WESTERN-PERIODICALS:adr,
pages = "vii + 173",
year = "1973",
LCCN = "QA276.A1 C67 1972",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
xxISBN = "none",
}
@Proceedings{Pereyra:1974:ADS,
editor = "V. Pereyra",
booktitle = "Actas Del Seminario Sobre Metodos Numericos Moderno",
title = "Actas Del Seminario Sobre Metodos Numericos Moderno",
volume = "I",
publisher = "Universidad Central de Venezuela",
address = "??, Venezuela",
pages = "??",
year = "1974",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Mon Jan 15 17:54:58 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:1975:SI,
editor = "Anonymous",
booktitle = "Seminaires {IRIA}",
title = "Seminaires {IRIA}",
publisher = "Inst. Rech. D'Informatique et d'Automatique",
address = "Rocquencourt, France",
pages = "????",
year = "1975",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Dec 20 18:47:30 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
xxnote = "There are at least 17 RLIN entries with this in their
titles. Which one is it??",
}
@Proceedings{Glowinski:1975:CMA,
editor = "R. Glowinski and Jacques Louis Lions",
booktitle = "Computing Methods in Applied Sciences and Engineering:
Second International Symposium, {December 15--19,
1975}",
title = "Computing Methods in Applied Sciences and Engineering:
Second International Symposium, {December 15--19,
1975}",
volume = "58",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 593",
year = "1975",
ISBN = "0-387-07990-4, 0-387-08003-1, 3-540-08003-1,
3-540-37550-3 (e-book)",
ISBN-13 = "978-0-387-07990-5, 978-0-387-08003-1,
978-3-540-08003-9, 978-3-540-37550-0 (e-book)",
LCCN = "TA345.I57 1975b",
bibdate = "Sun Jan 14 10:28:07 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Also as Lecture Notes in Economics and Mathematical
Systems, Vol. 134.",
series = "Lecture notes in physics",
URL = "http://www.springer.com/gp/book/9783540375500;
http://www.springer.com/us/book/9783540079903",
acknowledgement = ack-nhfb,
tableofcontents = "A simple theory of geometrical stiffness with
applications to beam and shell problems / Argyris, J.
H. (et al.) / 3--113 \\
Mod{\`e}les num{\'e}riques en m{\`e}canique des milieux
continus / Yanenko, N. N. / 114--132 \\
Infinite elements in the study of fluid-structure
interaction problems / Zienkiewicz, O. C. (et al.) /
133--172 \\
Galerkin approximations of a class of nonlinear
boundary-value problems and evolution problems in
elasticity / Oden, J. T. / 175--192 \\
Sur l'approximation num{\'e}rique des probl{\`e}mes
{\`a} fronti{\`e}re libre li{\'e}s {\`a} la filtration
dans les mat{\'e}riaux poreux / Comincioli, V. /
193--206 \\
Interior Penalty Procedures for Elliptic and Parabolic
Galerkin Methods / Douglas, Jim (et al.) / 207--216 \\
Analyse num{\'e}rique de probl{\`e}mes tridimensionnels
en magnetostatique / Marrocco, A. / 217--236 \\
Some aspects of a mixed finite element method applied
to fourth order partial differential equations /
Miyoshi, T. / 237--256 \\
Spectral methods applied to the integration of
meteorological equations / Hoskins, B. J. (et al.) /
259--274 \\
{\'E}tude num{\'e}rique des propri{\`e}t{\`e}s
ergodiques d'un syst{\`e}me construit sur les
{\'e}quations d'Euler d'un fluide parfait
bidimensionnel / Basdevant, C. (et al.) / 275--286 \\
General circulation models with examples taken from the
meteorological office model / Gilchrist, A. / 287--312
\\
Modelisation des flux turbulents dans une couche
convective / Andre, J. C. (et al.) / 313--330 \\
Prevision m{\'e}t{\'e}orologique par un mod{\`e}le
d'{\`e}coulement {\`a} maille fine / Rousseau, Daniel /
331--346 \\
Mathematical and physical characteristics and recent
results of ocean tide models / Zahel, Wilfried /
349--367 \\
On formulating anon-linear numerical model in three
dimensions for tides and storm surges / Heaps, N. S. /
368--387 \\
Une m{\'e}thode d'identification pour determiner des
param{\`e}tres oc{\'e}anographiques / Begis, D. (et
al.) / 388--406 \\
Utilisation des mod{\`e}les math{\'e}matiques pour
l'{\'e}tude de la r{\'e}frigeration des centrales
{\'e}lectriques install{\'e}es en bord de mer /
Daubert, A. (et al.) / 407--446 \\
Mathematical hydrodynamic models for the study of
marine circulation and dispersion of pollutants in a
shallow sea / Nihoul, Jacques C. J. / 447--472 \\
Some numerical methods in statistical hydrodynamics /
Chorin, Alexandre Joel / 475--496 \\
Determination num{\'e}rique de la configuration
d'{\'e}quilibre du plasma dans un tokomak / Laminie, J.
(et al.) / 497--509 \\
Stabilit{\'e} de la discretisation des {\'e}quations de
l'hydrodynamique lagrangienne 2D / Desgraz, J C. (et
al.) / 510--529 \\
Finite difference methods for ordinary boundary value
problems / Keller, Herbert B. / 530--543 \\
Numerical methods for singular perturbation problems /
Kreiss, Heinz-Otto (et al.) / 544--558 \\
On the numerical solution of linear mixed problems /
Aziz, A. K. (et al.) / 559--571 \\
Application of implicit difference schemes to the
solution of aerodynamic problems / Kovenya, V. M. /
572--593",
xxbooktitle = "Second International Symposium on Computing Methods in
Applied Sciences and Engineering: Summaries:
Versailles, December, 15--19, 1975",
xxtitle = "Second International Symposium on Computing Methods in
Applied Sciences and Engineering: Summaries:
Versailles, December, 15--19, 1975",
}
@Proceedings{ARO:1976:PAN,
key = "ANCAC '76",
booktitle = "Proceedings of the 1976 Army Numerical and Computers
Analysis Conference (13th)",
title = "Proceedings of the 1976 Army Numerical and Computers
Analysis Conference (13th)",
number = "76-3",
publisher = pub-US-ARO,
address = pub-US-ARO:adr,
pages = "xi + 524",
year = "1976",
ISBN = "??",
ISBN-13 = "??",
LCCN = "??",
bibdate = "Sat Oct 29 16:12:16 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "ARO report",
acknowledgement = ack-nhfb,
}
@Proceedings{Bunch:1976:SMC,
editor = "James R. Bunch and Donald J. Rose",
booktitle = "{Sparse Matrix Computations: Proceedings of the
Symposium on Sparse Matrix Computations at Argonne
National Laboratory on September 9--11, 1975}",
title = "{Sparse Matrix Computations: Proceedings of the
Symposium on Sparse Matrix Computations at Argonne
National Laboratory on September 9--11, 1975}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xi + 453",
year = "1976",
ISBN = "0-12-141050-1",
ISBN-13 = "978-0-12-141050-6",
LCCN = "QA188 .S989 1975",
bibdate = "Sat Oct 22 18:13:05 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Contributors / / ix \\
Preface / / xi \\
I. Design and Analysis of Elimination Algorithms / / 1
\\
1. Graph Theory and Gaussian Elimination / Robert Endre
Tarjan / 3 \\
2. Partitioning Using PAQ / Thomas D. Howell / 23 \\
3. Block Methods for Solving Sparse Linear Systems /
James R. Bunch / 39 \\
4. A Recursive Analysis of Dissection Strategies /
Donald J. Rose and Gregory F. Whitten / 59 \\
5. Applications of an Element Model for Gaussian
Elimination / S. C. Eisenstat, M. H. Schultz, and 4. H.
Sherman / 85 \\
6. An Optimization Problem Arising from Tearing Methods
/ Alberto Sangiovanni-Vincentelli / 97 \\
II. Eigenvalue Problems . / / 111 \\
1. A Bibliographical Tour of the Large, Sparse
Generalized Eigenvalue Problem / G. W. Stewart / 113
\\
2. How Far Should You Go With the Lanczos Process? / W.
Kahan and B. N. Parlett / 131 \\
III. Optimization, Least Squares and Linear Programming
/ / 145 \\
1. Optimization for Sparse Systems / T. L. Magnanti /
147 \\
2. Methods for Sparse Linear Least Squares Problems /
{AA}ke Bj{\"o}rck / 177 \\
3. The Orthogonal Factorization of a Large Sparse
Matrix / Philip E. Gill and Walter Murray / 201 \\
4. A Fast, Stable Implementation of the Simplex Method
Using Bartels-Golub Updating / Michael A. Saunders /
213 \\
5. Using the Steepest-edge Simplex Algorithm to Solve
Sparse Linear Programs / D. Goldfarb / 227 \\
IV. Mathematical Software / / 241 \\
1. Sparse Matrix Software / W. Morven Gentleman and
Alan George / 243 \\
2. Considerations in the Design of Software for Sparse
Gaussian Elimination / S. C. Eisenstat, M. H. Schultz,
and A. H. Sherman / 263 \\
3. Finding the Block Lower Triangular Form of a Sparse
Matrix / Fred Gustavson / 275 \\
V. Matrix Methods for Partial Difference Equations / /
291 \\
1. Marching Algorithms and Block Gaussian Elimination /
Randolph E. Bank / 293 \\
2. A Generalized Conjugate Gradient Method for the
Numerical Solution of Elliptic Partial Differential
Equations / Paul Concus, Gene H. Golub, and Dianne P.
O'Leary / 309 \\
3. Preconditioned Conjugate Gradient Iteration Applied
to Galerkin Methods for a Mildly-Nonlinear Dirichlet
Problem / Jim Douglas, Jr. and Todd Dupont / 333 \\
4. The Sparse Tableau Approach to Finite Element
Assembly / Gary Hachtel / 349 \\
5. A Capacitance Matrix Technique / B. L. Buzbee / 365
\\
6. M-Matrix Theory and Recent Results in Numerical
Linear Algebra / Richard S. Varga / 375 \\
VI. Applications / / 389 \\
1. Sparse Matrix Problems in a Finite Element Open
Ocean Model / Joel E. Hirsh and William L. Briggs / 391
\\
2. Calculation of Normal Modes of Oceans Using a
Lanczos Method / Alan K. Cline, Gene H. Golub, and
George W. Platzman / 409 \\
3. Application of Sparse Matrix Techniques to Reservoir
Simulation / P. T. Woo, S. C. Eisenstat, M. H. Schultz,
and A. H. Sherman / 427 \\
4. On the Origins and Numerical Solution of Some Sparse
Nonlinear Systems / T. A. Porsching / 439",
}
@Proceedings{Nashed:1976:GIA,
editor = "M. Zuhair Nashed",
booktitle = "Generalized Inverses and Applications: Proceedings of
an Advanced Seminar; Mathematics Research Center, the
University of Wisconsin, Madison, October 8--10, 1973",
title = "Generalized Inverses and Applications: Proceedings of
an Advanced Seminar; Mathematics Research Center, the
University of Wisconsin, Madison, October 8--10, 1973",
number = "32",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiv + 1054",
year = "1976",
ISBN = "0-12-514250-1",
ISBN-13 = "978-0-12-514250-2",
LCCN = "QA3 .U45 no. 32",
bibdate = "Mon Oct 24 08:49:52 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Publication of the Mathematics Research Center,
University of Wisconsin, Madison",
acknowledgement = ack-nhfb,
}
@Proceedings{Army:1977:TTC,
key = "ARMY MATH'76",
booktitle = "Transactions of the Twenty-Second Conference of Army
Mathematicians (Watervliet Arsenal, Watervliet, {NY,
1976)}",
title = "Transactions of the Twenty-Second Conference of Army
Mathematicians (Watervliet Arsenal, Watervliet, {NY},
1976)",
volume = "77-1 (or 77-7??)",
publisher = pub-US-ARO,
address = pub-US-ARO:adr,
pages = "xix + 613",
month = feb,
year = "1977",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Fri Dec 20 18:53:06 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "{ARO} Report",
acknowledgement = ack-nhfb,
}
@Proceedings{Kuck:1977:HSC,
editor = "David J. Kuck and D. Lawrie and A. Sameh",
booktitle = "High Speed Computer and Algorithm Organization:
Proceedings of the Symposium on High Speed Computer and
Algorithm Organization, held at the University of
Illinois, April 13--15, 1977",
title = "High Speed Computer and Algorithm Organization:
Proceedings of the Symposium on High Speed Computer and
Algorithm Organization, held at the University of
Illinois, April 13--15, 1977",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xii + 468",
year = "1977",
ISBN = "0-12-427750-0",
ISBN-13 = "978-0-12-427750-2",
LCCN = "QA76.5 S95 1977",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Rice:1977:MSI,
editor = "John R. Rice",
booktitle = "{Mathematical software III: Proceedings of a symposium
conducted by the Mathematics Research Center, the
University of Wisconsin--Madison, March 28--30, 1977}",
title = "{Mathematical software III: Proceedings of a symposium
conducted by the Mathematics Research Center, the
University of Wisconsin--Madison, March 28--30, 1977}",
number = "39",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 388",
year = "1977",
DOI = "https://doi.org/10.1016/C2013-0-11364-5",
ISBN = "0-12-587260-7",
ISBN-13 = "978-0-12-587260-7",
LCCN = "QA3 .U45 no. 39; QA297 .M36 1977",
bibdate = "Fri Dec 08 08:24:52 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/brandt-achi.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/Bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
series = "Publication of the Mathematics Research Center, the
University of Wisconsin, Madison",
URL = "https://www.sciencedirect.com/book/9780125872607/mathematical-software",
acknowledgement = ack-nhfb,
shorttableofcontents = "Contributors / / vii \\
Preface / / ix \\
Research, Development, and UNPACK / G. W. Stewart / 1
\\
A Technique that Gains Speed and Accuracy in the
Minimax Solution of Overdetermined Linear Equations /
M. J. Hopper and M. J. D. Powell / 15 \\
Infallible Calculation of Polynomial Zeros to Specified
Precision / G. E. Collins / 35 \\
Representation and Approximation of Surfaces / Robert
E. Barnhill / 69 \\
Simulation: Conflicts between Real-Time and Software /
C. W. Gear / 121 \\
Mathematical Software and Exploratory Data Analysis /
David C. Hoaglin / 139 \\
Software for $C^1$ Surface Interpolation / C. L. Lawson
/ 161 \\
Mathematical Software Production / W. R. Cowell and L.
D. Fosdick / 195 \\
Computational Aspects of the Finite Element Method / I.
Babuska and W. Rheinboldt / 225 \\
The Art of Writing a Runge-Kutta Code, Part I / L. F.
Shampine and H. A. Watts / 257 \\
Multi-Level Adaptive Techniques (MLAT) for Partial
Differential Equations: Ideas and Software / Achi
Brandt / 277 \\
ELLPACK: A Research Tool for Elliptic Partial
Differential Equations Software / John R. Rice / 319
\\
A Realistic Model of Floating-Point Computation / W. S.
Brown / 343 \\
The Block Lanczos Method for Computing Eigenvalues / G.
H. Golub and R. Underwood / 361 \\
Index / / 379",
tableofcontents = "Contributors \\
Preface \\
\\
1: Research, Development, and Linpack \\
Abstract \\
1. Introduction \\
2. Estimation of Condition Numbers \\
3. Stability of Least Squares Solutions \\
4. Scaling and Column Elimination \\
5. Downdating \\
6. Timing the BLAS \\
References \\
\\
2: A Technique That Gains Speed and Accuracy in the
Minimax Solution of Overdetermined Linear Equations \\
Abstract \\
1. Introduction \\
2. Numerical Instability in the Exchange Algorithm \\
3. The New Technique \\
4. Theory \\
5. Discussion \\
References \\
\\
3: Infallible Calculation Of Polynomial Zeros To
Specified Precision \\
Abstract \\
1. Introduction \\
2. Preliminaries \\
3. Sturm Sequences For Real Zeros \\
4. Sturm Sequences For Complex Zeros \\
5. Rolle's Theorem For Real Zeros \\
6. Descartes' Theorem For Real Zeros \\
7. Application of Interval Arithmetic \\
8. Complex Zeros Without Sturm Sequences \\
References \\
\\
4: Representation and Approximation of Surfaces \\
Abstract \\
1. Introduction \\
2. Interpolation Methods Defined Over Rectangles \\
3. Interpolation Schemes Defined Over Triangles \\
4. Interpolation Methods For Arbitrarily Placed Data 5.
Conclusions \\
References \\
Acknowledgements \\
\\
5: Simulation: Conflicts Between Real-Time And Software
\\
Abstract \\
1. Introduction \\
2. Simulation \\
3. Real-Time Operation \\
4. Numerical Integration in Real-Time \\
5. Errors in Numerical Integration \\
6. Methods For Reducing Delay and Improving Stability
\\
7. Conclusions \\
References \\
\\
6: Mathematical Software and Exploratory Data Analysis
\\
Abstract \\
1. Introduction \\
2. Overview of Exploratory Data Analysis \\
3. An Example: Timing Data \\
4. Software Needs of Exploratory Data Analysis \\
5. Summary \\
References \\
\\
7: Software For $C^1$ Surface Interpolation \\
1. Introduction \\
2. Problem Statement \\
3. Expected Applications \\
4. Published Work On Surface Interpolation To
Irregularly Located Data \\
5. Outline of the Algorithmic Approach Selected \\
6. Constructing a Triangular Grid \\
7. Estimating Partial Derivatives At the Grid Nodes \\
8. Lookup in the Triangular Grid \\
9. Interpolation in a Triangle \\
10. Examples \\
11. Three Criteria For Triangulation of a Strictly
Convex Quadrilateral \\
12. Global Consequences of the Local Optimization
Procedure \\
13. Mclain's Triangulation Method \\
14. Limits On Grid Changes When Adding a New Point \\
15. Conclusions \\
References \\
\\
8: Mathematical Software Production \\
Abstract \\
I. Introduction \\
II. The Evolution of Mathematical Software Production
\\
III. Intellectual Challenges \\
IV. Projects To Produce Mathematical Software \\
V. Trends in Mathematical Software Production \\
References \\
\\
9: Computational Aspects of the Finite Element Method
\\
1. Introduction \\
2. Goals of the Computational Analysis \\
3. The Principal Stages of the Computational Analysis
\\
4. Some Software Aspects \\
5. Some Computational Results \\
References",
}
@Proceedings{deBoor:1978:SRA,
editor = "Carl de Boor and Gene H. Golub",
booktitle = "{Symposium on Recent Advances in Numerical Analysis
(1978: Madison, Wis.). Recent Advances in Numerical
Analysis: Proceedings of a Symposium Conducted by the
Mathematics Research Center, the University of
Wisconsin, Madison, May 22--24, 1978}",
title = "{Symposium on Recent Advances in Numerical Analysis
(1978: Madison, Wis.). Recent Advances in Numerical
Analysis: Proceedings of a Symposium Conducted by the
Mathematics Research Center, the University of
Wisconsin, Madison, May 22--24, 1978}",
volume = "41",
organization = "Army Mathematics Research Center",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 270",
year = "1978",
ISBN = "0-12-208360-1",
ISBN-13 = "978-0-12-208360-0",
LCCN = "QA3 .U45 no. 41; QA297 S994 1978",
MRclass = "65-06",
MRnumber = "80a:65016",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "Publication of the Mathematics Research Center, the
University of Wisconsin, Madison",
URL = "http://catalog.hathitrust.org/api/volumes/oclc/65991765.html;
http://www.gbv.de/dms/hbz/toc/ht001227727.pdf",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "na; numerical analysis --- congresses; proceedings",
remark = "See review in Mathematics of Computation, Vol. 38, No.
158 (Apr., 1982), p. 654.",
tableofcontents = "Contributors / / vii \\
Preface / / ix \\
Positive Functions and Some Applications to Stability
Questions for Numerical Methods / Germund Dahlquist / 1
\\
Constructive Polynomial Approximation in Sobolev Spaces
/ Todd Dupont and Ridgway Scott / 31 \\
Questions of Numerical Condition Related to Polynomials
/ Walter Gautschi / 45 \\
Global Homotopies and Newton Methods / Herbert B.
Keller / 73 \\
Problems with Different Time Scales / Heinz-Otto Kreiss
/ 95 \\
Accuracy and Resolution in the Computation of Solutions
of Linear and Nonlinear Equations / Peter D. Lax / 107
\\
Finite Element Approximations to the One- Dimensional
Stefan Problem / J. A. Nitsche / 119 \\
The Hodie Method and Its Performance for Solving
Elliptic Partial Differential Equations / Robert E.
Lynch and John R. Rice / 143 \\
Solving ODE's with Discrete Data in SPEAKEASY / L. F.
Shampine / 177 \\
Perturbation Theory for the Generalized Eigenvalue
Problem / G. W. Stewart / 193 \\
Some Remarks on Good, Simple, and Optimal Quadrature
Formulas / H. F. Weinberger / 207 \\
Linear Differential Equations and Kronecker's Canonical
Form / J. H. Wilkinson / 231 \\
Index / / 267",
}
@Proceedings{Marek:1978:PFS,
editor = "Ivo Marek",
booktitle = "Proceedings of the Fourth Symposium on Basic Problems
of Numerical Mathematics (Plzen, Czechoslovakia)",
title = "Proceedings of the Fourth Symposium on Basic Problems
of Numerical Mathematics (Plzen, Czechoslovakia)",
publisher = "Reprograficke stredisko MFF UK",
address = "??",
pages = "200",
year = "1978",
ISBN = "??",
ISBN-13 = "??",
LCCN = "??",
bibdate = "Sat Oct 22 18:26:37 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Watson:1978:NAP,
editor = "G. A. Watson",
booktitle = "Numerical Analysis: Proceedings of the Biennial
Conference held at Dundee, June 28--July 1, 1977",
title = "Numerical Analysis: Proceedings of the Biennial
Conference held at Dundee, June 28--July 1, 1977",
volume = "630",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xii + 199",
year = "1978",
ISBN = "0-387-08538-6",
ISBN-13 = "978-0-387-08538-8",
LCCN = "QA1 .L471 v.630",
bibdate = "Sat Oct 29 18:52:59 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
price = "DM24.80",
series = "Lecture Notes in Mathematics",
acknowledgement = ack-nhfb,
}
@Proceedings{ARO:1979:PAN,
key = "Army Numerical Analysis '79",
booktitle = "Proceedings of the 1979 Army Numerical Analysis and
Computers Conference; sponsored by the Army Mathematics
Steering Committee; host, {U.S}. Army White Sands
Missile Range, 14--16 February 1979",
title = "Proceedings of the 1979 Army Numerical Analysis and
Computers Conference; sponsored by the Army Mathematics
Steering Committee; host, {U.S}. Army White Sands
Missile Range, 14--16 February 1979",
number = "79-3",
publisher = pub-US-ARO,
address = pub-US-ARO:adr,
pages = "xiii + 482",
year = "1979",
ISBN = "??",
ISBN-13 = "??",
LCCN = "??",
bibdate = "Mon Oct 24 09:18:51 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "ARO Report",
acknowledgement = ack-nhfb,
}
@Proceedings{Gasser:1979:STC,
editor = "Th. Gasser and M. Rosenblatt",
booktitle = "Smoothing Techniques for Curve Estimation: Proceedings
of Workshop Held in Heidelberg, April 2--4, 1979",
title = "Smoothing Techniques for Curve Estimation: Proceedings
of Workshop Held in Heidelberg, April 2--4, 1979",
volume = "757",
publisher = pub-SV,
address = pub-SV:adr,
pages = "245",
year = "1979",
ISBN = "0-387-09706-6",
ISBN-13 = "978-0-387-09706-0",
LCCN = "QA3 .L35 v.757",
bibdate = "Sat Oct 22 18:30:32 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Lecture Notes in Mathematics",
acknowledgement = ack-nhfb,
}
@Proceedings{Gentleman:1979:PCS,
editor = "Jane F. Gentleman",
booktitle = "Proceedings of the Computer Science and Statistics:
12th Annual Symposium on the Interface: May 10--11,
1979, University of Waterloo, Waterloo, Ontario,
Canada",
title = "Proceedings of the Computer Science and Statistics:
12th Annual Symposium on the Interface: May 10--11,
1979, University of Waterloo, Waterloo, Ontario,
Canada",
publisher = pub-WATERLOO,
address = pub-WATERLOO:adr,
pages = "xiii + 500",
year = "1979",
LCCN = "QA 276.4 C58 1979",
bibdate = "Sat Oct 29 15:12:07 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
xxISBN = "none",
}
@Proceedings{Glowinski:1979:CMA,
editor = "R. Glowinski and J. L. Lions",
key = "CMASE '79",
booktitle = "Computing methods in applied sciences and engineering:
proceedings of the fourth International Symposium on
Computing Methods in Applied Sciences and Engineering,
Versailles, France, December 10--14, 1979",
title = "Computing methods in applied sciences and engineering:
proceedings of the fourth International Symposium on
Computing Methods in Applied Sciences and Engineering,
Versailles, France, December 10--14, 1979",
publisher = pub-NH,
address = pub-NH:adr,
pages = "ix + 724",
year = "1979",
ISBN = "0-444-86008-8",
ISBN-13 = "978-0-444-86008-8",
LCCN = "TA345 .I57 1979",
bibdate = "Mon Jan 15 08:30:15 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Hettich:1979:SIP,
editor = "Rainer Hettich",
booktitle = "Semi-Infinite Programming: Proceedings of a Workshop,
Bad Honnef, August 30--September 1, 1978",
title = "Semi-Infinite Programming: Proceedings of a Workshop,
Bad Honnef, August 30--September 1, 1978",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 178",
year = "1979",
ISBN = "3-540-09479-2",
ISBN-13 = "978-3-540-09479-1",
LCCN = "QA402.5 .S43",
bibdate = "Sat Oct 29 16:21:33 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Lecture notes in control and information sciences",
acknowledgement = ack-nhfb,
}
@Proceedings{ISCMASE:1979:PIF,
key = "CMASE'79",
booktitle = "Proceedings of the {IRIA} Fourth International
Symposium on Computing Methods in Applied Science and
Engineering, Versailles, France, December 1979",
title = "Proceedings of the {IRIA} Fourth International
Symposium on Computing Methods in Applied Science and
Engineering, Versailles, France, December 1979",
publisher = "??",
address = "??",
pages = "??",
year = "1979",
bibdate = "Mon Jan 15 08:31:40 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
xxISBN = "??",
xxLCCN = "??",
}
@Proceedings{Glowinski:1980:CMA,
editor = "R. Glowinski and J. L. (Jacques Louis) Lions",
booktitle = "Computing methods in applied sciences and engineering:
proceedings of the fourth International Symposium on
Computing Methods in Applied Sciences and Engineering,
Versailles, France, December 10--14, 1979",
title = "Computing methods in applied sciences and engineering:
proceedings of the fourth International Symposium on
Computing Methods in Applied Sciences and Engineering,
Versailles, France, December 10--14, 1979",
publisher = pub-NH,
address = pub-NH:adr,
pages = "ix + 724",
year = "1980",
ISBN = "0-444-86008-8",
ISBN-13 = "978-0-444-86008-8",
LCCN = "TA345 .I57 1979",
bibdate = "Fri Dec 20 18:25:54 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Caussinus:1982:CSH,
editor = "H. Caussinus and others",
booktitle = "{COMPSTAT} 1982: 5th Symposium held at Toulouse,
1982",
title = "{COMPSTAT} 1982: 5th Symposium held at Toulouse,
1982",
publisher = pub-PHYSICA,
address = pub-PHYSICA:adr,
pages = "various",
year = "1982",
ISBN = "3-7051-0002-5 (v.1), 3-7051-0001-7 (v.2)",
ISBN-13 = "978-3-7051-0002-2 (v.1), 978-3-7051-0001-5 (v.2)",
LCCN = "QA276.4 .C194 1982",
bibdate = "Sat Oct 22 18:37:14 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{Watson:1982:NAP,
editor = "George Alistair Watson",
booktitle = "{Numerical Analysis: Proceedings of the 9th Biennial
Conference, held at Dundee, Scotland, June 23--26,
1981}",
title = "{Numerical Analysis: Proceedings of the 9th Biennial
Conference, held at Dundee, Scotland, June 23--26,
1981}",
volume = "912",
publisher = pub-SV,
address = pub-SV:adr,
bookpages = "xi + 245",
pages = "xi + 245",
year = "1982",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0093144",
ISBN = "0-387-11199-9 (softcover), 3-540-11199-9 (softcover),
3-540-39009-X (e-book)",
ISBN-13 = "978-0-387-11199-5 (softcover), 978-3-540-11199-3
(softcover), 978-3-540-39009-1 (e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
LCCN = "QA3 .L28 no. 912; QA1 .L471; QA297 .D915n 1981",
bibdate = "Sat Oct 29 15:16:39 1994",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/more-jorge.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1980.bib;
library.ox.ac.uk:210/ADVANCE;
melvyl.cdlib.org:210/CDL90",
series = ser-LECT-NOTES-MATH,
URL = "http://www.springerlink.com/content/978-3-540-39009-1",
acknowledgement = ack-nhfb,
subject = "Analisi numerica; Congressi; 1981; Dundee; Numerical
analysis; Congresses",
tableofcontents = "P. H. Calamai and A. R. Conn / A second-order
method for solving the continuous multifacility
location problem / 1--25 \\
M. P. Cullinan and M. J. D. Powell / Data smoothing by
divided differences / 26--37 \\
G. Dahlquist / On the control of the global error in
stiff initial value problems / 38--49 \\
L. M. Delves / Chebyshev methods for integral and
differential equations / 50--63 \\
J. Douglas, Jr. / Simulation of miscible displacement
in porous media by a modified method of characteristic
procedure / 64--70 \\
I. S. Duff / Full matrix techniques in sparse Gaussian
elimination / 71--84 \\
R. Fletcher / Second order corrections for
non-differentiable optimization / 85--114 \\
C. W. Gear and K. A. Gallivan / Automatic methods for
highly oscillatory ordinary differential equations /
115--124 \\
G. H. Golub and M. L. Overton / Convergence of a
two-stage Richardson iterative procedure for solving
systems of linear equations / 125--139 \\
J. G. Hayes: Curved knot lines and surfaces with ruled
segments / 140--156 \\
P. J. van der Houwen / On the time integration of
parabolic differential equations / 157--168 \\
T. E. Hull / Precision control, exception handling and
a choice of numerical algorithms / 169--178 \\
P. Lancaster / Generalized Hermitian matrices: a new
frontier for numerical analysis? / 179--189 \\
R. J. Y. McLeod / Some applications of geometry in
numerical analysis / 190--229 \\
L. B. Wahlbin / A quasioptimal estimate in piecewise
polynomial Galerkin approximation of parabolic problems
/ 230 --245 \\
Back matter / 249--251",
}
@Proceedings{Blackburn:1983:SIC,
editor = "J. F. Blackburn",
key = "CMASE '83",
booktitle = "Sixth International Conference on Computing Methods in
Applied Sciences and Engineering: December 12--16,
1983, Versailles, France",
title = "Sixth International Conference on Computing Methods in
Applied Sciences and Engineering: December 12--16,
1983, Versailles, France",
publisher = pub-ROCQUENCOURT,
address = pub-ROCQUENCOURT:adr,
pages = "500",
year = "1983",
ISBN = "??",
ISBN-13 = "??",
LCCN = "??",
bibdate = "Fri Dec 20 18:59:15 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Glowinski:1983:CMA,
editor = "R. Glowinski and J.-L. Lions",
booktitle = "Computing Methods in Applied Sciences and Engineering,
{VI}: Proceedings of the Sixth International Symposium
on Computing Methods in Applied Sciences and
Engineering, Versailles, France, December 12--16,
1983",
title = "Computing Methods in Applied Sciences and Engineering,
{VI}: Proceedings of the Sixth International Symposium
on Computing Methods in Applied Sciences and
Engineering, Versailles, France, December 12--16,
1983",
publisher = pub-ESP,
address = pub-ESP:adr,
pages = "xiii + 728",
year = "1983",
ISBN = "0-444-87597-2",
ISBN-13 = "978-0-444-87597-6",
LCCN = "QA297.I57 1983",
bibdate = "Sat Oct 22 18:42:10 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Dongarra:1984:IPS,
editor = "Jack Dongarra and Gene Golub and Jorge Mor{\'e} and
Danny Sorensen",
booktitle = "Informal Proceedings of the Symposium on Computational
Mathematics \emdash{} State of the Art, held at
{Argonne National Laboratory}, {September} 20--21,
1984, in honor of {James H. Wilkinson}",
title = "Informal Proceedings of the Symposium on Computational
Mathematics \emdash{} State of the Art, held at
{Argonne National Laboratory}, {September} 20--21,
1984, in honor of {James H. Wilkinson}",
publisher = inst-ANL,
address = inst-ANL:adr,
pages = "v + 264",
month = dec,
year = "1984",
LCCN = "??",
bibdate = "Sat Sep 24 01:25:08 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cody-william-j.bib",
note = "Technical Report MCS-TM-42. It consists of copies of
lecture slides from the ten symposium talks.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
xxISBN = "none",
}
@Book{Golub:1984:SNA,
editor = "Gene H. Golub",
booktitle = "Studies in Numerical Analysis",
title = "Studies in Numerical Analysis",
volume = "24",
publisher = pub-MATH-ASSOC-AMER,
address = pub-MATH-ASSOC-AMER:adr,
pages = "x + 415",
year = "1984",
ISBN = "0-88385-126-1 (v. 1), 0-88385-100-8 (set)",
ISBN-13 = "978-0-88385-126-5 (v. 1), 978-0-88385-100-5 (set)",
LCCN = "QA297 .S83 1984",
MRclass = "65-06",
MRnumber = "88i:65007",
bibdate = "Sat Oct 22 17:16:36 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/more-jorge.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
series = "Studies in mathematics",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "numerical analysis",
tableofcontents = "Gene H. Golub / Preface \\
James H. Wilkinson / The perfidious polynomial \\
Jorge J. Mor{\'e} and D. C. Sorensen / Newton's method
\\
Iain S. Duff / Research directions in sparse matrix
computations \\
Walter Gautschi / Questions of numerical conditions
related to polynomials \\
Paul Concus, Gene H. Golub, and Dianne P. O'Leary / A
generalized conjugate gradient method for the numerical
solution of elliptic partial differential equations \\
J. Barkley Rosser / Solving differential equations on a
hand held programmable calculator \\
V. Pereyra / Finite difference solution of boundary
value problems in ordinary differential equations \\
Dennis C. Jespersen / Multigrid methods for partial
differential equations \\
Paul N. Swarztrauber / Fast Poisson solvers \\
Peter Henrici / Poisson's equation in a hypercube:
discrete Fourier methods, eigenfunction expansions,
Pad{\'e} approximation to eigenvalues",
}
@Proceedings{Heiberger:1987:CSS,
editor = "R. M. Heiberger",
booktitle = "Computer Science and Statistics: Proceedings of the
19th Symposium on the Interface",
title = "Computer Science and Statistics: Proceedings of the
19th Symposium on the Interface",
publisher = "American Stat. Assoc",
address = "Alexandria, VA, USA",
pages = "xv + 588",
year = "1987",
bibdate = "Mon Sep 9 12:13:04 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
confdate = "8--11 March 1987",
conflocation = "Philadelphia, PA, USA",
}
@Proceedings{Noye:1987:CTA,
editor = "John Noye and others",
booktitle = "Computational Techniques and Applications, {CTAC}-87:
Proceedings of the 1987 International Conference on
Computational Techniques and Applications, held at the
University of Sydney, Australia",
title = "Computational Techniques and Applications, {CTAC}-87:
Proceedings of the 1987 International Conference on
Computational Techniques and Applications, held at the
University of Sydney, Australia",
publisher = pub-ENH,
address = pub-ENH:adr,
pages = "xix + 685",
year = "1987",
ISBN = "0-444-70400-0",
ISBN-13 = "978-0-444-70400-9",
LCCN = "QA299.6 .I561 1987",
bibdate = "Sat Oct 29 15:20:30 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Glowinski:1988:FIS,
editor = "Roland Glowinski and Gene H. Golub and G{\'e}rard
Meurant and Jacques P{\'e}riaux",
booktitle = "First International Symposium on Domain Decomposition
Methods for Partial Differential Equations: Proceedings
of the First International Symposium on Domain
Decomposition Methods for Partial Differential
Equations, Ecole Nationale des Ponts et Chauss{\'e}es,
Paris, France, January 7--9, 1987",
title = "First International Symposium on Domain Decomposition
Methods for Partial Differential Equations: Proceedings
of the First International Symposium on Domain
Decomposition Methods for Partial Differential
Equations, Ecole Nationale des Ponts et Chauss{\'e}es,
Paris, France, January 7--9, 1987",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "x + 431",
year = "1988",
ISBN = "0-89871-220-3",
ISBN-13 = "978-0-89871-220-9",
LCCN = "QA402.2 .I571 1987",
MRclass = "65-06 (76-06)",
MRnumber = "89f:65005",
bibdate = "Sun Jan 14 09:19:15 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/2008749",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
remark = "See review by J. H. B. in Mathematics of Computation,
Vol. 53, No. 188 (Oct., 1989), p. 775.",
}
@Book{Wilhelmson:1988:HSC,
editor = "Robert B. Wilhelmson",
booktitle = "High-Speed Computing: Scientific Applications and
Algorithm Design",
title = "High-Speed Computing: Scientific Applications and
Algorithm Design",
publisher = pub-U-ILLINOIS-PRESS,
address = pub-U-ILLINOIS-PRESS:adr,
pages = "228",
year = "1988",
ISBN = "0-252-01440-5",
ISBN-13 = "978-0-252-01440-6",
LCCN = "QA76.5 .H4831 1988",
bibdate = "Sat Oct 22 17:29:54 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Kowalik:1989:S,
editor = "Janusz S. Kowalik",
booktitle = "Supercomputing",
title = "Supercomputing",
volume = "62",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 425",
year = "1989",
ISBN = "3-540-52691-9 (Berlin), 0-387-52691-9 (New York)",
ISBN-13 = "978-3-540-52691-9 (Berlin), 978-0-387-52691-1 (New
York)",
LCCN = "QA76.5 .N344 1989",
bibdate = "Wed Aug 28 06:48:31 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
University of California MELVYL catalog.",
note = "``Proceedings of the NATO Advanced Research Workshop
on Supercomputing, held in Trondheim, Norway, June
19-23, 1989''--T.p. verso. ``Published in cooperation
with NATO Scientific Affairs Division.''",
series = "NATO ASI series. Series F, Computer and systems
sciences",
acknowledgement = ack-nhfb,
keywords = "supercomputers -- congresses",
}
@Proceedings{ARO:1990:TSA,
key = "TSACAMC '90",
booktitle = "Transactions of the Seventh Army Conference on Applied
Mathematics and Computing",
title = "Transactions of the Seventh Army Conference on Applied
Mathematics and Computing",
volume = "90-1",
publisher = pub-US-ARO,
address = pub-US-ARO:adr,
pages = "xx + 888",
year = "1990",
LCCN = "??",
bibdate = "Sat Oct 29 16:26:24 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "{ARO} Report",
acknowledgement = ack-nhfb,
xxISBN = "none",
}
@Proceedings{Cox:1990:RNC,
editor = "M. G. Cox and S. Hammarling",
booktitle = "Reliable numerical computation",
title = "Reliable numerical computation",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 339",
year = "1990",
ISBN = "0-19-853564-3",
ISBN-13 = "978-0-19-853564-5",
LCCN = "QA297 .R435 1990",
MRclass = "65-06",
MRnumber = "91k:65011",
bibdate = "Fri Dec 20 18:34:52 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Based on papers from a conference in honour of the
late James Hardy Wilkinson (died Sunday 5th October
1986) held at National Physical Laboratory, Teddington,
Middlesex, UK, 8th--10th July 1987.",
price = "US\$75.00",
abstract = "Published to honor the late Jim Wilkinson, the
respected pioneer in numerical analysis, this book
includes contributions from his colleagues and
collaborators, leading experts in their own right. The
breadth of Wilkinson's research is reflected in the
topics covered, which include linear algebra, error
analysis and computer arithmetic algorithms, and
mathematical software. An invaluable reference, the
book is completely up-to-date with the latest
developments on the Lanczos algorithm,
QR-factorizations, error propagation models, parameter
estimation problems, sparse systems, and
shape-preserving splines. Reflecting the current growth
and vitality of this field, the volume is an essential
reference for all numerical analysts.",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
tableofcontents = "List of contributors / / xv \\
Prologue. Reflections on Jim Wilkinson / Gene Golub / 1
\\
1. Misconvergence in the Lanczos algorithm / Beresford
Parlett / 7 \\
2. The Lanczos algorithm for a pure imaginary Hermitian
matrix / Charles L. Lawson and Kajal K. Gupta / 25 \\
3. Nearest defective matrices and the geometry of
ill-conditioning / James Demmel / 35 \\
4. Computational aspects of the Jordan canonical form /
Theo Beelen and Paul Van Dooren / 57 \\
5. Some aspects of generalized QR factorizations / C.
C. Paige / 73 \\
6. The multifrontal method in a parallel environment /
I. S. Duff, N. I. M. Gould, M. Lescrenier, and J. K.
Reid / 93 \\
7. A Schur-complement method for sparse quadratic
programming / Philip E. Gill, Walter Murray, Michael A.
Saunders, and Margaret H. Wright / 113 \\
8. A probabilistic round-off error propagation model.
Application to the eigenvalue problem / Fran{\c{c}}oise
Chatelin and Marie Christine Brunet / 139 \\
9. Analysis of the Cholesky decomposition of a
semi-definite matrix / Nicholas J. Higham / 161 \\
10. On the conditioning of parameter estimation
problems / James M. Varah / 187 \\
11. Rounding errors in algebraic process-in level-index
arithmetic / F. W J. Olver / 197 \\
12. Experiments in tearing large sparse systems / Mario
Arioli and lain S. Duff / 207 \\
13. The least-squares solution of linear equations with
block-angular observation matrix / M. G. Cox / 227 \\
14. An iterative method for solving linear inequalities
/ G. W Stewart / 241 \\
15. Iterative refinement and reliable computing / Ake
Bjorck / 249 \\
16. Software for shape-preserving spline interpolation
/ Christian H. Reinsch / 267 \\
17. Experiences with some software engineering
practices in numerical software / D. A. H. Jacobs and
G. Markham / 277 \\
18. Evolution of numerical software for dense linear
algebra / Jack Dongarra and Sven Hammarling / 297 \\
Epilogue. Jim Wilkinson: some after-dinner sentiments /
L. Fox / 329",
}
@Proceedings{Kincaid:1990:IML,
editor = "David R. Kincaid and Linda J. Hayes",
booktitle = "Iterative methods for large linear systems (Austin,
{TX}, October 19--21, 1988)",
title = "Iterative methods for large linear systems (Austin,
{TX}, October 19--21, 1988)",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "??",
year = "1990",
ISBN = "0-12-407475-8",
ISBN-13 = "978-0-12-407475-0",
LCCN = "QA432 .I84 1990",
bibdate = "Mon Jan 15 08:34:05 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Kowalik:1990:SNA,
editor = "Janusz S. Kowalik",
booktitle = "Supercomputing: {NATO} Advanced Research Workshop on
Supercomputing (1989: Trondheim, Norway)",
title = "Supercomputing: {NATO} Advanced Research Workshop on
Supercomputing (1989: Trondheim, Norway)",
volume = "62",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 425",
year = "1990",
ISBN = "0-387-52691-9 (New York), 3-540-52691-9 (Berlin)",
ISBN-13 = "978-0-387-52691-1 (New York), 978-3-540-52691-9
(Berlin)",
LCCN = "QA76.5 .N344 1989",
bibdate = "Sat Oct 29 15:25:18 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "NATO ASI series. Series F, Computer and systems
sciences",
acknowledgement = ack-nhfb,
}
@Proceedings{Anonymous:1991:PIS,
editor = "Anonymous",
booktitle = "{Proceedings of the International Symposium on
Supercomputing: Fukuoka, Japan, November 6--8, 1991}",
title = "{Proceedings of the International Symposium on
Supercomputing: Fukuoka, Japan, November 6--8, 1991}",
publisher = "Kyushu University Press",
address = "Fukuoka, Japan",
pages = "iv + 261",
year = "1991",
ISBN = "4-87378-284-8",
ISBN-13 = "978-4-87378-284-3",
LCCN = "QA76.88.I1991",
bibdate = "Fri Aug 30 08:01:51 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
keywords = "Supercomputers --- Congresses",
}
@Proceedings{Golub:1991:NLA,
editor = "Gene H. Golub and Paul {Van Dooren}",
booktitle = "Numerical Linear Algebra, Digital Signal Processing
and Parallel Algorithms",
title = "Numerical Linear Algebra, Digital Signal Processing
and Parallel Algorithms",
volume = "70",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiii + 729",
year = "1991",
ISBN = "0-387-52300-6 (New York), 3-540-52300-6 (Berlin)",
ISBN-13 = "978-0-387-52300-2 (New York), 978-3-540-52300-0
(Berlin)",
LCCN = "QA184 .N39 1988",
MRclass = "65Y10 (00B25 65Fxx 65Y05 94A12)",
MRnumber = "92i:65226",
bibdate = "Sun Jan 14 09:03:35 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "NATO ASI series. Series F, Computer and systems
sciences",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Proceedings{Vaccaro:1991:SSP,
editor = "Richard J. Vaccaro",
booktitle = "{SVD} and Signal Processing, {II}. Algorithms,
Analysis and Applications",
title = "{SVD} and Signal Processing, {II}. Algorithms,
Analysis and Applications",
publisher = pub-ELS,
address = pub-ELS:adr,
pages = "xv + 512",
year = "1991",
ISBN = "0-444-88896-9",
ISBN-13 = "978-0-444-88896-9",
LCCN = "TK5102.5.S93 1991",
bibdate = "Fri Dec 20 18:20:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
confdate = "25--27 June 1990",
conflocation = "Kingston, RI, USA",
confsponsor = "Coll. Eng. URI; IEEE; EURASIP; SIAM",
pubcountry = "Netherlands",
}
@Book{Iserles:1992:AN,
editor = "A. Iserles",
booktitle = "Acta Numerica 1992",
title = "Acta Numerica 1992",
publisher = pub-CUP,
address = pub-CUP:adr,
pages = "407",
year = "1992",
ISBN = "0-521-41026-6",
ISBN-13 = "978-0-521-41026-7",
LCCN = "QA297.A21 1992",
bibdate = "Mon Oct 24 09:39:37 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Golub:1993:RAI,
editor = "Gene H. Golub and Anne Greenbaum and Mitchell Luskin",
booktitle = "Recent Advances in Iterative Methods",
title = "Recent Advances in Iterative Methods",
volume = "60",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 225",
year = "1993",
ISBN = "0-387-94252-1 (New York), 3-540-94252-1 (Berlin)",
ISBN-13 = "978-0-387-94252-0 (New York), 978-3-540-94252-8
(Berlin)",
LCCN = "QA297.8 .R43 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib",
note = "Papers from the IMA Workshop on Iterative Methods for
Sparse and Structured Problems, held in Minneapolis,
Minn., Feb. 24--Mar. 1, 1992",
price = "DM98.00",
series = "The IMA volumes in mathematics and its applications",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
tableofcontents = "Some themes in Gene H. Golub's work on iterative
methods / Dianne P. O'Leary \\
Computing the sparse singular value decomposition via
SVDPACK / Michael W. Berry \\
Gaussian quadrature applied to adaptive Chebyshev
iteration / D. Calvetti, G.H. Golub, and L. Reichel \\
Ordering effects on relaxation methods applied to the
discrete convection-diffusion equation / Howard C.
Elman and Michael P. Chernesky \\
On the error computation for polynomial based iteration
methods / Bernd Fischer and Gene H. GolubTranspose-free
quasi-minimal residual methods for non-Hermitian linear
systems / Roland W. Freund \\
Matrices that generate the same Krylov residual spaces
/ Anne Greenbaum and Zdenek Strakos \\
Incomplete block factorizations as preconditioners for
sparse SPD matrices / L. Yu. Kolotilina and A. Yu
Yeremin \\
How fast can iterative methods be? / Olavi Nevanlinna
\\
Rational Krylov algorithms for nonsymmetric eigenvalue
problems / Axel Ruhe \\
Highly parallel preconditioners for general sparse
matrices / Youcef SaadA two-stage iteration for solving
nearly completely decomposable Markov chains / G.W.
Stewart, W.J. Stewart and D.F. McAllister \\
Minimum residual modifications to Bi-CG and to the
preconditioner / Henk A. Van der Vorst",
}
@Proceedings{Hussaini:1993:ATC,
editor = "M. Y. Hussaini and A. Kumar and M. D. Salas",
booktitle = "Algorithmic Trends in Computational Fluid Dynamics",
title = "Algorithmic Trends in Computational Fluid Dynamics",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 423",
year = "1993",
ISBN = "0-387-94014-6 (New York), 3-540-94014-6 (Berlin)",
ISBN-13 = "978-0-387-94014-4 (New York), 978-3-540-94014-2
(Berlin)",
LCCN = "QA911 .A555 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "ICASE/NASA LaRC Series",
acknowledgement = ack-sf,
remark = "Proceedings from a workshop held Sept. 15--17, 1991.",
tableofcontents = "Overviews \\
A Viewpoint on Discretization Schemes for Applied
Aerodynamic Algorithms for Complex Configurations /
Joseph L. Steger \\
Some Remarks about Computational Fluid Dynamics /
Heinz-Otto Kreiss \\
Algorithmic Trends in CFD in the 1990's for Aerospace
Flow Field Calculations / Robert W. MacCormack \\
Advances for the Simulation of Compressible Viscous
Flows on Unstructured Meshes / O. Pironneau \\
Some Challenges in Massively Parallel Computation /
Martin H. Schultz \\
Acceleration Techniques \\
Local Preconditioning of the Euler Equations and its
Numerical Implications / Bram van Leer \\
Incremental Unknowns in Finite Differences / Roger
Temam \\
Supercomputer Implementations of Preconditioned Krylov
Subspace Methods / Youcef Saad \\
Recent Advances in Lanczos-Based Iterative Methods for
Nonsymmetric Linear Systems / Roland Freund, Gene H.
Golub and Noel M. Nachtigal \\
Convergence Acceleration Algorithms / Mohamed Hafez \\
Spectral and Higher-Order Methods \\
Spectral Methods for Viscous, Incompressible Flows /
Claudio Canuto \\
Issues in the Application of High Order Schemes / David
Gottlieb \\
Essentially Nonoscillatory Postprocessing Filtering
Methods / F. Lafon and S. Osher \\
Some Novel Aspects of Spectral Methods / George Em
Karniadakis and Steven A. Orszag \\
Multi-Resolution and Subcell Resolution Schemes \\
Wavelet Methods in Computational Fluid Dynamics / R.
Glowinski, J. Periaux, M. Ravachol, T. W. Pan, R. O.
Wells and X. Zhou \\
Subcell Resolution Methods for Viscous Systems of
Conservation Laws / Eduard Harabetian \\
Multi-Resolution Analysis for ENO Schemes / Ami Harten
\\
Adaptive-Mesh Algorithms for Computational Fluid
Dynamics / Kenneth G. Powell, Philip L. Roe and James
Quirk \\
Inherently Multidimensional Schemes \\
Beyond the Riemann Problem, Part I / Philip L. Roe \\
Beyond the Riemann Problem, Part II / H. Deconinck \\
Three Dimensional Covolume Algorithms for Viscous Flows
/ R. A. Nicolaides \\
Comments on Session \\
Inherently Multidimensional Schemes / K. W. Morton",
}
@Proceedings{IEEE:1993:III,
editor = "{IEEE}",
booktitle = "{ICASSP 93}: 1993 {IEEE} International Conference on
Acoustics, Speech, and Signal Processing, April 27--30,
1993, Minneapolis Convention Center, Minneapolis,
Minnesota",
title = "{ICASSP} 93: 1993 {IEEE} International Conference on
Acoustics, Speech, and Signal Processing, April 27--30,
1993, Minneapolis Convention Center, Minneapolis,
Minnesota",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "652 + 735 + 606 + 559 + 681",
year = "1993",
ISBN = "0-7803-0946-4",
ISBN-13 = "978-0-7803-0946-3",
LCCN = "TK 7882 S65 I16 1993",
bibdate = "Fri Dec 20 18:21:35 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Five volumes.. IEEE Catalog No. 92CH3252-4.",
acknowledgement = ack-nhfb,
confdate = "27--30 April 1993",
conflocation = "Minneapolis, MN, USA",
confsponsor = "IEEE Signal Process. Soc",
}
@Proceedings{Moonen:1993:LAL,
editor = "Marc S. Moonen and Gene H. Golub and Bart L. R. {De
Moor}",
booktitle = "{Linear Algebra for Large Scale and Real-Time
Applications: Proceedings of the NATO Advanced Study
Institute, Leuven, Belgium, August 3--14, 1992}",
title = "{Linear Algebra for Large Scale and Real-Time
Applications: Proceedings of the NATO Advanced Study
Institute, Leuven, Belgium, August 3--14, 1992}",
volume = "232",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "ix + 435",
year = "1993",
ISBN = "0-7923-2151-0",
ISBN-13 = "978-0-7923-2151-4",
LCCN = "QA185.D37 L56 1993",
MRclass = "65-06 (65Fxx 65Y05)",
MRnumber = "94e:65009",
bibdate = "Mon Jan 15 17:53:04 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
series = "NATO ASI series. Series E, Applied sciences",
URL = "http://catdir.loc.gov/catdir/enhancements/fy0823/92046135-d.html;
http://www.gbv.de/dms/hbz/toc/ht004938330.pdf;
http://zbmath.org/?q=an:0810.00029",
ZMnumber = "0810.00029",
abstract = "In recent years there has been great interest in large
scale and real-time matrix computations; these
computations arise in a variety of fields, such as
computer graphics, imaging, speech and image
processing, telecommunication, biomedical signal
processing, optimization and so on. This volume, which
is an outgrowth of a NATO ASI, held at Leuven, Belgium,
August 1992, gives an account of recent research
advances in numerical techniques used in large scale
and real-time computations and their implementation on
high performance computers.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
tableofcontents = "Preface / / xi \\
Invited Lectures / / 1 \\
Large scale structural analysis on massively parallel
computers / P. E. Bj{\o}rstad and J. Cook / 3 \\
Data-parallel BLAS as a basis for LAPACK on massively
parallel computers / P. E. Bj{\o}rstad and T.
S{\o}revik / 13 \\
a Large-scale nonlinear constrained optimization / A.
R. Conn, N. Gould and Ph. L. Toint / 21 \\
Trading off parallelism and numerical stability / J. W.
Demmel / 49 \\
Subband filtering: CORDIC modulation and systolic
quadrature mirror filter tree / E. F. Deprettere / 69
\\
A parallel image rendering algorithm and architecture
based on ray tracing and radiosity shading / E. F.
Deprettere and L.-S. Shen / 91 \\
Reduction and approximation of linear computational
circuits / P. Dewilde and A.-J. van der Veen / 109 \\
The look-ahead Lanczos process for large nonsymmetric
matrices and related algorithms / R. W. Freund / 137
\\
Case studies of real-time processing in robotics / W.
M. Gentleman / 165 \\
Adaptive signal processing with emphasis on QRD-least
squares lattice / S. Haykin / 183 \\
A direct method for reordering eigenvalues in the
generalized real Schur form of a regular matrix pair
(A, B) / B. K{\aa}gstr{\"o}m / 195 \\
Block shift invariance and efficient system
identification algorithms / N. Kalouptsidis / 219 \\
Computing the singular value decomposition on a
fat-tree architecture / T. J. Lee, F. T. Luk and D. L.
Boley / 231 \\
A new matrix decomposition for signal processing / F.
T. Luk and S. Qiao / 241 \\
The linear algebra of perfect reconstruction filtering
/ M. Stewart and G. Cybenko / 249 \\
Determining rank in the presence of error / G. W.
Stewart / 275 \\
Approximation with Kronecker products / C. F. Van Loan
and N. Pitsianis / 293 \\
Some linear algebra issues in large-scale optimization
/ M. H. Wright / 315 \\
Contributed Lectures / / 339 \\
Direct and inverse unitary eigenproblems in signal
processing: an overview / G. S. Ammar, W. B. Gragg and
L. Reichel / 341 \\
Block implementations of the symmetric QR and Jacobi
algorithms / P. Arbenz and M. Oettli / 345 \\
Linear algebra for large-scale information retrieval
applications / M. W. Berry / 347 \\
Matched filter vs. least-squares approximation / L. H.
J. Bierens / 349 \\
Reordering diagonal blocks in real Schur form / A. W.
Bojanczyk and P. Van Dooren / 351 \\
Placing zeroes and the Kronecker canonical form / D. L.
Boley and P. Van Dooren / 353 \\
Analysis of the recursive least squares lattice
algorithm / J. R. Bunch and R. C. LeBorne / 355 \\
Adaptive Chebyshev iteration based on modified moments
/ D. Calvetti, G. H. Golub and L. Reichel / 357 \\
Continuous realization methods and their applications /
M. T. Chu / 359 \\
Asymptotic behavior of orthogonal polynomials / T. Dehn
/ 361 \\
CADCS and parallel computing / F. Dumortier, A. Van
Cauwenberghe and L. Boullart / 363 \\
Eigenvalue roulette and random test matrices / A.
Edelman / 365 \\
On numerical methods for unitary eigenvalue problems /
H. Fa{\sas}bender / 369 \\
Accurate singular values and differential qd algorithms
/ K. V. Fernando and B. N. Parlett / 371 \\
Orthogonal projection and total least squares / R. D.
Fierro and J. R. Bunch / 375 \\
Gauss quadratures associated with the Arnoldi process
and the Lanczos algorithm / R. W. Freund and M.
Hochbruck / 377 \\
An implementation of the QMR method based on coupled
two-term recurrences / R. W. Freund and N. M. Nachtigal
/ 381 \\
Computationally efficient homotopies for the H 2 model
order reduction problem / Y. Ge, L. T. Watson, E. G.
Collins, Jr. and L. D. Davis / 385 \\
A fast algorithm for $QR$ decomposition of Toeplitz
matrices / G. O. Glentis / 387 \\
Unitary Hessenberg methods for Toeplitz approximations
and applications / Ch. He and A. Bunse-Gerstner / 389
\\
Perturbation theory and backward error for $A X - X B =
C$ / N. J. Higham / 391 \\
Fast transforms and elliptic problems / T. Huckle / 393
\\
An interior-point method for minimizing the maximum
eigenvalue of a linear combination of matrices / F.
Jarre / 395 \\
The lattice-ladder with generalized forgetting / J.
Kadlec / 397 \\
Solving a least squares problem with boundary
constraints / L. Kaufman / 399 \\
Estimating the extremal eigenvalues and condition
number by the Lanczos algorithm with a random start /
J. Kuczy{\'n}ski and H. Wo{\'z}niakowski / 401 \\
A generalized ADI iterative method / N. Levenberg and
L. Reichel / 403 \\
Quaternions and the symmetric eigenvalue problem / N.
Mackey / 405 \\
Application of the Gauss-Seidel iteration to the RLS
algorithm / {\"O}. Morg{\"u}l and A. Mala{\c{s}} / 407
\\
Ranks of submatrices of a matrix and its inverse / C.
C. Paige and M. Wei / 409 \\
A QRD-based least-squares algorithm for multipulse
antenna array signal processing / I. K. Proudler / 411
\\
On displacement structures for covariance matrices and
lossless functions / P. A. Regalia and F. Desbouvries /
413 \\
Application of vector extrapolation and conjugate
gradient type methods to the semiconductor device
problem / W. H. A. Schilders / 415 \\
Accurate symmetric eigenreduction by a Jacobi method /
I. Slapni{\v{c}}ar / 417 \\
The order-recursive Chandrasekhar equations for fast
square-root Kalman filtering / D. T. M. Slock / 419 \\
Hybrid iterative methods based on Faber polynomials /
G. Starke / 421 \\
Aspects of implementing a 'C' matrix library / D. E.
Stewart / 423 \\
Intermediate fill-in in sparse QR decomposition / M.
T{\r{u}}ma / 425 \\
Shifting strategies for the parallel QR algorithm / D.
S. Watkins / 427 \\
List of Participants / / 429 \\
Authors Index / / 437",
}
@Proceedings{Brown:1994:PCL,
editor = "J. David Brown and Moody T. Chu and Donald C. Ellison
and Robert J. Plemmons",
booktitle = "{Proceedings of the Cornelius Lanczos International
Centenary Conference, Raleigh, North Carolina, December
12--17, 1993}",
title = "{Proceedings of the Cornelius Lanczos International
Centenary Conference, Raleigh, North Carolina, December
12--17, 1993}",
volume = "73",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "lxv + 644",
year = "1994",
ISBN = "0-89871-339-0",
ISBN-13 = "978-0-89871-339-8",
LCCN = "QC19.2 .C67 1993",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
z3950.loc.gov:7090/Voyager",
series = "Proceedings in Applied Mathematics",
acknowledgement = ack-nhfb,
meetingname = "Cornelius Lanczos International Centenary Conference
(1993:Raleigh, NC)",
subject = "Mathematical physics; Congresses; Astrophysics;
Mathematics; Lanczos, Cornelius; Physicists; Hungary;
Biography; Mathematicians",
subject-dates = "1893--1974",
tableofcontents = "The Life and Works of Cornelius Lanczos \\
\\
A Photographic Essay / / xvii \\
Cornelius Lanczos: A Biographical Essay / Barbara
Gellai / xxi \\
Cornelius Lanczos (1893-1974), and the Hungarian
Phenomenon in Science and Mathematics / Peter D. Lax /
xlix \\
The Roots of Cornelius Lanczos / George Marx / liii \\
Reminiscences of Cornelius Lanczos / Jon Todd / lviii
\\
Published Papers and Books of Cornelius Lanczos / / lx
\\
\\
Plenary Presentations: Computational Mathematics \\
\\
Lanczos and the FFT: A Discovery Before its Time /
James W. Cooley / 3 \\
Lanczos Algorithms for Large Scale Symmetric and
Nonsymmetric Matrix Eigenvalue Problems / Jane K.
Cullum / 11 \\
The Look-Ahead Lanczos Process for Nonsymmetric
Matrices and its Applications / Roland W Freund / 33
\\
The Lanczos and Conjugate Gradient Algorithms in Finite
Precision Arithmetic / Anne Greenbaum / 49 \\
The Lanczos Process and Pade Approximation / Martin H.
Gutknecht / 61 \\
The Tau Method and the Numerical Solution of
Differential Equations: Past Research and Recent
Research / Eduardo L. Ortiz / 77 \\
Krylov Subspace Processes, Krylov Subspace Methods, and
Iteration Polynomials / C. C. Paige / 83 \\
Do We Fully Understand the Symmetric Lanczos Algorithm
Yet? / Beresford N. Parlett / 93 \\
On Generalized Band Matrices and Their Inverses /
P{\'a}l R{\'o}sa, Francesco Romani, and Roberto
Bevilacqua / 109 \\
Theoretical Error Bounds and General Analysis of a Few
Lanczos-Type Algorithms / Youcef Saad / 123 \\
Lanczos and Linear Systems / G. W. Stewart / 135 \\
\\
Plenary Presentations: Theoretical Physics and
Astrophysics \\
\\
Integration on the Space of Connections Modulo Gauge
Transformations / Abbay Ashtekar, Donald Marolf, and
Jose Mourdo / 143 \\
Quasiclassical Domains in a Quantum Universe / James B.
Hartle / 161 \\
Gauge Invariant Energy-Momentum Tensor in Spinar
Electrodynamics / D. Petiot and Y. Takahashi / 173 \\
$\gamma$-Ray Bursts and Neutron Star Mergers / Tsvi
Piran / 187 \\
Lanczos's Early Contributions to Relativity and His
Relationship with Einstein / John Stachel / 201 \\
Topological Roots of Black Hole Entropy / Claudio
Teitelboim / 223 \\
Variational Principles, Local Symmetries, and Black
Hole Entropy / Robert M. Wald / 231 \\
\\
Mathematics Minisymposia \\
\\
Eigenvalue Computations: Theory and Algorithms / / 241
\\
Eigenvalue Computations: Applications / / 249 \\
Moments in Numerical Analysis / / 265 \\
Iterative Methods for Linear Systems / / 277 \\
Least Squares / / 301 \\
Software for Lanczos-based Algorithms / / 311 \\
Tau Method / / 335 \\
Chebyshev Polynomials / / 357 \\
Lanczos Methods in Control and Signal Processing / /
375 \\
Development of the FFT / / 393 \\
The FFT in Signal Processing / / 399 \\
Wavelets / / 411 \\
\\
Physics Minisymposia \\
\\
Computational Magnetohydrodynamics in Astrophysics / /
431 \\
Numerical Simulations of Collisionless Space Plasmas /
/ 453 \\
Detection of Gravitational Radiation from Astrophysical
Sources / / 477 \\
Lanczos $H$-tensor / / 489 \\
Cosmic Censorship / / 513 \\
Cauchy Problem of General Relativity / / 527 \\
Black Hole Evaporation and Thermodynamics / / 543 \\
The Problem of Time in Quantum Gravity / / 555 \\
New Variables and Loop Quantization / / 571 \\
Decoherence and the Foundations of Quantum Mechanics /
/ 589 \\
Open Questions in Particle Theory / / 603 \\
Supercollider Physics / / 621 \\
Symplectic Methods in Physics / / 633",
}
@Proceedings{Chatterji:1994:PIC,
editor = "S. D. Chatterji",
booktitle = "Proceedings of the International Congress of
Mathematicians: August 3--11, 1994, Z{\"u}rich,
Switzerland",
title = "Proceedings of the International Congress of
Mathematicians: August 3--11, 1994, {Z}{\"u}rich,
Switzerland",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "lxxi + 1605",
year = "1994",
ISBN = "3-7643-5153-5, 0-8176-5153-5",
ISBN-13 = "978-3-7643-5153-3, 978-0-8176-5153-4",
LCCN = "QA1 .I82 1994",
bibdate = "Fri Dec 20 18:43:45 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Two volumes.",
acknowledgement = ack-nhfb,
}
@Proceedings{Golub:1994:RAI,
editor = "Gene Golub and Anne Greenbaum and Mitchell Luskin",
booktitle = "{Recent advances in iterative methods: [papers from
the IMA Workshop on Iterative Methods for Sparse and
Structured Problems, held in Minneapolis, Minnesota,
February 24--March 1, 1992]}",
title = "{Recent advances in iterative methods: [papers from
the IMA Workshop on Iterative Methods for Sparse and
Structured Problems, held in Minneapolis, Minnesota,
February 24--March 1, 1992]}",
volume = "60",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 225",
year = "1994",
ISBN = "0-387-94252-1 (New York), 3-540-94252-1 (Berlin)",
ISBN-13 = "978-0-387-94252-0 (New York), 978-3-540-94252-8
(Berlin)",
LCCN = "QA297.8 .R43 1994",
MRclass = "65-06",
MRnumber = "95m:65001",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib",
series = "The IMA Volumes in Mathematics and its Applications",
URL = "http://zbmath.org/?q=an:0790.00015",
ZMnumber = "0790.00015",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
tableofcontents = "Some themes in Gene H. Golub's work on iterative
methods / Dianne P. O'Leary / 1 / \\
Computing the sparse singular value decomposition via
SVDPACK / Michael W. Berry / 13 \\
Gaussian quadrature applied to adaptive Chebyshev
iteration / D. Calvetti, G. H. Golub, and L. Reichel /
31 \\
Ordering effects on relaxation methods applied to the
discrete convection-diffusion equation / Howard C.
Elman and Michael P. Chernesky / 45 \\
On the error computation for polynomial based iteration
methods / Bernd Fischer and Gene H. Golub / 59 \\
Transpose-free quasi-minimal residual methods for
non-Hermitian linear systems / Roland W. Freund / 69
\\
Matrices that generate the same Krylov residual spaces
/ Anne Greenbaum and Zdenek Strakos / 95 \\
Incomplete block factorizations as preconditioners for
sparse SPD matrices / L. Yu. Kolotilina and A. Yu
Yeremin / 119 \\
How fast can iterative methods be? / Olavi Nevanlinna /
135 \\
Rational Krylov algorithms for nonsymmetric eigenvalue
problems / Axel Ruhe / 149 \\
Highly parallel preconditioners for general sparse
matrices / Youcef Saad / 165 \\
A two-stage iteration for solving nearly completely
decomposable Markov chains / G. W. Stewart, W. J.
Stewart and D. F. McAllister / 201 \\
Minimum residual modifications to Bi-CG and to the
preconditioner / Henk A. Van der Vorst / 217",
}
@Proceedings{Griffiths:1994:NAP,
editor = "D. F. (David Francis) Griffiths and G. A. (G.
Alistair) Watson",
booktitle = "{Numerical analysis 1993: proceedings of the 15th
Dundee Conference, June--July 1993}",
title = "{Numerical analysis 1993: proceedings of the 15th
Dundee Conference, June--July 1993}",
volume = "303",
publisher = pub-LONGMAN,
address = pub-LONGMAN:adr,
pages = "275",
year = "1994",
ISBN = "0-582-22568-X",
ISBN-13 = "978-0-582-22568-8",
ISSN = "0269-3674",
LCCN = "QA297 .D85 1993",
bibdate = "Mon Jan 2 16:37:00 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
library.ox.ac.uk:210/ADVANCE",
series = "Pitman research notes in mathematics series",
acknowledgement = ack-nhfb,
meetingname = "Dundee Biennial Conference on Numerical Analysis
(15th: 1993)",
remark = "The 15th Dundee Biennial Conference on Numerical
Analysis was held at the University of Dundee during
the 4 days June 29--July 2, 1993.",
subject = "Numerical analysis; Congresses",
tableofcontents = "J. W. Harrett \& Wenbin Liu: Finite Element
Approximation of Degenerate Quasilinear Elliptic and
Parabolic Problems / 1 \\
R. K. Beatson \& M. J. D. Powell: An Iterative Method
for Thin Plate Spline Interpolation that Employs
Approximations to Lagrange Functions / 17 \\
I. S. Duff: The Solution of Augmented Systems / 10 \\
C. M. Elliott \& A. R. Gardiner: One Dimensional Phase
Field Computations / 56 \\
J. de Frutos \& J. M. Sanz-Serna: Erring and being
Conservative / 75 \\
P. E. Gill, W. Murray, D. B. Poncele{\'o}n \& M. A.
Saunders: Solving Reduced KKT Systems in Barrier
Methods for Linear Programming / 89 \\
G. H. Golub \& Gerard Meurant: Matrices, Moments, and
Quadrature / 105 \\
J. Groeneweg \& M. N. Spijker: On the Error due to the
Stopping of the Newton Iteration in Implicit Linear
Multistep Methods / 157 \\
D. J. Higham: The Dynamics of a Discretised Nonlinear
Delay Differential Equation / 167 \\
A. R. Humphries, D. A. Jones \& A. M. Stuart:
Approximation of Dissipative Partial Differential
Equations over Long Time Intervals / 180 \\
N. K. Nichols: Differential--Algebraic Equations and
Control System Design / 208 \\
G. W. Stewart: $UTV$ Decompositions / 225 \\
M. J. Todd: A Lower Bound on the Number of Iterations
of an Interior-Point Algorithm for Linear Programming /
237 \\
P. Townsend \& M. F. Webster: Computational Analysis in
Rheological Flow Problems / 260 \\
List of Contributed Talks / / 267",
}
@Proceedings{Quarteroni:1994:DDM,
editor = "Alfio Quarteroni and others",
booktitle = "Domain Decomposition Methods in Science and
Engineering: The Sixth International Conference on
Domain Decomposition, June 15--19, 1992, Como, Italy",
title = "Domain Decomposition Methods in Science and
Engineering: The Sixth International Conference on
Domain Decomposition, June 15--19, 1992, Como, Italy",
volume = "157",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xxii + 484",
year = "1994",
DOI = "https://doi.org/10.1090/conm/157",
ISBN = "0-8218-5158-6, 0-8218-7748-8 (online)",
ISBN-13 = "978-0-8218-5158-6, 978-0-8218-7748-7 (online)",
LCCN = "QA402.2 .I55 1992",
bibdate = "Sat Oct 29 15:36:36 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "Contemporary Mathematics",
acknowledgement = ack-nhfb,
tableofcontents = "Domain decomposition methods using modified basis
functions / V. I. Agoshkov \\
https://doi.org/10.1090/conm/157/01400 : Uniform
convergence estimates for multigrid $V$-cycle
algorithms with less than full elliptic regularity /
James H. Bramble and Joseph E. Pasciak \\
https://doi.org/10.1090/conm/157/01401 : A three-field
domain decomposition method / F. Brezzi and L. D.
Marini \\
https://doi.org/10.1090/conm/157/01402 : Self-adaptive
coupling of mathematical models and/or numerical
methods / Claudio Canuto and Alessandro Russo \\
https://doi.org/10.1090/conm/157/01403 : Noniterative
domain decomposition for second order hyperbolic
problems / Clint N. Dawson and Todd F. Dupont \\
https://doi.org/10.1090/conm/157/01404 : Some recent
results on Schwarz type domain decomposition algorithms
/ Maksymilian Dryja and Olof B. Widlund \\
https://doi.org/10.1090/conm/157/01405 : Overlapping
domain decomposition methods for parabolic problems /
Yu. A. Kuznetsov \\
https://doi.org/10.1090/conm/157/01406 : Domain
decomposition and multilevel PCG method for solving
$3$-D fourth order problems / Jia Chang Sun \\
https://doi.org/10.1090/conm/157/01407 : Some two-grid
finite element methods / Jinchao Xu \\
https://doi.org/10.1090/conm/157/01408 : Interface
conditions for a kind of nonlinear elliptic-hyperbolic
problems / Gloria Aguilar and Francisco Lisbona \\
https://doi.org/10.1090/conm/157/01409 : A domain
decomposition for the transport equation / Lucia
Gastaldi \\
https://doi.org/10.1090/conm/157/1410 : Hybrid domain
decomposition with unstructured subdomains / Jan Mandel
\\
https://doi.org/10.1090/conm/157/01411 : Some Schwarz
algorithms for the $p$-version finite element method /
Luca F. Pavarino \\
https://doi.org/10.1090/conm/157/01412 : On the
robustness and efficiency of the fully adaptive
multigrid method / U. R{\"u}de \\
https://doi.org/10.1090/conm/157/01413 : Finite volume
variational formulation. Application to domain
decomposition methods / J.-M. Thomas and D. Trujillo
\\
https://doi.org/10.1090/conm/157/01414 : Multigrid
solvers on decomposed domains / Achi Brandt and Boris
Diskin \\
https://doi.org/10.1090/conm/157/01415 : Domain
decomposition preconditioners for convection diffusion
problems / Tony F. Chan and Tarek P. Mathew \\
https://doi.org/10.1090/conm/157/01416 : A domain
decomposition approach to solving the Helmholtz
equation with a radiation boundary condition / Oliver
Ernst and Gene H. Golub \\
https://doi.org/10.1090/conm/157/01417 : The dual Schur
complement method with well-posed local Neumann
problems / Charbel Farhat and Fran{\c{c}}ois-Xavier
Roux \\
https://doi.org/10.1090/conm/157/01418 : Implicit
domain decomposition algorithms for steady,
compressible aerodynamics / William D. Gropp, David E.
Keyes and Jon S. Mounts \\
https://doi.org/10.1090/conm/157/01419 : A new mixed
preconditioning method based on the clustered
element-by-element preconditioners / T. E. Tezduyar, M.
Behr, S. K. Aliabadi, S. Mittal and S. E. Ray \\
https://doi.org/10.1090/conm/157/1420 : A domain
decomposition method for the polar factorization of
vector fields / J.-D. Benamou and Y. Brenier \\
https://doi.org/10.1090/conm/157/01422 : An additive
Schwarz algorithm for piecewise Hermite bicubic
orthogonal spline collocation / B. Bialecki, X.-C. Cai,
M. Dryja and G. Fairweather \\
https://doi.org/10.1090/conm/157/01423 : An iterative
finite-element collocation method for parabolic
problems using domain decomposition / Mark C. Curran
\\
https://doi.org/10.1090/conm/157/01424 : A domain
decomposition method using sparse grids / Michael
Griebel \\
https://doi.org/10.1090/conm/157/01425 : Domain
decomposition for the Stokes equations in
streamfunction formulation / Wilhelm Heinrichs \\
https://doi.org/10.1090/conm/157/01426 : Overlapping
domain decomposition methods for the obstacle problem /
Yu. A. Kuznetsov, P. Neittaanm{\"a}ki and P. Tarvainen
\\
https://doi.org/10.1090/conm/157/01427 : An iteration
scheme for nonsymmetric interface operator / C.-H. Lai
\\
https://doi.org/10.1090/conm/157/01428 : Factorization
of the convection-diffusion operator and a (possibly)
nonoverlapping Schwarz method / F. Nataf and F. Rogier
\\
https://doi.org/10.1090/conm/157/01429 : Domain
decomposition method coupling finite elements and
preconditioned Chebyshev collocation to solve elliptic
problems / C. R. Schneidesch, M. O. Deville and E. H.
Mund \\
https://doi.org/10.1090/conm/157/01430 : Additive
Schwarz methods and acceleration with variable weights
/ Tsi Min Shih, Chin Bo Liem and Tao L{\"u} \\
https://doi.org/10.1090/conm/157/01431 : Parallel
domain decomposition for incompressible fluid dynamics
/ Paul F. Fischer \\
https://doi.org/10.1090/conm/157/01432 : Experiences
with domain decomposition in three dimensions:
overlapping Schwarz methods / William D. Gropp and
Barry F. Smith \\
https://doi.org/10.1090/conm/157/01433 : Parallel
iterative solution of symmetric coupled FE/BE-equations
via domain decomposition / U. Langer \\
https://doi.org/10.1090/conm/157/01434 : Implementation
of domain decomposition techniques on nCUBE2 parallel
machine / A. Brambilla, C. Carlenzoli, G. Gazzaniga, P.
Gervasio and G. Sacchi \\
https://doi.org/10.1090/conm/157/01435 : A class of
domain decomposition preconditioners for massively
parallel computers / Patrick Ciarlet, Jr. and
G{\'e}rard Meurant \\
https://doi.org/10.1090/conm/157/01436 : A domain
decomposition environment for local time dependent
problems / F. Dellagiacoma, S. Paoletti, F. Poggi and
M. Vitaletti \\
https://doi.org/10.1090/conm/157/01437 : A parallel
element-by-element method for large-scale computations
with $h$-$p$-finite elements / S. Foresti, S.
Hassanzadeh and V. Sonnad \\
https://doi.org/10.1090/conm/157/01438 : Coupling
Boltzmann and Euler equations without overlapping /
J.-F. Bourgat, P. Le Tallec, B. Perthame and Y. Qiu \\
https://doi.org/10.1090/conm/157/01439",
}
@Proceedings{Buxton:1996:CVE,
editor = "Bernard Buxton and Roberto Cipolla",
booktitle = "Computer vision, {ECCV '96}: 4th European Conference
on Computer Vision, Cambridge, {UK}, April 15--18,
1996: proceedings",
title = "Computer vision, {ECCV} '96: 4th European Conference
on Computer Vision, Cambridge, {UK}, April 15--18,
1996: proceedings",
volume = "1064--1065",
publisher = pub-SV,
address = pub-SV:adr,
pages = "various",
year = "1996",
ISBN = "3-540-61122-3 (vol. 1), 3-540-61123-1 (vol. 2)",
ISBN-13 = "978-3-540-61122-6 (vol. 1), 978-3-540-61123-3 (vol.
2)",
LCCN = "TA1634.E97 1996",
bibdate = "Wed May 7 11:56:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Two volumes.",
series = "Lecture notes in computer science",
acknowledgement = ack-nhfb,
conflocation = "Cambridge, UK; 14-18 April 1996",
conftitle = "Proceedings of Fourth European Conference on Computer
Vision. ECCV `96",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
pubcountry = "Germany",
sponsororg = "Eur. Vision Soc.; British Machine Vision Assoc",
tableofcontents = "Volume 1 \\
Self-calibration from image triplets \\
Parallax geometry of pairs of points for 3D scene
analysis \\
Euclidean 3D reconstruction from image sequences with
variable focal lengths \\
Eigenfaces vs. Fisherfaces: Recognition using class
specific linear projection \\
Rapid object indexing and recognition using enhanced
geometric hashing \\
Recognition of geons by parametric deformable contour
models \\
Automatic extraction of generic house roofs from high
resolution aerial imagery \\
Three dimensional object modeling via minimal surfaces
\\
Class based reconstruction techniques using singular
apparent contours \\
Reliable surface reconstruction from multiple range
images \\
Shape from appearance: A statistical approach to
surface shape estimation \\
Volumic segmentation using hierarchical representation
and triangulated surface \\
Oriented projective geometry for computer vision \\
Fast computation of the fundamental matrix for an
active stereo vision system \\
On binocularly viewed occlusion junctions \\
Understanding the shape properties of trihedral
polyhedra \\
Nonlinear scale-space from n-dimensional sieves \\
Hierarchical curve reconstruction. Part I: Bifurcation
analysis and recovery of smooth curves \\
Texture feature coding method for classification of
liver sonography \\
Local appropriate scale in morphological scale-space
\\
Scale-space with casual time direction \\
Tracing crease curves by solving a system of
differential equations \\
Flows under min/max curvature flow and mean curvature:
Applications in image processing \\
Decomposition of the Hough transform: Curve detection
with efficient error propagation \\
Image retrieval using scale-space matching \\
Optimal surface smoothing as filter design \\
Segmentation in dynamic image sequences by isolation of
coherent wave profiles \\
Texture segmentation using local energy in wavelet
scale space \\
Tracking medical 3D data with a deformable parametric
model \\
EigenTracking: Robust matching and tracking of
articulated objects using a view-based representation
\\
Contour tracking by stochastic propagation of
conditional density \\
Learning dynamics of complex motions from image
sequences \\
Quantitative analysis of grouping processes \\
Geometric saliency of curve correspondences and
grouping of symmetric contours \\
Computing contour closure \\
Visual organization of illusory surfaces \\
Uncalibrated relief reconstruction and model alignment
from binocular disparities \\
Dense depth map reconstruction: A minimization and
regularization approach which preserves discontinuities
\\
Stereo without search \\
Informative views and sequential recognition \\
Unsupervised texture segmentation using selectionist
relaxation \\
Robust affine structure matching for 3D object
recognition \\
Automatic face recognition: What representation? \\
Genetic search for structural matching \\
Automatic selection of reference views for image-based
scene representations \\
Object recognition using subspace methods \\
Detecting, localizing and grouping repeated scene
elements from an image \\
Image recognition with occlusions \\
Silhouette-based object recognition with occlusion
through curvature scale space \\
A focused target segmentation paradigm \\
Generalized image matching: Statistical learning of
physically-based deformations \\
Reasoning about occlusions during hypothesis
verification \\
Object recognition using multidimensional receptive
field histograms \\
Normalization by optimization \\
Extracting curvilinear structures: A differential
geometric approach \\
Affine / photometric invariants for planar intensity
patterns \\
Image synthesis from a single example image \\
Complexity of indexing: Efficient and learnable large
database indexing \\
Spatiotemporal representations for visual navigation
\\
Decoupling the 3D motion space by fixation \\
Automatic singularity test for motion analysis by an
information criterion \\
Shape ambiguities in structure from motion \\
Volume 2 \\
Colour constancy for scenes with varying illumination
\\
Color angular indexing \\
Bidirectional reflection distribution function
expressed in terms of surface scattering modes \\
Generalizing Lambert's Law for smooth surfaces \\
Local scale control for edge detection and blur
estimation \\
Regularization, scale-space, and edge detection filters
\\
Direct differential range estimation using optical
masks \\
Generalised epipolar constraints \\
Object models from contour sequences \\
Directions of motion fields are hardly ever ambiguous
\\
Euclidean reconstruction: From paraperspective to
perspective \\
Optical flow and phase portrait methods for
environmental satellite image sequences \\
Refinement of optical flow estimation and detection of
motion edges \\
Reliable extraction of the camera motion using
constraints on the epipole \\
Accuracy vs. efficiency trade-offs in optical flow
algorithms \\
Rigorous bounds for two-frame structure from motion \\
The rank 4 constraint in multiple (?3) view geometry
\\
Using singular displacements for uncalibrated monocular
visual systems \\
Duality of multi-point and multi-frame geometry:
Fundamental shape matrices and tensors \\
On the appropriateness of camera models \\
Ground plane motion camera models \\
Snakes and splines for tracking non-rigid heart motion
\\
Local quantitative measurements for cardiac motion
analysis \\
Application of model based image interpretation methods
to diabetic neuropathy \\
Global alignment of MR images using a scale based
hierarchical model \\
Reconstruction of blood vessel networks from x-ray
projections and a vascular catalogue \\
Combining multiple motion estimates for vehicle
tracking \\
Visual surveillance monitoring and watching \\
A robust active contour model for natural scene contour
extraction with automatic thresholding \\
A maximum-likelihood approach to visual event
classification \\
Measures for silhouettes resemblance and representative
silhouettes of curved objects \\
Real-time lip tracking for audio-visual speech
recognition applications \\
Matching object models to segments from an optical flow
field \\
Quantification of articular cartilage from MR images
using active shape models \\
Direct methods for self-calibration of a moving stereo
head \\
Dense reconstruction by zooming \\
Telecentric optics for computational vision \\
Recognition, pose and tracking of modelled polyhedral
objects by multi-ocular vision \\
Locating objects of varying shape using statistical
feature detectors \\
Generation of semantic regions from image sequences \\
Tracking of occluded vehicles in traffic scenes \\
Imposing hard constraints on soft snakes \\
X Vision: Combining image warping and geometric
constraints for fast visual tracking \\
Human body tracking by monocular vision \\
Computational perception of scene dynamics \\
A filter for visual tracking based on a stochastic
model for driver behaviour \\
Elastically adaptive deformable models \\
Statistical feature modelling for active contours \\
Motion deblurring and super-resolution from an image
sequence \\
Uncalibrated visual tasks via linear interaction \\
Finding naked people \\
Acquiring visual-motor models for precision
manipulation with robot hands \\
A system for reconstruction of missing data in image
sequences using sampled 3D AR models and MRF motion
priors \\
Elimination of specular surface-reflectance using
polarized and unpolarized light \\
Separating real and virtual objects from their
overlapping images \\
Goal-directed video metrology \\
Reconstructing polyhedral models of architectural
scenes from photographs \\
Algebraic varieties in multiple view geometry \\
3D model acquisition from extended image sequences \\
Computing structure and motion of general 3D curves
from monocular sequences of perspective images \\
A factorization based algorithm for multi-image
projective structure and motion",
treatment = "T Theoretical or Mathematical",
}
@Book{Griffiths:1996:NAR,
editor = "D. F. (David Francis) Griffiths and G. A. Watson",
booktitle = "Numerical analysis: {A. R. Mitchell} 75th birthday
volume",
title = "Numerical analysis: {A. R. Mitchell} 75th birthday
volume",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "ix + 370",
year = "1996",
ISBN = "981-02-2719-1, 981-281-287-3 (e-book)",
ISBN-13 = "978-981-02-2719-7, 978-981-281-287-2 (e-book)",
LCCN = "QA297 .N827 1996",
bibdate = "Fri Oct 17 06:21:22 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
tableofcontents = "A. R. Mitchell: Some Biographical and Mathematical
Notes / D. F. Griffiths, J. D. Lambert, G. A. Watson
and G. Fairweather \\
Addendum: The Finite Element Method and Computer Aided
Geometric Design / R. E. Barnhill \\
Appendix 1: List of Publications of A. R. Mitchell \\
Appendix 2: PhD Students of A. R. Mitchell \\
Fixed Points and Spurious Modes of a Nonlinear
Infinite-Step Map / M. A. Aves, P. J. Davies and D. J.
Higham \\
Rugge-Kutta Methods as Mathematical Objects / J. C.
Butcher \\
Runge-Kutta Methods on Manifolds / M. Calvo, A. Iserles
and A. Zanna \\
Numerical Solutions of One and Two Dimensional
Hyperbolic Systems Modelling a Fluidized Bed / I.
Christie, G. H. Ganser and J. W. Wilder \\
Numerical Experiments for a Nonoverlapping Domain
Decomposition Method for Partial Differential Equations
/ J. Douglas, Jr. and D. Yang \\
A Piecewise Uniform Adaptive Grid Algorithm for
Nonlinear Dispersive Wave Equations / E. S. Fraga and
J. Ll. Morris",
}
@Proceedings{Meinguet:1996:NAN,
editor = "Jean Meinguet",
booktitle = "{Numerical analysis: a numerical analysis conference
in honour of Jean Meinguet}",
title = "{Numerical analysis: a numerical analysis conference
in honour of Jean Meinguet}",
publisher = "Belgian Mathematical Society",
address = "Brussels, Belgium",
pages = "96 + 2",
year = "1996",
LCCN = "QA297 .N825 1996",
bibdate = "Mon May 24 09:18:39 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/taussky-todd-olga.bib;
z3950.loc.gov:7090/Voyager",
series = "Bulletin of the Belgian Mathematical Society, Simon
Stevin",
acknowledgement = ack-nhfb,
remark = "This volume is published as a supplement to the
Bulletin of the Belgian Mathematical Society, Simon
Stevin \ldots{} December 1996.",
subject = "numerical analysis; congresse",
tableofcontents = "Matrix computation and the theory of moments / Gene
H. Golub \\
Convergence of rational interpolants / Herbert Stahl
\\
Variations on Richardson's method and acceleration /
Claude Brezinski \\
Andr{\'e} Louis Cholesky / Claude Brezinski \\
On the convergence of multivariate Pad{\'e}
approximants / Annie Cuyt, Doron Lubinsky \\
Least-squares fitting of circles and ellipses / Walter
Gander, Gene H. Golub, Rolf Strebel \\
Entropy of Hermite polynomials with application to the
harmonic oscillator / Walter van Assche",
}
@Proceedings{Chan:1997:IMS,
editor = "Raymond H. Chan and Tony F. Chan and Gene H. (Gene
Howard) Golub",
booktitle = "Iterative methods in scientific computing",
title = "Iterative methods in scientific computing",
publisher = pub-SV,
address = pub-SV:adr,
pages = "vii + 384",
year = "1997",
ISBN = "981-3083-08-5 (paperback)",
ISBN-13 = "978-981-3083-08-0 (paperback)",
LCCN = "QA297.8 .I835 1997",
bibdate = "Sat Dec 31 10:07:00 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Winter School on Iterative Methods in Scientific
Computing and Their Applications (1995, Hong Kong).",
subject = "Iterative methods (Mathematics); Data processing;
Congresses",
tableofcontents = "Iterative methods for linear systems and
implementation on parallel computers / Henk A. Van der
Vorst \\
Matrices, moments and quadrature / Gene H. Golub \\
Wavelets from filter banks / Gilbert Strang \\
Constructing linear algebra software libraries for
high-performance computers / Jack J. Dongarra and David
W. Walker \\
An introduction to multigrid convergence theory /
Jinchao Xu \\
Preconditioning Toeplitz systems with circulant
preconditioners / Raymond H. Chan and Michael K. Ng",
}
@Proceedings{Duff:1997:SAN,
editor = "Iain S. Duff and G. Alistair Watson",
booktitle = "The state of the art in numerical analysis",
title = "The state of the art in numerical analysis",
volume = "63",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xiv + 562",
year = "1997",
ISBN = "0-19-850014-9",
ISBN-13 = "978-0-19-850014-8",
LCCN = "QA297.S775 1997",
MRclass = "65-06 (00B25)",
MRnumber = "MR1628339 (99a:65008)",
bibdate = "Thu Sep 16 11:59:48 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/gould-nicholas-ian.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
note = "Based on the proceedings of a conference on the state
of the art in numerical analysis. Organized by the
Institute of Mathematics and Its Applications and held
at York University in April 1996.",
series = "The Institute of Mathematics and Its Applications
conference series: new series",
URL = "https://global.oup.com/academic/product/the-state-of-the-art-in-numerical-analysis-9780198500148",
acknowledgement = ack-nhfb,
tableofcontents = "1. Recent Developments in Dense Numerical Linear
Algebra / N. J. Higham \\
2. Sparse Numerical Linear Algebra: Direct Methods and
Preconditioning / I. S. Duff \\
3. Closer to the Solution: Iterative Linear Solvers /
G. H. Golub and H. A. van der Vorst \\
4. 150 Years Old and Still Alive: Eigenproblems / H. A.
van der Vorst and G. H. Golub \\
5. Geometric Integration / J. M. Sanz-Serna \\
6. Convergence and Stability in the Numerical
Approximation of Dynamical Systems / A. Stuart \\
7. Beyond the Classical Theory of Computational
Ordinary Differential Equations / A. Iserles \\
8. Numerical Analysis of Volterra Functional and
Integral Equations / C. T. H. Baker \\
9. The Numerical Solution of Boundary Integral
Equations / K. E. Atkinson \\
10. Aspects of Approximation with Emphasis on the
Univariate Case / G. A. Watson \\
11. A Review of Methods for Multivariable Interpolation
at Scattered Data Points / M. J. D. Powell \\
12. Large Scale Unconstrained Optimization / J. Nocedal
\\
13. Interior Point Methods for Linear and Nonlinear
Programming / D. F. Shanno and E. M. Simantiraki \\
14. Methods for Nonlinear Constraints in Optimization
Calculations / A. R. Conn, N. I. M. Gould and Ph. L.
Toint \\
15. Stabilization Techniques and Subgrid Scales
Capturing, F. Brezzi, L. P. Franca / T. J. R. Hughes
and A. Russo \\
16. Approximation of Curvature Dependent Interface
Motion / C. M. Elliott \\
17. Finite Element Methods for Hyperbolic Problems: a
Posteriori Error Analysis and Adaptivity / E. S{\"u}li
and P. Houston \\
18. Approximation of Multidimensional Hyperbolic
Partial Differential Equations / K. W. Morton \\
19. Algorithms in Tomography / F. Natterer \\
20. Partial Differential Equations and Image Iterative
Filtering / F. Guichard and J.-M. Morel",
}
@Proceedings{Golub:1997:PWS,
editor = "Gene Howard Golub and Shui-Hong Lui and Franklin T.
Luk and Robert James Plemmons",
booktitle = "{Proceedings of the Workshop on Scientific Computing:
Hong Kong, 10--12 March, 1997}",
title = "{Proceedings of the Workshop on Scientific Computing:
Hong Kong, 10--12 March, 1997}",
publisher = pub-SV,
address = pub-SV:adr,
pages = "ix + 315",
year = "1997",
ISBN = "981-3083-60-3 (paperback)",
ISBN-13 = "978-981-3083-60-8 (paperback)",
LCCN = "QA75.5 .W626 1997",
bibdate = "Sun Apr 13 08:35:50 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0815/97034830-d.html;
http://www.loc.gov/catdir/enhancements/fy0815/97034830-t.html",
abstract = "This book concerns modern methods in scientific
computing and linear algebra, relevant to image and
signal processing. For these applications, it is
important to consider ingredients such as: (1)
sophisticated mathematical models of the problems,
including a priori knowledge, (2) rigorous mathematical
theories to understand the difficulties of solving
problems which are ill-posed, and (3) fast algorithms
for either real-time or data-massive computations. Such
are the topics brought into focus by these proceedings
of the Workshop on Scientific Computing (held in Hong
Kong on March 10--12, 1997, the sixth in such series of
Workshops held in Hong Kong since 1990), where the
major themes were on numerical linear algebra, signal
processing, and image processing.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
meetingname = "Workshop on Scientific Computing (6th : 1997 : Hong
Kong)",
subject = "Electronic data processing; Congresses; Science; Data
processing",
tableofcontents = "Tikhonov regularization for large scale problems
(G. H. Golub and U. von Matt)\\
Numerical stability of some fast algorithms for
structured matrices (R. P. Brent)\\
The role of coordinates in accurate computation of
discontinuous flow (W. H. Hui)\\
Regularized blind deconvolution using recursive inverse
filtering (M. K. Ng and others)\\
Solution of linear systems arising in nonlinear image
deblurring (C. R. Vogel)\\
3-D Jacobi rotation method for eigenvalue problems of
matrices (D. Y. Cai and W. M. Xue)\\
Wavelets, signal processing and textile surfaces (H.
Kraus)\\
Efficient image compression scheme using tree structure
wavelet transforms (J. M. Li and J. S. Jin)\\
A note on adaptive restarting procedure for pseudo
residual algorithms (T. Nodera and T. Inadu)\\
Adaptive methods for singular perturbation problems (T.
Tang and D. M. Sloan)\\
Image reconstruction from projections based on wavelet
decomposition (J. H. Yin); \ldots{}",
}
@Proceedings{VanHuffel:1997:RAT,
editor = "Sabine {Van Huffel}",
booktitle = "Recent advances in total least squares techniques and
errors-in-variables modeling [{Proceedings of the
Second International Workshop on Total Least Squares
and Errors-in-Variables Modeling, Leuven, Belgium,
August 21--24, 1996}]",
title = "Recent advances in total least squares techniques and
errors-in-variables modeling [{Proceedings of the
Second International Workshop on Total Least Squares
and Errors-in-Variables Modeling, Leuven, Belgium,
August 21--24, 1996}]",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xxii + 377",
year = "1997",
ISBN = "0-89871-393-5",
ISBN-13 = "978-0-89871-393-0",
LCCN = "QA275 .R4 1997",
bibdate = "Tue May 8 11:30:40 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Proceedings of the Second International Workshop on
Total Least Squares and Errors-in-Variables Modeling,
Leuven, Belgium, August 21--24, 1996.",
subject = "Least squares; Congresses; Error analysis
(Mathematics)",
}
@Proceedings{Gautschi:1999:ACO,
editor = "Walter Gautschi and Gene H. Golub and Gerhard Opfer",
booktitle = "Applications and computation of orthogonal
polynomials: conference at the Mathematical Research
Institute Oberwolfach, Germany, March 22--28, 1998",
title = "Applications and computation of orthogonal
polynomials: conference at the Mathematical Research
Institute Oberwolfach, Germany, March 22--28, 1998",
volume = "131",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xii + 268",
year = "1999",
ISBN = "3-7643-6137-9, 0-8176-6137-9 (paperback)",
ISBN-13 = "978-3-7643-6137-2, 978-0-8176-6137-3 (paperback)",
LCCN = "QA404.5 .A67 1999",
bibdate = "Thu Oct 16 11:26:28 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
series = "International series of numerical mathematics",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
tableofcontents = "The sensitivity of least squares polynomial
approximation / Bernhard Beckermann and Edward B. Saff
\\
Transpose-free look-ahead algorithms for Lanczos'
method / Claude Brezinski and Michela Redivo-Zaglia \\
Applications of anti-Gauss quadrature rules in linear
algebra / Daniela Calvetti, Lothar Reichel and Fiorella
Sgallari \\
Stieltjes polynomials and the error of Gauss--Kronrod
quadrature formulas / Sven Ehrich \\
Fast solution of confluent Vandermonde-like linear
systems using polynomial arithmetic / Hans-J{\"u}rgen
Fischer \\
On discrete polynomial least-squares approximation in
moving time windows / Erich Fuchs \\
Quadrature rules based on $s$-orthogonal polynomials
for evaluating integrals with strong singularities /
Laura Gori and Elisabetta Santi \\
Gegenbauer weight functions admitting $L_2$ Duffin and
Schaeffer type inequalities / David B. Hunter and Geno
Nikolov \\
Questions related to Gaussian quadrature formulas and
two-term recursions / Dirk P. Laurie \\
Construction and computation of a new set of orthogonal
polynomials / Shikang Li \\
Fourier transforms of orthogonal polynomials of
singular continuous spectral measures / Giorgio Mantica
\\
On a sequence of fast decreasing polynomial operators /
Hrushikesh N. Mhaskar and J{\"u}rgen Prestin \\
Muntz orthogonal polynomials and their numerical
evaluation / Gradimir V. Milovanovic \\
Positivity of Gauss--Kronrod formulae for a certain
ultraspherical weight function / Knut Petras \\
A Christoffel--Darboux-type formula for Szego
polynomials and polynomial evaluation / Michael-Ralf
Skrzipek \\
Applications of tensor-valued tri-variate Hermite
polynomials and spherical harmonics in the kinetic
theory of gases / Kurt Suchy \\
Indeterminate moment problems and a conjecture on the
growth of the entire functions in the Nevanlinna
parametrization / Galliano Valent \\
Spectral methods based on nonclassical orthogonal
polynomials / J. Andre C. Weideman",
}
@Book{Engquist:2001:MUB,
editor = "Bj{\"o}rn Engquist and Wilfried Schmid",
booktitle = "Mathematics unlimited: 2001 and beyond",
title = "Mathematics unlimited: 2001 and beyond",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xv + 1237",
year = "2001",
ISBN = "3-540-66913-2",
ISBN-13 = "978-3-540-66913-5",
LCCN = "QA7 .M32423 2001",
bibdate = "Mon Oct 31 14:18:00 MST 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
Jonathan/0000-0002-1263-0646",
subject = "Mathematics; Science; Math\'ematiques; Sciences",
tableofcontents = "Nonlinear Continuum Physics / Stuart S. Antman \\
Computational Mechanics: Where Is It Going? / Ivo
Babu{\v{s}}ka and J. Tinsley Oden \\
From Finite Sets to Feynman Diagrams / John C. Baez and
James Dolan \\
Experimental Mathematics: Recent Developments and
Future Outlook / David H. Bailey and Jonathan M.
Borwein \\
Mathematical Aspects of Econometrics / Badi H. Baltagi
\\
Quantum Information / Ole E. Barndorff-Nielsen, Richard
D. Gill and Peter E. Jupp \\
$p$-Adic $L$-Functions of Modular Elliptic Curves /
Massimo Bertolini and Henri Darmon \\
Basis for a New Relationship Between Mathematics and
Society / Jean-Pierre Bourguignon \\
New Issues in the Mathematics of Control / Roger
Brockett",
}
@Book{Golub:2002:IMM,
author = "Gene H. Golub and Lev A. Krukier",
booktitle = "Iterative Methods and Matrix Computations",
title = "Iterative Methods and Matrix Computations",
publisher = "Rostov State University",
address = "Rostov-on-Don, Russia",
pages = "????",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed May 07 08:25:11 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Lectures of Instructor and Abstracts of Young
Scientists (2--9 June, 2002).",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Book{Chan:2007:MMC,
editor = "Raymond H. Chan and Chen Greif and Dianne P. O'Leary",
booktitle = "Milestones in Matrix Computation: the Selected Works
of {Gene H. Golub} with Commentaries",
title = "Milestones in Matrix Computation: the Selected Works
of {Gene H. Golub} with Commentaries",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xi + 565 + 3",
year = "2007",
ISBN = "0-19-920681-3",
ISBN-13 = "978-0-19-920681-0",
LCCN = "QA188 .G67 2007",
MRclass = "65-06 (01A75 65Fxx)",
MRnumber = "MR2281939 (2008b:65004)",
MRreviewer = "David Scott Watkins",
bibdate = "Sat Apr 07 10:23:33 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib",
URL = "http://www.loc.gov/catdir/enhancements/fy0737/2007276086-d.html",
abstract = "The text presents and discusses some of the most
influential papers in Matrix Computation authored by
Gene H. Golub, one of the founding fathers of the
field. The collection of 21 papers in divided into five
main areas: iterative methods for linear systems,
solution of least squares problems, matrix
factorizations and applications, orthogonal polynomials
and quadrature, and eigenvalue problems an commentaries
for each area are provided by leading experts: Anne
Greenbaum, {\AA}ke Bj{\"o}rck, Nicholas Higham, Walter
Gautschi, and G. W. (Pete) Stewart. Comments on each
paper are also provided by the original authors,
providing the reader with historical information on how
the paper came to be written and under what
circumstances the collaboration was undertaken.
Including a brief biography and facsimiles of the
original papers, this text will be of great interest to
students and researchers in numerical analysis and
scientific computation.",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
tableofcontents = "List of Plates / x \\
I: Gene H. Golub \\
1 Gene H. Golub Biography, by Chen Greif / 3 \\
2 Publications of Gene H. Golub / 13 \\
3 Major Awards / 30 \\
4 Students of Gene H. Golub / 32 \\
II: Iterative Methods for Linear Systems \\
5 Commentary, by Anne Greenbaum / 35 \\
References / 43 \\
6 Chebyshev semi-iterative methods, successive
over-relaxation iterative methods, and second-order
Richardson iterative methods, Parts I and II (with R.
S. Varga) / 45 \\
7 A generalized conjugate gradient method for
non-symmetric systems of linear equations (with Paul
Concus) / 68 \\
8 A generalized conjugate gradient method for the
numerical solution of elliptic partial differential
equations (with Paul Concus and Dianne P. O'Leary) / 79
\\
9 Hermitian and Skew-Hermitian Splitting Methods for
Non-Hermitian Positive Definite Linear Systems (with
Zhong-Zhi Bai and Michael K. Ng) / 102 \\
III: Solution of Least Squares Problems \\
10 Commentary, by {\AA}ke Bj{\"o}rck / 129 \\
References / 141 \\
11 Numerical methods for solving linear least squares
problems / 148 \\
12 Singular value decomposition and least squares
solutions (with C. Reinsch) / 160 \\
13 The differentiation of pseudo-inverses and
non-linear least squares problems whose variables
separate (with V. Pereyra) / 181 \\
14 Generalized cross-validation as a method for
choosing a good ridge parameter (with M. Heath and G.
Wahba) / 202 \\
15 An analysis of the total least squares problem (with
C. Van Loan) / 213 \\
IV: Matrix Factorizations and Applications \\
16 Commentary, by Nicholas Higham / 227 \\
References / 233 \\
17 Calculating the singular values and pseudo-inverse
of a matrix (with W. Kahan) / 236 \\
18 The simplex method of linear programming using $ L U
$ decomposition (with R. H. Bartels) / 257 \\
19 On direct methods for solving Poisson's equation
(with B. L. Buzbee and C. W. Nielson) / 261 \\
20 Numerical methods for computing angles between
linear subspaces (with {\AA}. Bj{\"o}rck) / 292 \\
21 Methods for modifying matrix factorizations (with P.
E. Gill, W. Murray and M. A. Saunders) / 309 \\
V: Orthogonal Polynomials and Quadrature \\
22 Commentary, by Walter Gautschi / 345 \\
References / 354 \\
23 Calculation of Gauss quadrature rules (with J. H.
Welsch) / 359 \\
24 Matrices, moments, and quadrature (with G{\'e}rard
Meurant) / 380 \\
25 Computation of Gauss--Kronrod Quadrature Rules (with
D. Calvetti, W. B. Gragg and L. Reichel) / 434 \\
VI: Eigenvalue Problems \\
26 Commentary, by G. W. Stewart / 457 \\
References / 465 \\
27 Some modified matrix eigenvalue problems / 467 \\
28 Ill-conditioned eigensystems and the computation of
the Jordan canonical form (with J. H. Wilkinson) / 485
\\
29 The block Lanczos method for computing eigenvalues
(with R. Underwood) / 528 \\
30 The numerically stable reconstruction of a Jacobi
matrix from spectral data (with C. de Boor) / 546 Index
/ 563",
}
@Proceedings{Du:2007:SSA,
editor = "Ding-Zhu Du and Charles Farbat and Walter Murray and
Michael Overton and Haesun Park and Michael Saunders
and James Varah",
booktitle = "{STANFORD 50: State of the Art \& Future Directions of
Computational Mathematics \& Numerical Computing: A
conference celebrating the 50th anniversary George
Forsythe's arrival at Stanford and Gene Golub's 75th
birthday, Stanford University, March 29--31, 2007}",
title = "{STANFORD 50: State of the Art \& Future Directions of
Computational Mathematics \& Numerical Computing: A
conference celebrating the 50th anniversary George
Forsythe's arrival at Stanford and Gene Golub's 75th
birthday, Stanford University, March 29--31, 2007}",
publisher = "????",
address = "????",
pages = "????",
year = "2007",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Apr 07 09:04:27 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
acknowledgement = ack-nhfb,
}
