%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author-1 = "Nelson H. F. Beebe", %%% author-2 = "Stefano Foresti", %%% version = "1.81", %%% date = "10 October 2019", %%% time = "07:04:11 MDT", %%% filename = "golub-gene-h.bib", %%% address-1 = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% address-2 = "Center for High-Performance Computing %%% University of Utah %%% Salt Lake City, UT 84112 %%% USA", %%% telephone-1 = "+1 801 581 5254", %%% telephone-2 = "+1 801 581 3173", %%% FAX-1 = "+1 801 581 4148", %%% FAX-2 = "+1 801 585 5366", %%% URL-1 = "http://www.math.utah.edu/~beebe", %%% checksum = "10537 15975 73363 731808", %%% email-1 = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% email-2 = "stefano at chpc.utah.edu (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography, linear algebra, numerical %%% analysis, singular value decomposition, SVD", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a fairly complete bibliography of %%% publications of the late Gene Howard Golub %%% (February 29, 1932--November 16, 2007). %%% %%% Part 1 covers his publications, and Part 2 %%% covers publications about him by others. %%% %%% At version 1.81, the year coverage looked %%% like this: %%% %%% 1959 ( 1) 1980 ( 8) 2001 ( 9) %%% 1960 ( 0) 1981 ( 5) 2002 ( 8) %%% 1961 ( 2) 1982 ( 8) 2003 ( 10) %%% 1962 ( 2) 1983 ( 8) 2004 ( 12) %%% 1963 ( 3) 1984 ( 7) 2005 ( 14) %%% 1964 ( 1) 1985 ( 5) 2006 ( 13) %%% 1965 ( 7) 1986 ( 4) 2007 ( 16) %%% 1966 ( 1) 1987 ( 14) 2008 ( 11) %%% 1967 ( 2) 1988 ( 9) 2009 ( 7) %%% 1968 ( 3) 1989 ( 14) 2010 ( 2) %%% 1969 ( 9) 1990 ( 17) 2011 ( 2) %%% 1970 ( 7) 1991 ( 22) 2012 ( 0) %%% 1971 ( 7) 1992 ( 16) 2013 ( 2) %%% 1972 ( 3) 1993 ( 13) 2014 ( 0) %%% 1973 ( 16) 1994 ( 18) 2015 ( 0) %%% 1974 ( 8) 1995 ( 8) 2016 ( 2) %%% 1975 ( 6) 1996 ( 13) 2017 ( 0) %%% 1976 ( 13) 1997 ( 19) 2018 ( 1) %%% 1977 ( 13) 1998 ( 10) 2019 ( 1) %%% 1978 ( 12) 1999 ( 16) %%% 1979 ( 19) 2000 ( 7) %%% %%% Article: 276 %%% Book: 29 %%% InBook: 1 %%% InCollection: 22 %%% InProceedings: 62 %%% Misc: 2 %%% PhdThesis: 1 %%% Proceedings: 60 %%% TechReport: 33 %%% %%% Total entries: 486 %%% %%% This bibliography was collected from %%% multiple sources: %%% %%% * the authors' own files; %%% * the TeX User Group bibliography %%% collection on ftp.math.utah.edu in %%% /pub/tex/bib; %%% * the very large Computer Science %%% bibliography collection on ftp.ira.uka.de %%% in /pub/bibliography, to which many people %%% have contributed; %%% * the ACM Computing Archive CD ROM, %%% covering literature of the 1980s; %%% * the IEEE Inspec CD ROMs for 1989--1996; %%% * Internet library catalogs, including %%% University of California MELVYL, Stanford %%% University RLIN, Library of Congress, %%% OCLC; %%% * the OCLC Contents1st and Article1st %%% databases; %%% * the AMS MathSciNet database; %%% * Gene Golub's personal curriculum vita %%% file. %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% In this bibliography, entries are sorted %%% first by ascending year, and within each %%% year, alphabetically by author or editor, %%% and then, if necessary, by the 3-letter %%% abbreviation at the end of the BibTeX %%% citation tag, using the bibsort -byyear %%% utility. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi"}

%%% ==================================================================== %%% Acknowledgement abbreviations:

@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|http://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|"}

%%% ==================================================================== %%% Institutional abbreviations:

@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"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-ACTA-NUMERICA= "Acta Numerica"} @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"}

%%% ==================================================================== %%% Miscellaneous abbreviations:

@String{prep-latex= "Prepared with {\LaTeX}."}

%%% ==================================================================== %%% Publishers and their addresses:

@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"}

%%% ==================================================================== %%% %%% Part 1 (of 2): publications by Gene H. Golub %%% %%% Bibliography entries, sorted by year, and then by citation label %%% (with ``bibsort -byyear''):

@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; http://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, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "numerical analysis; numerical calculations; relaxation methods (mathematics)", advisor = "Abraham Haskel Taub", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 (paper), 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 = "http://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; http://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", ISSN-L = "0003-4851", MRclass = "62.55", MRnumber = "27\#5336", MRreviewer = "A. C. Cohen", bibdate = "Sat May 31 09:11:02 MDT 2014", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 (paper), 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 = "http://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.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314185; http://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 = "http://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 = "http://www.jstor.org/page/journal/amermathmont/about.html", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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 = "http://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/; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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/; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Sat Nov 26 10:31:36 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Sat Nov 26 10:31:36 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 (paper), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", } @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; http://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", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "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", MRclass = "65.40", MRnumber = "42\#7056", MRreviewer = "J. D. P. Donnelly", bibdate = "Sun Jan 14 09:57:25 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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", pages = "24", month = "????", year = "1972", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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, 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 (paper), 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 = "http://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; http://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 = "http://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 = "http://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 = "http://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", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; http://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 = "http://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 (paper), 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 = "http://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 (paper), 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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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", } @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 = "http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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:MSS", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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} $}", type = "Technical Report", number = "STAN-CS-79-713", institution = inst-STANFORD-CS, address = inst-STANFORD-CS:adr, pages = "50", month = "????", year = "1979", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, author-dates = "Gene Howard Golub (February 29, 1932--November 16, 2007)", keywords = "matrix mechanics; numerical analysis", } @Article{Golub:1979:HSMb, author = "G. H. Golub and S. Nash and C. {Van Loan}", title = "A {Hessenberg--Schur} Method for the Matrix Problem {$ 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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{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 = "http://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 = "http://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/; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", } @InProceedings{Golub:1981: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 = "1981", MRclass = "65F10", MRnumber = "83f:65045", bibdate = "Sun Jan 14 09:32:52 1996", bibsource = "http://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{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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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; http://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", } @InCollection{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", MRclass = "65F10", MRnumber = "83f:65045", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "http://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: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; http://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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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 (paper), 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 = "http://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 = "http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "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; http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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; http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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{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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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; http://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 (paper), 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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.math.utah.edu/pub/bibnet/subjects/domain-decomp.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib; http://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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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", } @TechReport{Moor: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 = "http://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{Moor: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 = "http://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)", } @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; http://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 (paper), 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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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", bibdate = "Sun Jan 14 08:07:16 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; http://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 = "http://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 = "http://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 (paper), 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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 (paper), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "33C45", MRnumber = "92d:33015", MRreviewer = "J. Prasad", bibdate = "Sun Jan 14 09:06:36 1996", bibsource = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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; http://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", } @Article{Moor: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 = "????", year = "1991", CODEN = "SJMAEL", 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 08:25:42 1996", bibsource = "http://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{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 = "http://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; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; http://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib; http://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://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 = prep-latex, 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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://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; http://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; http://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; http://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; http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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; http://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 (paper), 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; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; http://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; http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; http://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; http://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://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www3.interscience.wiley.com/journalfinder.html", 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; http://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; http://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 = "http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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; http://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; http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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; http://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 = "http://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 = "http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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; http://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 = "http://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; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 (paper), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F10", MRnumber = "MR2261022", bibsource = "http://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 = "http://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 = "http://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 = "http://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; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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/; http://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 = "http://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 = "http://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/; http://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 = "http://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 = "http://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/; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; http://www.math.utah.edu/pub/tex/bib/numana2010.bib", series = "Princeton Series in Applied Mathematics", ZMnumber = "1217.65056", ZMnumber = "pre05661633", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://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: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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", }

%%% ==================================================================== %%% Part 2 (of 2): publications about Gene H. Golub and his works %%% %%% Bibliography entries, sorted by year, and then by citation label %%% (with ``bibsort -byyear'')

@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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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/; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", note = "Transcript recorded 22--23 October 2005.", pages = "75", year = "2005", bibdate = "Tue Jan 08 12:18:07 2019", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib; http://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/; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www.math.utah.edu/pub/tex/bib/numlinaa.bib; http://www3.interscience.wiley.com/journalfinder.html", 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{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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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{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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; http://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", }

%%% ==================================================================== %%% These entries must come last because they are cross-referenced %%% by others above. From version 0.04, "bibsort -byyear" will %%% correctly position Book entries that contain booktitle information.

@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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib; http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.math.utah.edu/pub/tex/bib/gnu.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; http://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, 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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @Book{Rice:1977:MSS, editor = "John R. Rice", booktitle = "Mathematical Software Symposium, University of Wisconsin, Madison, 1977. 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 Symposium, University of Wisconsin, Madison, 1977. 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", ISBN = "0-12-587260-7", ISBN-13 = "978-0-12-587260-7", LCCN = "QA297 .M36 1977", bibdate = "Sat Oct 22 18:23:16 1994", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", series = "Publication of the Mathematics Research Center, the University of Wisconsin, Madison", acknowledgement = ack-nhfb, tableofcontents = "Contributors \\ Preface \\ Chapter 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 \\ Chapter 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 \\ Chapter 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 \\ Chapter 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 \\ Chapter 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 \\ Chapter 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 \\ Chapter 7. Software for C1 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 \\ Chapter 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 \\ Chapter 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; http://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib; http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Two volumes.", acknowledgement = ack-nhfb, } @Proceedings{Watson:1982:NAP, editor = "G. A. 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, pages = "xi + 245", year = "1982", ISBN = "0-387-11199-9", ISBN-13 = "978-0-387-11199-5", LCCN = "QA3.L28 no.912", bibdate = "Sat Oct 29 15:16:39 1994", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", series = "Lecture notes in mathematics", acknowledgement = ack-sf, } @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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", } @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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; http://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, 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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; http://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib; http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; http://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; http://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; http://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.math.utah.edu/pub/tex/bib/einstein.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib; http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; http://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 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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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 = "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/g/gould-nicholas-ian.bib; http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; http://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; http://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 = "http://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 = "http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; http://www.math.utah.edu/pub/bibnet/authors/f/feynman-richard-p.bib; http://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 = "http://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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; http://www.math.utah.edu/pub/tex/bib/numana2000.bib; http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; http://www.math.utah.edu/pub/tex/bib/siamreview.bib; http://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, 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 = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; http://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib; http://www.math.utah.edu/pub/tex/bib/numana2000.bib", acknowledgement = ack-nhfb, } @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; http://www.math.utah.edu/pub/tex/bib/numana2010.bib; prodorbis.library.yale.edu:7090/voyager; z3950.loc.gov:7090/Voyager http://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", }