%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.70", %%% date = "29 November 2023", %%% time = "10:31:05 MST", %%% filename = "parlett-beresford-n.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "27410 8219 36944 379286", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "BibTeX; bibliography", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of publications of %%% Beresford Neill Parlett, B.A. (Oxford, 1955), %%% Ph.D. (Stanford, 1962), Professor Emeritus of %%% Computer Science, and Professor Emeritus of %%% Mathematics, University of California, %%% Berkeley. The companion LaTeX file %%% parlett-beresford-n.ltx can be used to %%% typeset this bibliography. %%% %%% Part 1 covers his publications, and Part 2 %%% covers publications about him by others. %%% %%% Beresford N. Parlett's personal Web site is %%% %%% http://math.berkeley.edu/~parlett/ %%% %%% This bibliography contains a few additional %%% entries that refer to the work of Beresford %%% N. Parlett in their titles. %%% %%% At version 1.70, the year coverage looked %%% like this: %%% %%% 1962 ( 1) 1983 ( 7) 2004 ( 4) %%% 1963 ( 0) 1984 ( 7) 2005 ( 6) %%% 1964 ( 4) 1985 ( 8) 2006 ( 4) %%% 1965 ( 2) 1986 ( 4) 2007 ( 4) %%% 1966 ( 7) 1987 ( 10) 2008 ( 4) %%% 1967 ( 6) 1988 ( 7) 2009 ( 7) %%% 1968 ( 1) 1989 ( 2) 2010 ( 2) %%% 1969 ( 4) 1990 ( 9) 2011 ( 3) %%% 1970 ( 2) 1991 ( 6) 2012 ( 1) %%% 1971 ( 3) 1992 ( 10) 2013 ( 0) %%% 1972 ( 3) 1993 ( 7) 2014 ( 1) %%% 1973 ( 3) 1994 ( 9) 2015 ( 0) %%% 1974 ( 5) 1995 ( 9) 2016 ( 1) %%% 1975 ( 3) 1996 ( 8) 2017 ( 1) %%% 1976 ( 5) 1997 ( 6) 2018 ( 0) %%% 1977 ( 9) 1998 ( 2) 2019 ( 0) %%% 1978 ( 5) 1999 ( 0) 2020 ( 2) %%% 1979 ( 4) 2000 ( 7) 2021 ( 0) %%% 1980 ( 7) 2001 ( 0) 2022 ( 1) %%% 1981 ( 10) 2002 ( 5) %%% 1982 ( 10) 2003 ( 5) %%% %%% Article: 138 %%% Book: 9 %%% InCollection: 1 %%% InProceedings: 28 %%% Misc: 2 %%% PhdThesis: 1 %%% Proceedings: 26 %%% TechReport: 58 %%% %%% Total entries: 263 %%% %%% Data for this bibliography have been %%% collected from the University of Utah %%% Mathematics Department bibliography archives, %%% the TeX User Group bibliography archives, the %%% Karlsruhe Computer Science bibliography %%% archives, from the European Mathematical %%% Society Zentralblatt fuer Mathematik %%% database, from the American Mathematical %%% Society MathSciNet database, from the %%% publication list at Beresford N. Parlett's %%% personal Web site, and from several online %%% library catalogs, including those of the %%% British Library, the Karlsruhe Virtual %%% Library catalog, the Oxford University %%% Library, and the US Library of Congress. %%% %%% This file is available as part of the BibNet %%% Project. The master copy is available for %%% public access on ftp.math.utah.edu in the %%% directory tree /pub/bibnet/authors. It is %%% mirrored to netlib.bell-labs.com in the directory %%% tree /netlib/bibnet/authors, from which it is %%% available via anonymous ftp and the Netlib %%% service. %%% %%% 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" # "\ifx \undefined \operatorname \def \operatorname #1{{\rm #1}}\fi" }

%%% ==================================================================== %%% Institutions and their addresses:

@String{inst-CPAM-UCB= "Center for Pure and Applied Mathematics, University of California, Berkeley"} @String{inst-CPAM-UCB:adr= "Berkeley, CA, USA"} @String{inst-ERL-CE-UCB= "Electronics Research Laboratory, College of Engineering, University of California, Berkeley"} @String{inst-ERL-CE-UCB:adr= "Berkeley, CA, USA"} @String{inst-UCB-EECS= "Department of Electrical Engineering and Computer Science, University of California, Berkeley"} @String{inst-UCB-EECS:adr= "Berkeley, CA, USA"} @String{inst-UTK-CS= "Department of Computer Science, University of Tennessee, Knoxville"} @String{inst-UTK-CS:adr= "Knoxville, TN 37996, USA"}

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

@String{j-ACTA-NUMERICA= "Acta Numerica"} @String{j-AMER-MATH-MONTHLY= "American Mathematical Monthly"} @String{j-BIT= "BIT (Nordisk tidskrift for informationsbehandling)"} @String{j-BIT-NUM-MATH= "BIT Numerical Mathematics"} @String{j-BULL-AMS-N-S= "Bulletin of the American Mathematical Society (new series)"} @String{j-CACM= "Communications of the ACM"} @String{j-COMM-PURE-APPL-MATH= "Communications on Pure and Applied Mathematics (New York)"} @String{j-COMP-J= "The Computer Journal"} @String{j-COMP-PHYS-COMM= "Computer Physics Communications"} @String{j-COMP-STRUCTURES= "Computers and Structures"} @String{j-COMPUT-SCI-ENG= "Computing in Science and Engineering"} @String{j-FOUND-COMPUT-MATH= "Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics"} @String{j-IEEE-TRANS-VIS-COMPUT-GRAPH= "IEEE Transactions on Visualization and Computer Graphics"} @String{j-IMA-J-NUMER-ANAL= "IMA Journal of Numerical Analysis"} @String{j-INT-J-HIGH-SPEED-COMPUTING= "International Journal of High Speed Computing (IJHSC)"} @String{j-INT-J-NUMER-METHODS-ENG= "International Journal for Numerical Methods in Engineering"} @String{j-J-ACM= "Journal of the ACM"} @String{j-J-COMPUT-APPL-MATH= "Journal of Computational and Applied Mathematics"} @String{j-J-COMPUT-PHYS= "Journal of computational physics"} @String{j-J-MATH-PHYS= "Journal of Mathematical Physics"} @String{j-J-NUM-LIN-ALG-APPL= "Journal of Numerical linear algebra with applications"} @String{j-LINEAR-ALGEBRA-APPL= "Linear Algebra and its Applications"} @String{j-MATH-COMPUT= "Mathematics of Computation"} @String{j-NUM-LIN-ALG-APPL= "Numerical Linear Algebra with Applications"} @String{j-NUM-MATH= "Numerische Mathematik"} @String{j-PARALLEL-ALGORITHMS-APPL= "Parallel Algorithms and Applications"} @String{j-PARALLEL-COMPUTING= "Parallel Computing"} @String{j-SIAM-J-ALG-DISC-METH= "SIAM Journal on Algebraic and 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-SCI-COMP= "SIAM Journal on Scientific Computing"} @String{j-SIAM-J-SCI-STAT-COMP= "SIAM Journal on Scientific and Statistical Computing"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-SIGNUM= "ACM SIGNUM Newsletter"} @String{j-THEOR-POPUL-BIOL= "Theoretical Population Biology"} @String{j-TOMS= "ACM Transactions on Mathematical Software"} @String{j-Z-ANGE-MATH-MECH= "Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik"}

%%% ==================================================================== %%% Publisher abbreviations:

@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-AW= "Ad{\-d}i{\-s}on-Wes{\-l}ey"} @String{pub-AW:adr= "Reading, MA, USA"} @String{pub-BIRKHAUSER= "Birkh{\"a}user"} @String{pub-BIRKHAUSER:adr= "Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland"} @String{pub-BIRKHAUSER-BOSTON= "Birkh{\"a}user Boston Inc."} @String{pub-BIRKHAUSER-BOSTON:adr= "Cambridge, MA, USA"} @String{pub-CAMBRIDGE= "Cambridge University Press"} @String{pub-CAMBRIDGE:adr= "Cambridge, UK"} @String{pub-DUNOD= "Dunod"} @String{pub-DUNOD:adr= "Paris, France"} @String{pub-EDITORIAL-MIR= "Editorial Mir"} @String{pub-EDITORIAL-MIR:adr= "Moscow, USSR"} @String{pub-ELSEVIER= "Elsevier"} @String{pub-ELSEVIER:adr= "Amsterdam, The Netherlands"} @String{pub-ELSEVIER-SCIENCE= "Elsevier Science, Inc."} @String{pub-ELSEVIER-SCIENCE:adr= "Amsterdam, The Netherlands"} @String{pub-GRUYTER= "Walter de Gruyter"} @String{pub-GRUYTER:adr= "Berlin, Germany"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-KLUWER= "Kluwer Academic Publishers"} @String{pub-KLUWER:adr= "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-LONGMAN= "Longman Scientific and Technical"} @String{pub-LONGMAN:adr= "Harlow, Essex, UK"} @String{pub-MIT= "MIT Press"} @String{pub-MIT:adr= "Cambridge, MA, USA"} @String{pub-NORTH-HOLLAND= "North-Hol{\-}land"} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PH= "Pren{\-}tice-Hall"} @String{pub-PH:adr= "Upper Saddle River, NJ 07458, USA"} @String{pub-PLENUM= "Plenum Press"} @String{pub-PLENUM:adr= "New York, NY, USA; London, UK"} @String{pub-SIAM= "Society for Industrial and Applied Mathematics"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-SV= "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA; London, UK; Sydney, Australia"}

%%% ==================================================================== %%% Series abbreviations:

@String{ser-LECT-NOTES-MATH= "Lecture Notes in Mathematics"}

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

@PhdThesis{Parlett:1962:BML, author = "Beresford Neill Parlett", title = "{I}. Bundles of matrices and the linear independence of their minors; {II}. Applications of {Laguerre}'s method to the matrix eigenvalue problem", type = "{Ph.D.} dissertation", school = "Department of Mathematics, Stanford University", address = "Stanford, CA, USA", pages = "v + 118", year = "1962", bibdate = "Fri Nov 11 05:07:47 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.genealogy.math.ndsu.nodak.edu/html/id.phtml?id=32898; http://wwwlib.umi.com/dxweb/details?doc_no=5023767", acknowledgement = ack-nhfb, advisor = "George E. Forsythe", } @Article{Forsythe:1964:TPA, author = "George E. Forsythe", title = "Tests of {Parlett}'s {ALGOL} Eigenvalue Procedure {$ E i g 3 $} (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "18", number = "87", pages = "486--487", month = jul, year = "1964", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2003771", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65.40", MRnumber = "0165669", MRreviewer = "James H. Wilkinson", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Parlett:1964:DUM, author = "Beresford Parlett", title = "The Development and Use of Methods of {$ L R $} Type", journal = j-SIAM-REVIEW, volume = "6", number = "3", pages = "275--295", month = jul, year = "1964", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1006066", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65.35", MRnumber = "MR0172450 (30 \#2669)", MRreviewer = "James H. Wilkinson", bibdate = "Thu Mar 27 09:05:15 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/6/3; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", ZMnumber = "0242.65039", acknowledgement = ack-nhfb, classmath = "65F15 Eigenvalues (numerical linear algebra)", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "July 1964", } @Article{Parlett:1964:LMA, author = "Beresford N. Parlett", title = "{Laguerre}'s Method Applied to the Matrix Eigenvalue Problem", journal = j-MATH-COMPUT, volume = "18", number = "87", pages = "464--485", month = jul, year = "1964", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65.40", MRnumber = "MR0165668 (29 \#2948)", MRreviewer = "James H. Wilkinson", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database; Theory/Matrix.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib", ZMnumber = "0124.33004", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "numerical analysis", kwds = "nla, eig, Laguerre's method, polynomial", } @Article{Parlett:1964:NBA, author = "Beresford Parlett", title = "A Note on {La Budde}'s Algorithm (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "18", number = "87", pages = "505--506", month = jul, year = "1964", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65.35", MRnumber = "MR0165671 (29 \#2951)", MRreviewer = "A. S. Householder", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib", ZMnumber = "0208.39902", acknowledgement = ack-nhfb, classmath = "*65F99 Numerical linear algebra", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @Article{Parlett:1965:CA, author = "Beresford Parlett", title = "Convergence of the {$ Q R $} algorithm", journal = j-NUM-MATH, volume = "7", pages = "187--193", year = "1965", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.40", MRnumber = "MR0176600 (31 \#872)", MRreviewer = "E. R. Hansen", bibdate = "Sun Oct 17 19:01:15 MDT 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "See correction \cite{Parlett:1967:CCA}.", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", ZMnumber = "0132.36301", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "numerical analysis", } @Article{Parlett:1965:MEP, author = "Beresford Parlett", title = "Matrix Eigenvalue Problems", journal = j-AMER-MATH-MONTHLY, volume = "72", number = "2, part II", pages = "59--66", year = "1965", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "65.40", MRnumber = "MR0172452 (30 \#2671)", MRreviewer = "P. J. Davis", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", ZMnumber = "0123.11302", acknowledgement = ack-nhfb, fjournal = "The American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", keywords = "numerical analysis", } @Article{Parlett:1966:BRB, author = "B. N. Parlett", title = "Book Review: {{\booktitle{The Algebraic Eigenvalue Problem}} (J. H. Wilkinson)}", journal = j-SIAM-REVIEW, volume = "8", number = "4", pages = "543--545", month = "????", year = "1966", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1008125", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:05:39 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/8/4; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "October 1966", } @Article{Buchanan:1966:UCM, author = "M. L. Buchanan and B. N. Parlett", title = "The uniform convergence of matrix powers", journal = j-NUM-MATH, volume = "9", pages = "51--54", year = "1966", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.40", MRnumber = "MR0205434 (34 \#5262)", MRreviewer = "H.-O. Kreiss", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/nummath.bib", ZMnumber = "0143.05104", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "linear algebra, forms", } @Article{Parlett:1966:ADD, author = "Beresford Parlett", title = "Accuracy and dissipation in difference schemes", journal = j-COMM-PURE-APPL-MATH, volume = "19", number = "1", pages = "111--123", year = "1966", CODEN = "CPAMAT, CPMAMV", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", MRclass = "65.65", MRnumber = "MR0196957 (33 \#5141)", MRreviewer = "H.-O. Kreiss", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0173.44703", acknowledgement = ack-nhfb, fjournal = "Communications on Pure and Applied Mathematics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", keywords = "numerical analysis", } @Article{Parlett:1966:CQR, author = "Beresford Parlett", title = "Convergence of the {Q-R} algorithm for {Hessenberg} matrices", journal = j-CACM, volume = "9", number = "7", pages = "475--475", month = jul, year = "1966", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Fri Nov 25 18:20:07 MST 2005", bibsource = "http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", } @Article{Parlett:1966:SIM, author = "Beresford N. Parlett", title = "Singular and Invariant Matrices Under the {$ {QR} $} Transformation (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "20", number = "96", pages = "611--615", month = oct, year = "1966", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65.35", MRnumber = "MR0213005 (35 \#3870)", MRreviewer = "N. Gastinel", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database; Theory/Matrix.bib", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib", ZMnumber = "0238.65018", acknowledgement = ack-nhfb, classmath = "*65F30 Other matrix algorithms", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", kwds = "nla, eig, QR algorithm", } @Article{Rust:1966:SAC, author = "B. Rust and W. R. Burrus and C. Schneeberger", title = "A simple algorithm for computing the generalized inverse of a matrix", journal = j-CACM, volume = "9", number = "5", pages = "381--385, 387", month = may, year = "1966", CODEN = "CACMA2", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", MRclass = "65.35", MRnumber = "33\#3448", bibdate = "Tue May 28 07:33:09 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib", abstract = "The generalized inverse of a matrix is important in analysis because it provides an extension of the concept of an inverse which applies to all matrices. It also has many applications in numerical analysis, but it is not widely used because the existing algorithms are fairly complicated and require considerable storage space. A simple extension has been found to the conventional orthogonalization method for inverting non-singular matrices, which gives the generalized inverse with little extra effort and with no additional storage requirements. The algorithm gives the generalized inverse for any $m$ by n matrix {$A$}, including the special case when $ m + n $ and {$A$} is non-singular and the case when $ m > n $ and {$ \mbox {rank}(A) = n $}. In the first case the algorithm gives the ordinary inverse of {$A$}. In the second case the algorithm yields the ordinary least squares transformation matrix {$ \mbox {INV}(A'A)A' $} and has the advantage of avoiding the loss of significance which results in forming the product {$ A'A $} explicitly.", acknowledgement = ack-nhfb, fjournal = "Communications of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79", kwds = "nla, ginv", reviewer = "B. N. Parlett", } @Article{Varah:1966:CPA, author = "J. M. Varah", title = "Certification of {Parlett}'s {ALGOL} Eigenvalue Procedure {$ \operatorname {Eig} $} 3 (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "20", number = "95", pages = "437--438", month = jul, year = "1966", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @InProceedings{Parlett:1967:A, author = "B. N. Parlett", title = "The {$ L U $} and {$ Q R $} algorithms", crossref = "Ralston:1967:MMD", pages = "116--130", year = "1967", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1967:CCA, author = "Beresford Parlett", title = "Correction to: ``{Convergence of the $ Q R $ algorithm}''", journal = j-NUM-MATH, volume = "10", pages = "163--164", year = "1967", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65.35", MRnumber = "MR0214278 (35 \#5129)", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "See \cite{Parlett:1965:CA}.", URL = "https://www.math.utah.edu/pub/tex/bib/nummath.bib", ZMnumber = "0171.36004", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "numerical analysis", } @Article{Parlett:1967:CDH, author = "Beresford Parlett", title = "Canonical Decomposition of {Hessenberg} Matrices (in {Technical Notes and Short Papers})", journal = j-MATH-COMPUT, volume = "21", number = "98", pages = "223--227", month = apr, year = "1967", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "15.30 (65.00)", MRnumber = "MR0228519 (37 \#4099)", MRreviewer = "A. S. Householder", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib", ZMnumber = "0159.20501", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "numerical analysis", } @Article{Parlett:1967:EA, author = "B. N. Parlett", title = "Eigenvalues, anyone?", journal = j-SIGNUM, volume = "1", number = "3", pages = "7--8", month = feb, year = "1967", CODEN = "SNEWD6", ISSN = "0163-5778 (print), 1558-0237 (electronic)", ISSN-L = "0163-5778", bibdate = "Mon Mar 5 17:26:25 MST 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "ACM SIGNUM Newsletter", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690", } @Article{Parlett:1967:LEF, author = "Beresford Parlett", title = "Letter to the Editor: On finding the eigenvalues of real symmetric tridiagonal matrices", journal = j-COMP-J, volume = "9", number = "4", pages = "344--345", month = feb, year = "1967", CODEN = "CMPJA6", ISSN = "0010-4620 (print), 1460-2067 (electronic)", ISSN-L = "0010-4620", bibdate = "Thu Aug 25 09:00:35 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://comjnl.oxfordjournals.org/content/9/4/344.full.pdf", acknowledgement = ack-nhfb, fjournal = "The Computer Journal", journal-URL = "http://comjnl.oxfordjournals.org/", } @Article{Parlett:1968:GCB, author = "Beresford N. Parlett", title = "Global Convergence of the Basic {QR} Algorithm on {Hessenberg} Matrices", journal = j-MATH-COMPUT, volume = "22", number = "104", pages = "803--817", month = oct, year = "1968", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65.35", MRnumber = "MR0247759 (40 \#1020)", MRreviewer = "J. Vandergraft", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database; Theory/Matrix.bib", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib", ZMnumber = "0184.37602", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "numerical analysis", kwds = "nla, eig, QR algorithm, Hessenberg matrix", } @Article{Parlett:1969:BMC, author = "B. N. Parlett and C. Reinsch", title = "Balancing a matrix for calculation of eigenvalues and eigenvectors", journal = j-NUM-MATH, volume = "13", pages = "293--304", year = "1969", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; Theory/Matrix.bib", note = "Also in \cite[pp. 315--326]{Wilkinson:1971:LA}.", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", ZMnumber = "0184.37703", acknowledgement = ack-nhfb, author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "eig; nla; numerical analysis; scaling; software", xxpages = "292--304", } @InProceedings{Parlett:1969:CPA, author = "B. N. Parlett and W. Kahan", title = "On the convergence of a practical {$ Q R $} algorithm. ({With} discussion)", crossref = "Morrell:1969:IPP", volume = "1", pages = "114--118", year = "1969", MRclass = "65.40", MRnumber = "MR0255035 (40 \#8242)", bibdate = "Mon Apr 25 18:24:02 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0195.45002", acknowledgement = ack-nhfb, keywords = "numerical analysis", } @Article{Parlett:1969:NNM, author = "B. N. Parlett", title = "Notes on the number of multiplications required to form the product of two {$ N \times N $} matrices", journal = j-SIGNUM, volume = "4", number = "2", pages = "9--12", month = jun, year = "1969", CODEN = "SNEWD6", ISSN = "0163-5778 (print), 1558-0237 (electronic)", ISSN-L = "0163-5778", bibdate = "Mon Mar 5 17:26:28 MST 2007", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "ACM SIGNUM Newsletter", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690", } @Article{Parlett:1970:EPP, author = "Beresford Parlett", title = "Ergodic properties of populations. {I}. {The} one sex model", journal = j-THEOR-POPUL-BIOL, volume = "1", number = "??", pages = "191--207", year = "1970", CODEN = "TLPBAQ", DOI = "https://doi.org/10.1016/0040-5809(70)90034-1", ISSN = "0040-5809 (print), 1096-0325 (electronic)", ISSN-L = "0040-5809", MRclass = "92A15", MRnumber = "MR0325180 (48 \#3529)", MRreviewer = "N. Keyfitz", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0239.92007", acknowledgement = ack-nhfb, classmath = "*92D25 Population dynamics", fjournal = "Theoretical Population Biology. An International Journal", journal-URL = "http://www.sciencedirect.com/science/journal/00405809", } @Article{Parlett:1970:SSL, author = "B. Parlett and J. K. Reid", title = "On the Solution of a System of Linear Equations whose Matrix is Symmetric but not Definite", journal = j-BIT, volume = "10", number = "3", pages = "386--397", year = "1970", CODEN = "BITTEL, NBITAB", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Sat Nov 14 09:14:57 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, fjournal = "BIT (Nordisk tidskrift for informationsbehandling)", journal-URL = "http://link.springer.com/journal/10543", } @Article{Bunch:1971:DMS, author = "James R. Bunch and Beresford N. Parlett", title = "Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations", journal = j-SIAM-J-NUMER-ANAL, volume = "8", number = "4", pages = "639--655", month = dec, year = "1971", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F05", MRnumber = "MR0305564 (46 \#4694)", MRreviewer = "John Todd", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib", ZMnumber = "0199.49802", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", keywords = "numerical analysis", remark = "Zentralblatt MATH database records this as number 3, 1970.", } @Article{Parlett:1971:AAR, author = "Beresford N. Parlett", title = "Analysis of Algorithms for Reflections in Bisectors", journal = j-SIAM-REVIEW, volume = "13", number = "2", pages = "197--208", month = "????", year = "1971", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1013037", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65.80", MRnumber = "MR0290608 (44 \#7788)", MRreviewer = "G. Fairweather", bibdate = "Thu Mar 27 09:06:28 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/13/2; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", ZMnumber = "0217.52606", acknowledgement = ack-nhfb, classmath = "65F99 Numerical linear algebra 65G99 Error analysis 65Y20 Complexity and performance of numerical algorithms", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "April 1971", } @Article{Partlett:1972:BRB, author = "B. Partlett", title = "Book Review: {{\booktitle{Handbook for Automatic Computation, Vol. II, Linear Algebra}} (J. H. Wilkinson and C. Reinsch)}", journal = j-SIAM-REVIEW, volume = "14", number = "4", pages = "658--661", month = "????", year = "1972", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1014116", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:06:44 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/14/4; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "October 1972", subject-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022); James H. Wilkinson (27 September 1919--5 October 1986)", } @InProceedings{Parlett:1972:CTM, author = "B. Parlett", title = "Can there be a marriage function?", crossref = "Greville:1972:PDP", pages = "107--135", year = "1972", MRclass = "92A15", MRnumber = "MR0446591 (56 \#4916)", MRreviewer = "R. Fischler", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1973:GTP, author = "B. N. Parlett and W. G. {Poole, Jr.}", title = "A Geometric Theory for the {$ {QR} $}, {$ {LU} $} and Power Iterations", journal = j-SIAM-J-NUMER-ANAL, volume = "10", number = "2", pages = "389--412", month = apr, year = "1973", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F15", MRnumber = "MR0336979 (49 \#1752)", MRreviewer = "J. Vandergraft", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", note = "Collection of articles dedicated to the memory of George E. Forsythe", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib", ZMnumber = "0227.65027; 0253.65018", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @Article{Parlett:1973:NHM, author = "Beresford Parlett", title = "Normal {Hessenberg} and moment matrices", journal = j-LINEAR-ALGEBRA-APPL, volume = "6", number = "??", pages = "37--43", month = "????", year = "1973", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F15", MRnumber = "MR0324887 (48 \#3236)", MRreviewer = "James H. Wilkinson", bibdate = "Tue Feb 16 18:54:52 MST 2016", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/linala1970.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379573900050", ZMnumber = "0251.15022", acknowledgement = ack-nhfb, classmath = "*15A57 Other types of matrices 65F30 Other matrix algorithms", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", } @Article{Parlett:1973:PGM, author = "B. N. Parlett", title = "Pr{\'e}sentation g{\'e}om{\'e}trique des m{\'e}thodes de calcul des valeurs propres. ({French}) [{Geometric} presentation of methods for calculation of eigenvalues]", journal = j-NUM-MATH, volume = "21", number = "3", pages = "223--233", year = "1973", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F15", MRnumber = "MR0329229 (48 \#7571)", MRreviewer = "A. S. Householder", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/nummath.bib", ZMnumber = "0255.65020", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra)", classmath = "*65F15 Eigenvalues (numerical linear algebra)", corpsource = "Univ. California, Berkeley, CA, USA", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "calculation; convergence; convergence of numerical methods; eigenvalues; eigenvalues and eigenfunctions; eigenvectors; geometric presentation; matrices; matrix algebra; methods", language = "French", treatment = "T Theoretical or Mathematical", } @TechReport{Kahan:1974:ALA, author = "W. Kahan and B. N. Parlett", title = "An Analysis of {Lanczos} Algorithms for Symmetric Matrices", type = "Memo", number = "ERL-M467", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, year = "1974", bibdate = "Mon Apr 25 18:24:02 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", URL = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1974:BRB, author = "B. N. Parlett", title = "Book Review: {{\booktitle{Large Sparse Sets of Linear Equations (J. K. Reid, ed.); Sparse Matrices and Their Applications}} (Donald J. Rose and Ralph A. Willoughby, ed.)}", journal = j-SIAM-REVIEW, volume = "16", number = "3", pages = "396--398", month = "????", year = "1974", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1016066", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Thu Mar 27 09:07:02 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/16/3; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "July 1974", } @Article{Parlett:1974:BRH, author = "Beresford N. Parlett", title = "Book Review: {H. R. Schwarz, H. Rutishauser \& E. Stiefel, translated by P. Hertelendy, \booktitle{Numerical Analysis of Symmetric Matrices}, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1973, xi + 276 pp., 24 cm.}", journal = j-MATH-COMPUT, volume = "28", number = "125", pages = "328--328", month = jan, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", bibdate = "Wed Aug 26 06:30:00 2020", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib", URL = "https://www.jstor.org/stable/2005845", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @TechReport{Parlett:1974:CFT, author = "Beresford N. Parlett", title = "Computation of Functions of Triangular Matrices", type = "Memorandum", number = "ERL-M481", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "18", month = nov, year = "1974", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1974:RQI, author = "B. N. Parlett", title = "The {Rayleigh} Quotient Iteration and Some Generalizations for Nonnormal Matrices", journal = j-MATH-COMPUT, volume = "28", number = "127", pages = "679--693", month = jul, year = "1974", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F15", MRnumber = "MR0405823 (53 \#9615)", MRreviewer = "James H. Wilkinson", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database; Theory/Matrix.bib", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib", ZMnumber = "0293.65023", acknowledgement = ack-nhfb, classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18 Eigenvalues of matrices, etc", corpsource = "Univ. California, Berkeley, CA, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "eigenvector; generalizations; iterative methods; local convergence; matrices; matrix algebra; nonnormal; Rayleigh Quotient Iteration", kwds = "nla, eig, Rayleigh quotient, nonnormal matrix", treatment = "T Theoretical or Mathematical", } @TechReport{Chan:1975:PCC, author = "Sai-Pak Chan and R. Feldman and Beresford N. Parlett", title = "A program to compute the condition numbers of matrix eigenvalues without computing eigenvectors", type = "Memorandum", number = "ERL-M517", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "44", year = "1975", bibdate = "Fri Nov 11 05:22:23 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1975:ICC, author = "B. N. Parlett and Y. Wang", title = "The Influence of the Compiler on the Cost of Mathematical Software{}\emdash in Particular on the Cost of Triangular Factorization", journal = j-TOMS, volume = "1", number = "1", pages = "35--46", month = mar, year = "1975", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355626.355633", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", ZMnumber = "0312.68017", acknowledgement = ack-nhfb, classmath = "*68N01 General", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "cs; lud; nla; software", } @TechReport{Parlett:1975:PCR, author = "Beresford N. Parlett and R. Feldman", title = "A program to compute the real {Schur} Form of a real square matrix", type = "Memorandum", number = "ERL-M526", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "28", year = "1975", bibdate = "Fri Nov 11 05:21:27 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Bunch:1976:DSM, author = "James R. Bunch and Linda Kaufman and Beresford N. Parlett", title = "Decomposition of a Symmetric Matrix", journal = j-NUM-MATH, volume = "27", number = "1", pages = "95--109", year = "1976", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF01399088", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; Theory/Matrix.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", ZMnumber = "0342.65026", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra)", classmath = "*65F35 Matrix norms, etc. (numerical linear algebra) 68W99 None of the above, but in this section", corpsource = "Dept. of Math., Univ. of California, San Diego, CA, USA", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "Cholesky; indefinite system; inertia; linear equations; linear system; lud; matrix algebra; nla; permutation matrix; symmetric matrix; triangular factorisation", treatment = "T Theoretical or Mathematical", } @InProceedings{Kahan:1976:HFS, author = "W. Kahan and B. N. Parlett", title = "How far should you go with the {Lanczos} process?", crossref = "Bunch:1976:SMC", pages = "131--144", year = "1976", MRclass = "65F15", MRnumber = "MR0458836 (56 \#17036)", MRreviewer = "Michael S. Martin", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib", ZMnumber = "0345.65017", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18 Eigenvalues of matrices, etc", } @Article{Parlett:1976:RAE, author = "B. N. Parlett", title = "A Recurrence Among the Elements of Functions of Triangular Matrices", journal = j-LINEAR-ALGEBRA-APPL, volume = "14", number = "2", pages = "117--121", month = "????", year = "1976", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(76)90018-5", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F30", MRnumber = "MR0448846 (56 \#7151)", MRreviewer = "C. G. Cullen", bibdate = "Tue Feb 16 18:49:27 MST 2016", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/linala1970.bib", URL = "http://www.sciencedirect.com/science/article/pii/0024379576900185", ZMnumber = "0353.65027", acknowledgement = ack-nhfb, classmath = "*65F99 Numerical linear algebra 15A15 Special matrix functions", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795/", keywords = "nla, matrix function, triangular matrix", } @TechReport{Parlett:1976:RES, author = "Beresford N. Parlett", title = "Roundoff error in the solution of finite element systems", type = "Report", number = "????", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "21", year = "1976", bibdate = "Fri Nov 11 05:48:59 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Chan:1977:APC, author = "S. P. Chan and R. Feldman and B. N. Parlett", title = "{Algorithm 517}: {A} Program for Computing the Condition Numbers of Matrix Eigenvalues Without Computing Eigenvectors [{F2}]", journal = j-TOMS, volume = "3", number = "2", pages = "186--203", month = jun, year = "1977", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/355732.355741", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Sat Aug 27 22:34:22 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", ZMnumber = "0353.65026", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F35 Matrix norms, etc. (numerical linear algebra)", fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "condition estimation; eig; nla; nonsymmetric matrix; pert; software", } @TechReport{Hoffman:1977:NPG, author = "W. Hoffman and Beresford N. Parlett", title = "A new proof of global convergence for the tridiagonal {QL} algorithm", type = "Memorandum", number = "UCB/ERL M77/48", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "18", day = "7", month = jul, year = "1977", bibdate = "Fri Nov 11 05:18:34 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Kahan:1977:CYC, author = "W. M. Kahan and B. N. Parlett", title = "Can You Count on Your Calculator?", type = "Memorandum", number = "UCB/ERL M77/21", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "ii + 28", day = "6", month = apr, year = "1977", bibdate = "Fri Jan 12 11:37:56 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", note = "German Transl. Published In: Jahrbuch {\"U}berblicke Mathematik 1978, Ed. by B. Fuchssteiner and others, Bibliographisches Institut, Mannheim-Wien-Z{\"u}rich, 199--216, 1978", URL = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-jr, } @Article{Parlett:1977:ICC, author = "B. N. Parlett and Y. Wang", title = "The influence of the compiler on the cost of mathematical software---in particular on the cost of triangular factorization", journal = j-TOMS, volume = "1", pages = "35--46", year = "1977", CODEN = "ACMSCU", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", } @TechReport{Parlett:1977:LAI, author = "B. N. Parlett and D. S. Scott", title = "The {Lanczos} algorithm with implicit deflation", type = "Memorandum", number = "UCB/ERL M77/70", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "29", day = "2", month = dec, year = "1977", bibdate = "Fri Nov 11 05:16:39 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Parlett:1977:PNA, author = "Beresford N. Parlett", title = "Progress in numerical analysis", type = "Memorandum", number = "UCB/ERL M77/26", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "30", day = "13", month = apr, year = "1977", bibdate = "Fri Nov 11 05:19:27 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Parlett:1977:PSD, author = "Beresford N. Parlett", title = "A program to swap diagonal blocks", type = "Memorandum", number = "UCB/ERL M77/66", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "30", day = "3", month = nov, year = "1977", bibdate = "Fri Nov 11 05:17:40 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @InProceedings{Parlett:1977:RES, author = "Beresford Parlett", title = "Roundoff error in the solution of finite element systems", crossref = "Bathe:1977:FCA", pages = "632--654", year = "1977", MRclass = "65G05 (65N30)", MRnumber = "MR0488692 (58 \#8211)", MRreviewer = "Peter Lancaster", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Hoffmann:1978:NPG, author = "W. Hoffmann and B. N. Parlett", title = "A new proof of global convergence for the tridiagonal {QL} algorithm", journal = j-SIAM-J-NUMER-ANAL, volume = "15", number = "5", pages = "929--937", month = oct, year = "1978", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0715060", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F15", MRnumber = "MR507555 (80a:65075)", MRreviewer = "S. F. McCormick", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib", ZMnumber = "0402.65019", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", keywords = "Eigenpairs of Matrices; Global Convergence; Ql Algorithm; Wilkinson'S Shift", } @TechReport{Kahan:1978:HFS, author = "W. Kahan and B. N. Parlett", title = "How far should you go with the {Lanczos} process?", type = "Memorandum", number = "UCB/ERL M78/48", institution = inst-ERL-CE-UCB, address = inst-ERL-CE-UCB:adr, pages = "16", year = "1978", bibdate = "Fri Nov 11 05:15:08 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Kahan:1978:KSI, author = "W. Kahan and B. N. Parlett", title = "{K{\"o}nnen Sie sich auf Ihren Rechner verlassen?} ({German}) [Can you count on your calculator?]", journal = "{Jahrbuch {\"U}berblicke Mathematik}", volume = "??", pages = "199--216", year = "1978", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0397.65081", acknowledgement = ack-nhfb, classmath = "*65Y99 Computer aspects of numerical algorithms 65D20 Computation of special functions 00A99 Miscellaneous topics in general mathematics", keywords = "Automated Algorithms; Error of Computation; Pocket Calculator", language = "German", } @Article{Parlett:1978:NPG, author = "B. N. Parlett and W. Hoffman", title = "New Proof of Global Convergence for Tridiagonal {$ Q L $} Algorithm", journal = j-SIAM-REVIEW, volume = "20", number = "3", pages = "632--632", month = "????", year = "1978", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Fri Jun 21 11:25:02 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Parlett:1978:PNA, author = "Beresford N. Parlett", title = "Progress in Numerical Analysis", journal = j-SIAM-REVIEW, volume = "20", number = "3", pages = "443--456", year = "1978", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1020066", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65-02", MRnumber = "MR0494816 (58 \#13601)", bibdate = "Sat Mar 29 09:52:53 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/20/3; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", ZMnumber = "0408.65002", acknowledgement = ack-nhfb, classmath = "*65-02 Research monographs (numerical analysis) 68Nxx Software 00A06 Mathematics for non-mathematicians", fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", keywords = "Iterative Methods for Linear Equations; Library Functions; Matrix Computations; Minimization; Numerical Methods; Ordinary Differential Equations; Packages; Program Libraries; Programming Languages; Progress in Numerical Analysis; Quadrature; Small Matrix Computations; Stored Matrices; Theoretical Treatment", onlinedate = "July 1978", } @Article{Gear:1979:NCR, author = "C. W. Gear and J. M. Ortega and B. Parlett and J. R. Rice and M. Schultz and L. F. Shampine and P. Wolfe", title = "Numerical Computation: {A} Report on Past, Present, and Future Research", journal = j-SIGNUM, volume = "14", number = "si-1", pages = "1--48", month = feb, year = "1979", CODEN = "SNEWD6", DOI = "https://doi.org/10.1145/1057517.1057518", ISSN = "0163-5778 (print), 1558-0237 (electronic)", ISSN-L = "0163-5778", bibdate = "Sat Dec 29 14:38:45 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", note = "Also published in \cite{Gear:1980:NCR}.", acknowledgement = ack-nhfb, fjournal = "ACM SIGNUM Newsletter", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690", } @Article{Parlett:1979:BRH, author = "Beresford N. Parlett", title = "Book Review: {Herman H. Goldstine, {\em A history of numerical analysis from the 16th through the 19th century}. Studies in the History of Mathematics and Physical Sciences 2, Springer-Verlag, New York, Heidelberg, Berlin, 1977, xiv + 348 pp., \$24.80}", journal = j-BULL-AMS-N-S, volume = "1", number = "2", pages = "388--390", month = "????", year = "1979", CODEN = "BAMOAD", ISSN = "0273-0979 (print), 1088-9485 (electronic)", ISSN-L = "0273-0979", bibdate = "Wed Jun 08 12:29:41 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://projecteuclid.org/euclid.bams/1183544086", acknowledgement = ack-nhfb, fjournal = "Bulletin of the American Mathematical Society (new series)", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", } @Article{Parlett:1979:LAS, author = "B. N. Parlett and D. S. Scott", title = "The {L{\'a}nczos} Algorithm with Selective Orthogonalization", journal = j-MATH-COMPUT, volume = "33", number = "145", pages = "217--238", month = jan, year = "1979", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2006037", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F15", MRnumber = "MR514820 (80c:65090)", MRreviewer = "Colette Lebaud", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database; Theory/Matrix.bib", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib", ZMnumber = "0405.65015", acknowledgement = ack-nhfb, classcodes = "C4140 (Linear algebra)", classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F25 Orthogonalization (numerical linear algebra)", corpsource = "Univ. California, Berkeley, CA, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "eigenvalues; eigenvalues and eigenfunctions; eigenvectors; Eigenvectors; extreme; Extreme Eigenvalues of a Large Symmetric Matrix; independence; Lanczos algorithm; Lanczos Process; large symmetric matrix; linear; Modification; selective orthogonalization; Selective Orthogonalization", kwds = "nla, eig, Lanczos Algorithm, orthogonalization", treatment = "T Theoretical or Mathematical", } @Article{Rice:1979:NCN, author = "J. R. Rice and C. W. Gear and J. Ortega and B. Parlett and M. Schultz and L. F. Shampine and P. Wolfe and J. F. Traub", title = "Numerical computation: its nature and research directions", journal = j-SIGNUM, volume = "14", number = "3S (Special issue)", pages = "1--48", month = feb, year = "1979", CODEN = "SNEWD6", ISSN = "0163-5778 (print), 1558-0237 (electronic)", ISSN-L = "0163-5778", bibdate = "Tue Apr 12 07:50:06 MDT 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/signum.bib", acknowledgement = ack-nhfb, classcodes = "C1180 (Optimisation techniques); C4140 (Linear algebra); C4170 (Differential equations)", corpsource = "Purdue Univ., Lafayette, IN, USA", fjournal = "ACM SIGNUM Newsletter", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690", keywords = "curves; graphics; linear algebra; mathematical software; nonlinear equations; numerical computation; optimisation; optimization; ordinary differential equations; partial differential equations; surfaces", treatment = "G General Review", } @InCollection{Gear:1980:NCR, author = "C. W. Gear and J. M. Ortega and B. Parlett and J. R. Rice and M. Schultz and L. F. Shampine and P. Wolfe", title = "Numerical Computation: {A} Report on Past, Present, and Future Research", crossref = "Arden:1980:WCA", pages = "51--136", year = "1980", bibdate = "Sat Dec 29 14:40:07 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib", note = "Also published in \cite{Gear:1979:NCR}.", acknowledgement = ack-nhfb, } @TechReport{Nour-Omid:1980:LVS, author = "Bahram Nour-Omid and Beresford N. Parlett and Robert L. Taylor", title = "{Lanczos} versus subspace iteration for solution of eigenvalue problems", type = "Report", number = "UC SESM 80-8", institution = "Structural Engineering Laboratory, University of California, Berkeley", address = "Berkeley, CA, USA", pages = "16", year = "1980", bibdate = "Fri Nov 11 05:12:33 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @InProceedings{Parlett:1980:HSK, author = "B. N. Parlett", title = "How to solve {$ (K - \lambda M)z = 0 $} for large {$K$} and {$M$}", crossref = "Absi:1980:NME", volume = "1", pages = "97--106", year = "1980", MRclass = "65F15", MRnumber = "MR660669 (83g:65044)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0455.65027", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", keywords = "comparison; Lanczos algorithm; large eigenvalue problems; numerical example; subspace iteration method", } @Article{Parlett:1980:NLL, author = "B. N. Parlett", title = "A new look at the {Lanczos} algorithm for solving symmetric systems of linear equations", journal = j-LINEAR-ALGEBRA-APPL, volume = "29", pages = "323--346", year = "1980", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(80)90248-7", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F10", MRnumber = "MR562767 (83e:65064)", bibdate = "Wed Jan 22 17:57:24 MST 1997", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", ZMnumber = "0431.65016", acknowledgement = ack-nhfb, classmath = "*65F10 Iterative methods for linear systems 65-04 Machine computation, programs (numerical analysis) 65F15 Eigenvalues (numerical linear algebra)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "conjugate gradient algorithm; implementation; Lanczos algorithm; large sparse symmetric matrix; linear system; selective orthogonalization; tridiagonalization", } @Book{Parlett:1980:SEP, author = "Beresford N. Parlett", title = "The Symmetric Eigenvalue Problem", publisher = pub-PH, address = pub-PH:adr, pages = "xix + 348", year = "1980", ISBN = "0-13-880047-2", ISBN-13 = "978-0-13-880047-5", LCCN = "QA188 .P3", MRclass = "65F15 (15A18)", MRnumber = "MR570116 (81j:65063)", MRreviewer = "Robert Todd Gregory", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib; https://www.math.utah.edu/pub/tex/bib/all_brec.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", note = "Prentice-Hall Series in Computational Mathematics", series = "Series in Computational Mathematics", ZMnumber = "0431.65017", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18 Eigenvalues of matrices, etc. 15A57 Other types of matrices 15-02 Research monographs (linear algebra) 65-02 Research monographs (numerical analysis) 15A23 Factorization of matrices 65F25 Orthogonalization (numerical linear algebra)", keywords = "bandmatrices; bounds for eigenvalues; eigenvalues; generalized eigenvalue problem; Krylov sequences; localization of eigenvalues; orthogonal transformations; tridiagonal matrices; vector iteration", tableofcontents = "Notation: Inside Front Cover \\ Preface / xii \\ Introduction / xv \\ 1: Basic Facts about Self-Adjoint Matrices / 1 \\ 2: Tasks, Obstacles, and Aids / 17 \\ 3: Counting Eigenvalues / 38 \\ 4: Simple Vector Iterations / 58 \\ 5: Deflation / 81 \\ 6: Useful Orthogonal Matrices (Tools of the Trade) / 87 \\ 7: Tridiagonal Form / 111 \\ 8: The $QL$ and $QR$ Algorithms / 139 \\ 9: Jacobi Methods / 174 \\ 10: Eigenvalue Bounds / 185 \\ 11: Approximations from a Subspace / 209 \\ 12: Krylov Subspaces / 235 \\ 13: Lanczos Algorithms / 257 \\ 14: Subspace Iteration / 288 \\ 15: The General Linear Eigenvalue Problem / 302 \\ A Appendix: Rank One and Elementary Matrices / 329 \\ B: Appendix: Chebyshev Polynomials / 331 \\ References / 334 \\ Annotated Bibliography / 341 \\ Author and Subject Index / 345", tableofcontents = "Notation: Inside Front Cover \\ Preface / xii \\ Introduction / xv \\ 1: Basic Facts about Self-Adjoint Matrices / 1 \\ 1-1 Introduction / 1 \\ 1-2 Euclidean Space / 1 \\ 1-3 Eigenvalues / 5 \\ l-4 Self-Adjoint Matrices / 6 \\ 1-5 Quadratic Forms / 10 \\ 1-6 Matrix Norms / 13 \\ 1-7 The Generalized Eigenvalue Problem / 16 \\ 2: Tasks, Obstacles, and Aids / 17 \\ 2-1 What is Small? What is Large? / 17 \\ 2-2 Tasks / 19 \\ 2-3 Conflicting Requirements / 20 \\ 2-4 Finite Precision Arithmetic / 23 \\ 2-5 Cancellation / 25 \\ 2-6 Inner Product Analysis / 29 \\ 2-7 Can Small Eigenvalues Be Found with Low Relative Error? / 33 \\ 2-8 Available Programs / 34 \\ 2-9 Representative Timings / 36 \\ 2-10 Alternative Computer Architecture / 37 \\ 3: Counting Eigenvalues / 38 \\ 3-1 Triangular Factorization / 38 \\ 3-2 Error Analysis of Triangular Factorization / 43 \\ 3-3 Slicing the Spectrum / 46 \\ 3-4 Relation to Sturm Sequences / 52 \\ 3-5 Bisection and Secant Methods / 53 \\ 3-6 Hidden Eigenvalues / 55 \\ 3-7 The Characteristic Polynomial / 57 \\ 4: Simple Vector Iterations / 58 \\ 4-1 Eigenvectors of Rank One Matrices / 58 \\ 4-2 Direct and Inverse Iteration / 59 \\ 4-3 Advantages of an Ill Conditioned System / 65 \\ 4-4 Convergence and Orthogonality / 68 \\ 4-5 Simple Error Bounds / 69 \\ 4-6 The Rayleigh Quotient Iteration / 70 \\ 4-7 Local Convergence / 72 \\ 4-8 Monotonic Residuals / 75 \\ *4-9 Global Convergence / 76 \\ 5: Deflation / 81 \\ 5-1 Deflation by Subtraction / 81 \\ 5-2 Deflation by Restriction / 84 \\ 5-3 Deflation by Similarity Transformations / 85 \\ 6: Useful Orthogonal Matrices (Tools of the Trade) / 87 \\ 6-1 Orthogonals are Important / 87 \\ 6-2 Permutations / 88 \\ 6-3 Reflections (or Symmetries) / 90 \\ 6-4 Plane Rotations / 92 \\ 6-5 Error Propagation in a Sequence of Orthogonal Congruences / 94 \\ 6-6 Backward Error Analysis / 97 \\ 6-7 The $QR$ Factorization and Gram--Schmidt / 98 \\ *6-8 Fast Scaled Rotations / 100 \\ *6-9 Orthogonalization in the Face of Roundoff / 105 \\ 7: Tridiagonal Form / 111 \\ 7-1 Introduction / 111 \\ 7-2 Uniqueness of Reduction / 112 \\ 7-3 Minimizing Characteristics / 114 \\ 7-4 Explicit Reduction of a Full Matrix / 117 \\ 7-5 Reduction of a Banded Matrix / 120 \\ 7-6 Irrelevant Instability / 122 \\ 7-7 Eigenvalues are Simple / 124 \\ 7-8 Orthogonal Polynomials / 125 \\ 7-9 Eigenvectors of T / 127 \\ 7-10 Sturm Sequences / 131 \\ 7-11 When to Neglect an Off-Diagonal Element / 133 \\ 7-12 Inverse Eigenvalue Problems / 136 \\ 8: The $QL$ and $QR$ Algorithms / 139 \\ 8-1 Introduction / 139 \\ 8-2 The $QL$ Transformation / 140 \\ 8-3 Preservation of Bandwidth / 141 \\ 8-4 Relation between $QL$ and $QR$ / 142 \\ 8-5 $QL$, the Power Method, and Inverse Iteration / 144 \\ 8-6 Convergence of the Basic $QL$ Algorithm / 145 \\ 8-7 The Rayleigh Quotient Shift / 146 \\ 8-8 The Off-Diagonal Elements / 148 \\ 8-9 Residual Bounds Using Wilkinson's Shift / 149 \\ 8-10 Tridiagonal $QL$ Always Converges / 151 \\ 8-11 Asymptotic Convergence Rates / 154 \\ 8-12 Tridiagonal $QL$ with Explicit Shift / 157 \\ 8-13 Chasing the Bulge / 159 \\ 8-14 Shifts for all Seasons / 162 \\ 8-15 Casting Out Square Roots / 164 \\ 8-16 $QL$ for Banded Matrices / 170 \\ 9: Jacobi Methods / 174 \\ 9-1 Rotation in the Plane / 174 \\ 9-2 Jacobi Rotations / 176 \\ 9-3 Convergence / 178 \\ 9-4 Various Strategies / 180 \\ 9-5 Ultimate Quadratic Convergence / 181 \\ 9-6 Assessment of Jacobi Methods / 183 \\ 10: Eigenvalue Bounds / 185 \\ 10-1 Cauchy's Interlace Theorem / 186 \\ 10-2 The Minimax Characterization / 188 \\ 10-3 The Monotonicity Theorem / 191 \\ 10-4 The Residual Interlace Theorem / 194 \\ 10-5 Lehmann's Optimal Intervals / 198 \\ 10-6 Use of Bounds on the Missing Submatrix / 203 \\ 10-7 Use of Gaps in A's Spectrum / 206 \\ 11: Approximations from a Subspace / 209 \\ 11-1 Subspaces and Their Representation / 209 \\ 11-2 Invariant Subspaces / 211 \\ 11-3 The Rayleigh--Ritz Procedure / 213 \\ 11-4 Optimality / 215 \\ 11-5 Residual Bounds on Clustered Ritz Values / 218 \\ 11-6 No Residual Bounds on Ritz Vectors / 221 \\ 11-7 Gaps in the Spectrum / 221 \\ 11-8 Condensing the Residual / 225 \\ *11-9 A Priori Bounds for Interior Ritz Approximations / 226 \\ *11-10 Nonorthogonal Bases / 229 \\ *11-11 An Extension Theorem / 231 \\ 12: Krylov Subspaces / 235 \\ 12-1 Introduction / 235 \\ 12-2 Basic Properties / 237 \\ 12-3 Representation by Polynomials / 239 \\ 12-4 The Error Bounds of Kaniel and Saad / 242 \\ 12-5 Comparison with the Power Method / 250 \\ 12-6 Partial Reduction to Tridiagonal Form / 252 \\ 13: Lanczos Algorithms / 257 \\ 13-1 Krylov + Rayleigh--Ritz = Lanczos / 257 \\ 13-2 Assessing Accuracy / 260 \\ 13-3 The Effects of Finite Precision Arithmetic / 262 \\ 13-4 Paige's Theorem / 264 \\ 13-5 An Alternative Formula for 13 1 / 268 \\ 13-6 Convergence=> Loss of Orthogonality / 270 \\ 13-7 Maintaining Orthogonality / 272 \\ *13-8 Selective Orthogonalization / 275 \\ 13-9 Analysis of Selective Orthogonalization / 279 \\ *13-10 Band (or Block) Lanczos / 284 \\ 14: Subspace Iteration / 288 \\ 14-1 Introduction / 288 \\ 14-2 Implementations / 289 \\ 14-3 Improvements / 293 \\ *14-4 Convergence / 296 \\ 14-5 Sectioning / 299 \\ 15: The General Linear Eigenvalue Problem / 302 \\ 15-1 Introduction / 302 \\ 15-2 Symmetry is Not Enough / 303 \\ 15-3 Simultaneous Diagonalization of Two Quadratic Forms / 306 \\ 15-4 Explicit Reduction to Standard Form / 309 \\ *15-5 The Fix--Heiberger Reduction / 311 \\ 15-6 The $QZ$ Algorithm / 314 \\ 15-7 Jacobi Generalized / 315 \\ 15-8 Implicit Reduction to Standard Form / 316 \\ 15-9 Simple Vector Iterations / 317 \\ 15-10 Rayleigh Ritz Approximations / 321 \\ 15-11 Lanczos Algorithms / 323 \\ 15-12 Subspace Iteration / 325 \\ 15-13 Practical Considerations / 327 \\ A Appendix: Rank One and Elementary Matrices / 329 \\ B: Appendix: Chebyshev Polynomials / 331 \\ References / 334 \\ Annotated Bibliography / 341 \\ Author and Subject Index / 345", } @Article{Berman:1981:DSO, author = "A. Berman and B. N. Parlett and R. J. Plemmons", title = "Diagonal scaling to an orthogonal matrix", journal = j-SIAM-J-ALG-DISC-METH, volume = "2", number = "1", pages = "57--65", month = mar, year = "1981", CODEN = "SJAMDU", DOI = "https://doi.org/10.1137/0602008", ISSN = "0196-5212 (print), 2168-345X (electronic)", ISSN-L = "0196-5212", MRclass = "65F35 (15A21)", MRnumber = "MR604511 (82d:65040)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/siamjalgdiscmeth.bib", ZMnumber = "0498.65024", acknowledgement = ack-nhfb, classification = "C4140 (Linear algebra); C4170 (Differential equations)", classmath = "*65F35 Matrix norms, etc. (numerical linear algebra) 35L45 First order hyperbolic systems, initial value problems", corpsource = "Dept. of Math., Technion-Israel Inst. of Technol., Haifa, Israel", fjournal = "Society for Industrial and Applied Mathematics. Journal on Algebraic and Discrete Methods", journal-URL = "http://epubs.siam.org/loi/sjamdu", keywords = "algorithm; diagonal matrix; diagonal scaling; energy conserving norm; Hadamard quotient; hyperbolic equations; matrix algebra; orthogonal matrix; partial differential equation; partial differential equations; positive matrix; scaling factors", treatment = "A Application; T Theoretical or Mathematical", } @TechReport{Parlett:1981:ACT, author = "Beresford N. Parlett", title = "Analytic complexity theory and the solution of {$ A X = b $}", type = "Technical Report", number = "PAM-40", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jun, year = "1981", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @TechReport{Parlett:1981:FSF, author = "Beresford N. Parlett and B. Nour-Omid and M. R. Li", title = "A fast solver free of fill-in for finite element problems", type = "Technical Report", number = "PAM-42", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jun, year = "1981", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @TechReport{Parlett:1981:HSK, author = "Beresford N. Parlett", title = "How to solve {$ (K - \lambda M)z = 0 $} for large {$K$} and {$M$}", type = "Technical Report", number = "PAM-39", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jun, year = "1981", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @TechReport{Parlett:1981:LAL, author = "Beresford N. Parlett and D. Taylor", title = "A look-ahead {Lanczos} algorithm for unsymmetric matrices", type = "Technical Report", number = "PAM-43", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jun, year = "1981", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1981:BRBa, author = "B. Parlett and R. Tolimieri", title = "Book Review: {{\booktitle{A Matrix Eigenvalue Problem}} (G. Efroymson, A. Steger and S. Steinberg)}", journal = j-SIAM-REVIEW, volume = "23", number = "1", pages = "105--105", month = "????", year = "1981", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1023014", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Sat Mar 29 09:53:16 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/23/1; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 1981", } @Article{Parlett:1981:BRBb, author = "B. N. Parlett", title = "Book Review: {{\booktitle{{LINPACK} Users' Guide}} (J. J. Dongarra, J. R. Bunch, C. B. Moler and G. W. Stewart)}", journal = j-SIAM-REVIEW, volume = "23", number = "1", pages = "126--128", month = "????", year = "1981", CODEN = "SIREAD", DOI = "https://doi.org/10.1137/1023033", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", bibdate = "Sat Mar 29 09:53:16 MDT 2014", bibsource = "http://epubs.siam.org/toc/siread/23/1; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", onlinedate = "January 1981", } @TechReport{Parlett:1981:MSD, author = "Beresford N. Parlett and T. L. Landis", title = "Methods for scaling to doubly stochastic form", type = "Technical Report", number = "PAM-44", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jun, year = "1981", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1981:PNA, author = "Beresford Parlett", title = "Progress in numerical analysis", journal = "Yingyong Shuxue yu Jisuan Shuxue", volume = "3", pages = "1--10", year = "1981", MRclass = "65-02", MRnumber = "MR656304 (83d:65005)", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Translated from the English by Wu Mu", acknowledgement = ack-nhfb, fjournal = "Yingyong Shuxue yu Jisuan Shuxue. Applied Mathematics and Computational Mathematics", } @Article{Parlett:1981:TPL, author = "B. N. Parlett and J. K. Reid", title = "Tracking the Progress of the {Lanczos} Algorithm for Large Symmetric Eigenproblems", journal = j-IMA-J-NUMER-ANAL, volume = "1", number = "2", pages = "135--155", year = "1981", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/1.2.135", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65F15", MRnumber = "MR616327 (82e:65039)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; MathSciNet database", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib", ZMnumber = "0474.65022", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65Y99 Computer aspects of numerical algorithms", fjournal = "IMA (Institute of Mathematics and its Applications). Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", keywords = "interpolation procedures; Lanczos algorithm; large symmetric matrix", } @Article{Kahan:1982:RBA, author = "W. Kahan and B. N. Parlett and E. Jiang", title = "Residual Bounds on Approximate Eigensystems of Nonnormal Matrices", journal = j-SIAM-J-NUMER-ANAL, volume = "19", number = "3", pages = "470--484", month = jun, year = "1982", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0719030", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F15 (65F35)", MRnumber = "MR656463 (83h:65050)", MRreviewer = "William W. Hager", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @Article{Li:1982:FSF, author = "M. R. Li and B. Nour-Omid and B. N. Parlett", title = "A Fast Solver Free of Fill-in for Finite-element Problems", journal = j-SIAM-J-NUMER-ANAL, volume = "19", number = "6", pages = "1233--1242", month = dec, year = "1982", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0719088", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F10 (65F05 65N30)", MRnumber = "MR679662 (84b:65031)", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @TechReport{Parlett:1982:AUE, author = "Beresford N. Parlett and B. Nour-Omid", title = "An algorithm to update eigenvalues of a growing symmetric tridiagonal matrix", type = "Technical Report", number = "PAM-104", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = oct, year = "1982", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @Article{Parlett:1982:ELE, author = "B. N. Parlett and H. Simon and L. M. Stringer", title = "On Estimating the Largest Eigenvalue with the {L{\'a}nczos} Algorithm", journal = j-MATH-COMPUT, volume = "38", number = "157", pages = "153--165", month = jan, year = "1982", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2007471", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F15", MRnumber = "MR637293 (82m:65033)", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database; Theory/Matrix.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib", acknowledgement = ack-nhfb, classcodes = "B0210 (Algebra); B0290H (Linear algebra); C1110 (Algebra); C4140 (Linear algebra)", corpsource = "Dept. of Math., Univ. of California, Berkeley, CA, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "definite matrix; eigenvalue; eigenvalues and eigenfunctions; Lanczos algorithm; large matrices; matrix algebra; methods; misconvergence; numerical; positive", kwds = "nla, eig, Lanczos algorithm", treatment = "T Theoretical or Mathematical", } @TechReport{Parlett:1982:EP, author = "Beresford N. Parlett and B. Nour-Omid", title = "Element preconditioning", type = "Technical Report", number = "PAM-103", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = oct, year = "1982", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @Article{Parlett:1982:MSD, author = "B. N. Parlett and T. L. Landis", title = "Methods for Scaling to Doubly Stochastic Form", journal = j-LINEAR-ALGEBRA-APPL, volume = "48", number = "??", pages = "53--79", year = "1982", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(82)90099-4", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A12 (15A51 65F35)", MRnumber = "MR683210 (84b:15007)", MRreviewer = "Ray C. Shiflett", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", ZMnumber = "0508.15003", acknowledgement = ack-nhfb, classmath = "*15A12 Conditioning of matrices 65F35 Matrix norms, etc. (numerical linear algebra) 15A51 Stochastic matrices", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "convergence theorem; doubly stochastic matrices; nla, eig, nonnegative matrix, doubly stochastic matrix; scaling", xxtitle = "Methods for Scaling to Double Stochastic Form", } @InProceedings{Parlett:1982:TMS, author = "B. N. Parlett", title = "Two monitoring schemes for the {Lanczos} algorithm", crossref = "Glowinski:1982:CMA", year = "1982", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0499.65017", acknowledgement = ack-nhfb, classmath = "*65F10 Iterative methods for linear systems 65F15 Eigenvalues (numerical linear algebra) 65F25 Orthogonalization (numerical linear algebra)", keywords = "Lanczos algorithm; monitoring schemes; symmetric matrices", } @Article{Parlett:1982:WFT, author = "B. N. Parlett", title = "{Winograd}'s {Fourier} transform via circulants", journal = j-LINEAR-ALGEBRA-APPL, volume = "45", number = "??", pages = "137--155", year = "1982", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(82)90217-8", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65T05 (68C25)", MRnumber = "MR660985 (83f:65222)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", ZMnumber = "0515.65099", acknowledgement = ack-nhfb, classmath = "*65T40 Trigonometric approximation and interpolation 65F30 Other matrix algorithms 15A23 Factorization of matrices 42A15 Trigonometric interpolation", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "associated circulant matrices; discrete Fourier transform; eigenvalue-eigenvector decomposition; na, nla, eig, fft, fast algorithm, circulant matrix; real arithmetic; Winograd's algorithm", } @TechReport{McCurdy:1983:ACD, author = "A. McCurdy and K. C. Ng and Beresford N. Parlett", title = "Accurate computation of divided differences of the exponential function", type = "Technical Report", number = "PAM-160", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jun, year = "1983", bibdate = "Fri Nov 11 09:06:19 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Nour-Omid:1983:LVS, author = "Bahram Nour-Omid and Beresford N. Parlett and Robert L. Taylor", title = "{Lanczos} versus subspace iteration for solution of eigenvalue problems", journal = j-INT-J-NUMER-METHODS-ENG, volume = "19", number = "6", pages = "859--871", year = "1983", CODEN = "IJNMBH", DOI = "https://doi.org/10.1002/nme.1620190608", ISSN = "0029-5981 (print), 1097-0207 (electronic)", ISSN-L = "0029-5981", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0521.65024", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 74S05 Finite element methods", fjournal = "International Journal for Numerical Methods in Engineering", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207", keywords = "comparison of methods; Lanczos algorithm; large eigen problems; subspace iteration", } @Article{Nour-Omid:1983:NLM, author = "Bahram Nour-Omid and Beresford N. Parlett and Robert L. Taylor", title = "A {Newton--Lanczos} method for solution of nonlinear finite element equations", journal = j-COMP-STRUCTURES, volume = "16", number = "1--4", pages = "241--252", year = "1983", CODEN = "CMSTCJ", DOI = "https://doi.org/10.1016/0045-7949(83)90164-5", ISSN = "0045-7949 (print), 1879-2243 (electronic)", ISSN-L = "0045-7949", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0499.73058", acknowledgement = ack-nhfb, classmath = "*74S05 Finite element methods 65H10 Systems of nonlinear equations (numerical methods)", fjournal = "Computers and Structures", journal-URL = "http://www.sciencedirect.com/science/journal/00457949", keywords = "asymptotic cost estimates; initial-boundary value problems; Lanczos algorithm; linearized set of equations; local convergence characteristics; modified Newton method; Newton's method; Newton--Lanczos method; partial reorthogonalization; quasi-Newton; rate of convergence; selective orthogonalization; varied from superlinear to quadratic by controlling certain tolerance", } @TechReport{Parlett:1983:EMS, author = "Beresford N. Parlett and H. Wu and W. D. Wu", title = "Eigenvector matrices of symmetric tridiagonals", type = "Technical Report", number = "PAM-174", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = aug, year = "1983", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @Book{Parlett:1983:SPS, author = "Beresford N. Parlett", title = "Simmetrichnaya problema sobstvennykh znachenii. Chislennye metody ({Russian}) [The symmetric eigenvalue problem. Numerical methods]", publisher = pub-EDITORIAL-MIR, address = pub-EDITORIAL-MIR:adr, pages = "384", year = "1983", MRclass = "65-02 (15A18 65F15)", MRnumber = "MR702348 (85b:65003)", MRreviewer = "K. Moszy{\'n}ski", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Translated from the English by Kh. D. Ikranov and Yu. A. Kuznetsov.", ZMnumber = "0524.65023", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18 Eigenvalues of matrices, etc. 15-02 Research monographs (linear algebra) 65-02 Research monographs (numerical analysis) 15A23 Factorization of matrices 15A57 Other types of matrices 65F25 Orthogonalization (numerical linear algebra)", keywords = "bandmatrices; bounds for eigenvalues; eigenvalues; generalized eigenvalue problem; Krylov sequences; localization of eigenvalues; orthogonal transformations; tridiagonal matrices; vector iteration", language = "Russian", } @TechReport{Parlett:1983:SSE, author = "Beresford N. Parlett", title = "The software scene in the extraction of eigenvalues from sparse matrices", type = "Technical Report", number = "PAM-132", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = mar, year = "1983", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @TechReport{Parlett:1983:URE, author = "Beresford N. Parlett and B. Nour-Omid", title = "The use of refined error bound when updating eigenvalues of tridiagonals", type = "Technical Report", number = "PAM-175", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = sep, year = "1983", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @Article{McCurdy:1984:ACD, author = "A. McCurdy and K. C. Ng and B. N. Parlett", title = "Accurate Computation of Divided Differences of the Exponential Function", journal = j-MATH-COMPUT, volume = "43", number = "168", pages = "501--528", month = oct, year = "1984", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2008291", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65D20 (33A10 65G05)", MRnumber = "MR758198 (86e:65029)", MRreviewer = "S. Conde", bibdate = "Tue Oct 13 08:06:19 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib", acknowledgement = ack-nhfb, fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", } @TechReport{Nour-Omid:1984:HIS, author = "N. Nour-Omid and B. N. Parlett", title = "How to implement the spectral transformation", type = "Technical Report", number = "PAM-224", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, pages = "????", year = "1984", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @TechReport{Parlett:1984:ECM, author = "Beresford N. Parlett and B. Nour-Omid and J. Natvig", title = "Effect of the {CYBER 205} on methods for computing natural frequencies of structures", type = "Technical Report", number = "PAM-218", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = apr, year = "1984", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @Article{Parlett:1984:EMS, author = "B. N. Parlett and W. D. Wu", title = "Eigenvector matrices of symmetric tridiagonals", journal = j-NUM-MATH, volume = "44", number = "1", pages = "103--110", month = jun, year = "1984", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/BF01389758", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F15", MRnumber = "MR745089 (85h:65083)", bibdate = "Mon May 26 11:49:34 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/nummath.bib", acknowledgement = ack-nhfb, classification = "B0210 (Algebra); C1110 (Algebra)", corpsource = "Maths. Dept., Univ. of California, Berkeley, CA, USA", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "eigenvalues and eigenfunctions; eigenvector matrix; matrix algebra; symmetric tridiagonals", treatment = "T Theoretical or Mathematical", } @InProceedings{Parlett:1984:LAL, author = "B. N. Parlett and D. R. Taylor and Z. S. Liu", title = "The look ahead {L{\'a}nczos} algorithm for large unsymmetric eigenproblems", crossref = "Glowinski:1984:CMA", pages = "87--96", year = "1984", MRclass = "65F15", MRnumber = "MR806772 (86k:65028)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0564.65021", abstract = "A modification of the Lanczos algorithm for solving eigenproblems for large unsymmetric matrices is proposed. The algorithm is based on the idea of the pivoting strategy introduced in the paper of {\it J. R. Bunch} and {\it B. N. Parlett} [SIAM J. Numer. Anal. 8, 639-655 (1971; Zbl 0199.498)], which reduces the occurrence of breakdown of the algorithm. Some details of the modified algorithm are discussed", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", keywords = "breakdown; Lanczos algorithm; large unsymmetric matrices; pivoting strategy", reviewer = "T. Reginska", } @Article{Parlett:1984:SSE, author = "B. N. Parlett", title = "The Software Scene in the Extraction of Eigenvalues from Sparse Matrices", journal = j-SIAM-J-SCI-STAT-COMP, volume = "5", number = "3", pages = "590--604", month = sep, year = "1984", CODEN = "SIJCD4", DOI = "https://doi.org/10.1137/0905042", ISSN = "0196-5204", ISSN-L = "0196-5204", MRclass = "65F15 (65F50)", MRnumber = "MR754487 (85i:65048)", MRreviewer = "David R. Kincaid", bibdate = "Mon Mar 31 09:59:24 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/fortran2.bib; https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib", ZMnumber = "0573.65025", acknowledgement = ack-nhfb, classification = "C4140 (Linear algebra); C7310 (Mathematics computing)", classmath = "*65F15 Eigenvalues (numerical linear algebra) 15-04 Machine computation, programs (linear algebra) 65F50 Sparse matrices 68N99 Software", conflocation = "Fairfield Glade, TN, USA; 25-27 Oct. 1982", conftitle = "Sparse Matrix Symposium", corpsource = "Dept. of Math., California Univ., Berkeley, CA, USA", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", keywords = "dense matrices; efficiency; eigenvalue programs; eigenvalues; eigenvalues and eigenfunctions; EISPACK; FORTRAN subroutines; Lanczos; Lanczos algorithm; matrix algebra; reliability; software; software packages; sparse matrices; subspace iteration; survey on available software; users", reviewer = "F. M{\'o}ricz", sponsororg = "Army Res. Office; Office of Naval Res.; Oak Ridge Nat. Lab", treatment = "P Practical", } @Book{Cullum:1985:LAL, author = "Jane K. Cullum and Ralph A. Willoughby", title = "{Lanczos} Algorithms for Large Symmetric Eigenvalue Computations, Volume {I} Theory", publisher = pub-BIRKHAUSER, address = pub-BIRKHAUSER:adr, pages = "xiv + 273", year = "1985", ISBN = "0-8176-3058-9", ISBN-13 = "978-0-8176-3058-4", bibdate = "Mon Mar 6 15:34:09 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, mynote = "Only skimmed. Tiny typeface. Emphasizes `local orthogonality is enough' approach, as opposed to Parlett \cite{Parlett:1980:SEP}'s `global orthogonality is crucial'. They summarize Paige's error analysis but don't (?) given any of their own.", } @Article{Nour-Omid:1985:EPU, author = "B. Nour-Omid and B. N. Parlett", title = "Element preconditioning using splitting techniques", journal = j-SIAM-J-SCI-STAT-COMP, volume = "6", number = "3", pages = "761--770", month = jul, year = "1985", CODEN = "SIJCD4", DOI = "https://doi.org/10.1137/0906051", ISSN = "0196-5204", ISSN-L = "0196-5204", MRclass = "65F10 (49D07 65N20)", MRnumber = "MR791197 (86h:65046)", MRreviewer = "Beny Neta", bibdate = "Mon Mar 31 09:59:33 MDT 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib; Parallel/mgnet.bib; Parallel/Multi.grid.bib", URL = "https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib", ZMnumber = "0582.65019", abstract = "For large sparse linear systems {$ A x = b $} arising in the solution of partial differential equations via the finite element method, preconditioning of the conjugate gradient method is considered. Splitting techniques are used for the preconditioning. The resulting method is examined and it's behaviour tested on a model problem.", acknowledgement = ack-nhfb, classification = "B0290P (Differential equations); C4170 (Differential equations)", classmath = "*65F10 Iterative methods for linear systems 65N30 Finite numerical methods (BVP of PDE) 65F35 Matrix norms, etc. (numerical linear algebra) 35J25 Second order elliptic equations, boundary value problems", corpsource = "Center for Pure and Appl. Math., California Univ., Berkeley, CA, USA", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", keywords = "assembly process; boundary-value problems; code; conjugate gradient algorithm; conjugate gradient method; element preconditioning; elliptic boundary value problems; finite element analysis; finite element method; large sparse linear systems; large symmetric systems; numerical example; preconditioning; Splitting; splitting techniques", onlinedate = "July 1985", reviewer = "V. Mehrmann", treatment = "T Theoretical or Mathematical", } @TechReport{Parlett:1985:CSI, author = "Beresford N. Parlett and Y. Saad", title = "Complex shift and invert strategies for real matrices", type = "Research report", number = "RR-424", institution = "Department of Computer Science, Yale University", address = "New Haven, CT, USA", pages = "17", year = "1985", bibdate = "Fri Nov 11 05:42:25 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Parlett:1985:DAA, author = "Beresford N. Parlett and K. C. Ng", title = "Development of an accurate algorithm for {$ \exp (B t) $}", type = "Technical Report", number = "PAM-294", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = aug, year = "1985", bibdate = "Fri Nov 11 09:06:19 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @InProceedings{Parlett:1985:ILA, author = "B. Parlett and B. Nour-Omid and J. Jatvig", title = "Implementation of {Lanczos} Algorithms on Vector Computers", crossref = "Numrich:1985:SA", pages = "1--18", year = "1985", bibdate = "Thu Nov 10 18:36:35 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/ovr.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1985:LAL, author = "Beresford N. Parlett and Derek R. Taylor and Zhishun A. Liu", title = "A look-ahead {L{\'a}nczos} algorithm for unsymmetric matrices", journal = j-MATH-COMPUT, volume = "44", number = "169", pages = "105--124", month = jan, year = "1985", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2007796", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F15", MRnumber = "MR771034 (86f:65072)", MRreviewer = "Youcef Saad", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database; Parallel/par.lin.alg.bib", URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib", ZMnumber = "0564.65022", abstract = "The Lanczos algorithm for nonsymmetric matrices is studied. It is shown how breakdown caused by a pair of corresponding basis vectors being orthogonal can be remedied by computing further vectors in the Krylov sequences. This corresponds to performing $ 2 \times 2 $ pivots when factorizing the moment matrix, which may be indefinite for nonsymmetric eigenproblems. It is stated that when $ 2 \times 2 $ pivots are insufficient to continue the process, all eigenvalues have converged. Results of a few numerical tests are reported.", acknowledgement = ack-nhfb, classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", classmath = "*65F15 Eigenvalues (numerical linear algebra)", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "eigenvalues and eigenfunctions; instability; Krylov sequences; Lanczos algorithm; look-ahead Lanczos algorithm; matrix; matrix algebra; moment; nonsymmetric eigenproblems; numerical tests; plasma; triangular factorization; tridiagonal matrix; unsymmetric matrices", reviewer = "A. Ruhe", treatment = "T Theoretical or Mathematical", } @Article{Parlett:1985:URE, author = "B. N. Parlett and B. Nour-Omid", title = "The Use of a Refined Error Bound When Updating Eigenvalues of Tridiagonals", journal = j-LINEAR-ALGEBRA-APPL, volume = "68", number = "??", pages = "179--219", year = "1985", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(85)90213-7", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F15 (65-04)", MRnumber = "MR794821 (86j:65046)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/gvl.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", ZMnumber = "0629.65037", abstract = "For computing some eigenvalues of a given symmetric matrix {$A$} the Lanczos algorithm is used. It provides a nested sequence of tridiagonal matrices {$ T \sb j $}, whose eigenvalues approximate those of A. The eigenvalues of {$ T \sb j $} tend to stagnate quite early (as functions of j). An algorithm (ANALYZE T) is described, which is a part of the inner loops of the Lanczos algorithm, and which monitors the convergence behaviour of the Ritz values. It helps, e.g., to avoid the so-called misconvergence.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 15-04 Machine computation, programs (linear algebra)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "convergence; eigenvalues; Lanczos algorithm; misconvergence; nested sequence of tridiagonal matrices; nla, eig, pert, tridiagonal matrix; Ritz values", reviewer = "L. Elsner", xxpages = "179--220", } @Article{Natvig:1986:ECC, author = "J. Natvig and B. Nour-Omid and B. N. Parlett", title = "Effect of the {CYBER 205} on the choice of method for solving the eigenvalue problem {$ (A - \lambda M) x = 0 $}", journal = j-J-COMPUT-APPL-MATH, volume = "15", number = "2", pages = "137--159", month = jun, year = "1986", CODEN = "JCAMDI", DOI = "https://doi.org/10.1016/0377-0427(86)90023-3", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", bibdate = "Sat Feb 25 11:59:56 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib", URL = "http://www.sciencedirect.com/science/article/pii/0377042786900233", ZMnumber = "0635.65032", abstract = "For the eigenvalue problem {$ A x = \lambda M x $}, {$A$}, {$B$} large, sparse, symmetric matrices, two methods, subspace iteration and Lanczos method, are compared when running on typical examples from structural dynamic analysis (order of {$A$}, {$B$} up to 8000) on a Cyber 205. A fixed number of eigenpairs is calculated. As on serial computers it turns out on this vector computer that the Lanczos algorithm is considerably faster. However, on problems with substantial overhead in reading\slash writing, a block Lanczos method is preferable.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F50 Sparse matrices", fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", keywords = "comparison of methods; eigenvalue problem; Lanczos method; large, sparse, symmetric matrices; subspace iteration; vector computer; vectorization", reviewer = "L. Elsner", } @InProceedings{Parlett:1986:ACM, author = "B. N. Parlett and K. C. Ng", title = "Accurate computation of the matrix exponential", crossref = "Glowinski:1986:CMA", pages = "107--116", year = "1986", MRclass = "65F30", MRnumber = "MR905289 (89f:65048)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0677.65040", abstract = "This document describes a program to compute the exponential of a given $ n \times n $ matrix B multiplied by a scalar $ \tau $ that is to be thought of as representing time. Our primary goal has been to achieve as much accuracy as working precision permits without resorting to simulated higher precision. The final product is more complicated than we anticipated at the outset. How these complications came to be accepted is the theme of this story. The cases we consider may be of interest to those who wish to use the matrix exponential in their work. We hasten to add that the code acts simply on simple cases.", acknowledgement = ack-nhfb, classmath = "*65F30 Other matrix algorithms 15-04 Machine computation, programs (linear algebra) 15A60 Appl. of functional analysis to matrix theory", keywords = "accuracy; accurate computation; matrix exponential; program; working precision", } @InProceedings{Schreiber:1986:BRC, author = "Robert S. Schreiber and Beresford N. Parlett", title = "Block reflectors: Computation and applications", crossref = "Glowinski:1982:CMA", pages = "71--79", year = "1986", MRclass = "65F30 (65W05)", MRnumber = "MR905287 (88h:65090)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0677.65039", abstract = "A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimension may be greater than one. We shall develop the properties of block reflectors and give an algorithm for computing a block reflector that introduces a block of zero into a matrix. We consider the compact representation of block reflectors, some applications, and their use in parallel computers.", acknowledgement = ack-nhfb, classmath = "*65F30 Other matrix algorithms 65Y05 Parallel computation (numerical methods)", keywords = "algorithm; block reflector; orthogonal, symmetric matrix; parallel computers", } @Article{Nour-Omid:1987:HIS, author = "Bahram Nour-Omid and Beresford N. Parlett and Thomas Ericsson and Paul S. Jensen", title = "How to Implement the Spectral Transformation", journal = j-MATH-COMPUT, volume = "48", number = "178", pages = "663--673", month = apr, year = "1987", CODEN = "MCMPAF", DOI = "https://doi.org/10.2307/2007835", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65F15", MRnumber = "MR878698 (88f:65062)", MRreviewer = "William W. Hager", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database", URL = "https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib", ZMnumber = "0638.65026", acknowledgement = ack-nhfb, classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", classmath = "*65F15 Eigenvalues (numerical linear algebra)", corpsource = "Lockheed Palo Alto, Res. Lab., CA, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "algebra; Cholesky factor; eigenpairs; eigenvalue; eigenvalue equations; eigenvalues and eigenfunctions; factorization; inverse; iteration; iterative methods; Lanczos algorithm; linear; matrix; numerical methods; reductions; Ritz vectors; spectral transformation; symmetric matrices; transformation step", reviewer = "L. Boubel{\'\i}kov{\'a}", treatment = "T Theoretical or Mathematical", } @TechReport{Parlett:1987:BRT, author = "Beresford N. Parlett and Robert Schreiber", title = "Block reflectors: theory and computation", type = "Technical Report", number = "PAM-378", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = may, year = "1987", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @TechReport{Parlett:1987:CJH, author = "Beresford N. Parlett", title = "A contribution of {J. H. Wilkinson} to numerical analysis", type = "Technical Report", number = "PAM-372", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = apr, year = "1987", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @TechReport{Parlett:1987:CLC, author = "Beresford N. Parlett and B. Nour-Omid and A. Raefsky", title = "Comparison of {Lanczos} with conjugate gradient using element preconditioning", type = "Technical Report", number = "PAM-363", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = feb, year = "1987", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @Article{Parlett:1987:CSI, author = "Beresford N. Parlett and Youcef Saad", title = "Complex Shift and Invert Strategies for Real Matrices", journal = j-LINEAR-ALGEBRA-APPL, volume = "88/89", number = "??", pages = "575--595", year = "1987", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(87)90126-1", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F05", MRnumber = "MR882464 (88d:65056)", MRreviewer = "H. R. Schwarz", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib", URL = "https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib; https://www.math.utah.edu/pub/tex/bib/linala1980.bib", ZMnumber = "0623.65045", abstract = "Algorithms for the nonsymmetric eigenvalue problem {$ (F - \lambda M)X = 0 $} with real matrices are studied. It is shown that the symmetry around the real axis can be exploited in algorithms based on inverse iteration. Algorithm are developed which use either the real or the imaginary part of {$ (F - \lambda M) \sp {-1}M $}, obtained by a complex banded Gaussian elimination. Numerical results are given for an example arising from a brusselator model of a tubular chemical reactor.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 80A32 Chemically reacting flows", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "Algorithm; banded Gaussian elimination; inverse iteration; nonsymmetric eigenvalue problem; Numerical results; tubular chemical reactor", reviewer = "A. Ruhe", } @InProceedings{Parlett:1987:JHW, author = "B. N. Parlett", title = "{J. H. Wilkinson}'s work and influence on matrix computations", crossref = "Crane:1987:HAC", pages = "133--138", year = "1987", DOI = "https://doi.org/10.1145/41579.41593", bibdate = "Fri Nov 17 09:59:14 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", acknowledgement = ack-nhfb, subject-dates = "James H. Wilkinson (27 September 1919--5 October 1986)", } @TechReport{Parlett:1987:MLA, author = "Beresford N. Parlett", title = "Misconvergence in the {Lanczos} algorithm", type = "Technical Report", number = "PAM-404", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = dec, year = "1987", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Parlett:1987:PSD, author = "Beresford N. Parlett and K. C. Ng", title = "Programs to swap diagonal blocks", type = "Technical Report", number = "PAM-381", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jun, year = "1987", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @TechReport{Parlett:1987:SAE, author = "Beresford N. Parlett", title = "The state-of-the-art in extracting eigenvalues and eigenvectors in structural mechanics", type = "Technical Report", number = "PAM-373", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = apr, year = "1987", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @TechReport{Gao:1988:CCS, author = "F. Gao and Beresford N. Parlett", title = "Communication cost of sparse {Cholesky} factorization on a hypercube", type = "Technical Report", number = "PAM-436", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = dec, year = "1988", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Le:1988:FIT, author = "J. Le and Beresford N. Parlett", title = "On the forward instability of the {$ Q R $} transformation", type = "Technical Report", number = "PAM-419", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jul, year = "1988", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @InProceedings{Nour-Omid:1988:CLC, author = "B. Nour-Omid and B. Parlett and A. Raefsky", title = "Comparison of {Lanczos} with Conjugate Gradient Using Element Preconditioning", crossref = "Glowinski:1988:FIS", pages = "250--260", year = "1988", bibdate = "Thu Nov 10 18:35:12 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/ovr.bib", ZMnumber = "0658.65034", acknowledgement = ack-nhfb, classmath = "*65F10 Iterative methods for linear systems 65F35 Matrix norms, etc. (numerical linear algebra) 65N30 Finite numerical methods (BVP of PDE) 35J25 Second order elliptic equations, boundary value problems", keywords = "conjugate gradients; finite elements; Lanczos method; preconditioning", reviewer = "H. R. Schwarz", } @TechReport{Parlett:1988:HMS, author = "Beresford N. Parlett and B. Nour-Omid and Zhishun A. Liu", title = "How to maintain semi-orthogonality among {Lanczos} vectors", type = "Technical Report", number = "PAM-420", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jul, year = "1988", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Parlett:1988:UII, author = "Beresford N. Parlett and H. C. Chen", title = "Use of an indefinite inner product for computing damped natural modes", type = "Technical Report", number = "PAM-435", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = nov, year = "1988", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Schreiber:1988:BRT, author = "Robert S. Schreiber and Beresford N. Parlett", title = "Block Reflectors: {Theory} and Computation", journal = j-SIAM-J-NUMER-ANAL, volume = "25", number = "1", pages = "189--205", month = feb, year = "1988", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/0725014", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65F05 (65F20)", MRnumber = "MR923934 (89c:65040)", MRreviewer = "David R. Hill", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; JSTOR database; Theory/Matrix.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/ovr.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib", ZMnumber = "0637.65017", abstract = "Block reflectors are the generalization of the Householder transformation to block elimination (instead of single element). A complete theory is presented. Some stable algorithms are introduced. Block reflectors are advantageous on parallel computers.", acknowledgement = ack-nhfb, classmath = "*65F05 Direct methods for linear systems 65F20 Overdetermined systems (numerical linear algebra) 65Y05 Parallel computation (numerical methods)", fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", keywords = "block elimination; Block reflectors; Householder transformation; parallel computers; QR-factorization; stable algorithms", kwds = "math, la, nla, Householder transformation, qrd, prll", reviewer = "W. Sch{\"o}nauer", } @TechReport{Parlett:1989:SBI, author = "Beresford N. Parlett", title = "Some basic information on information-based complexity theory", type = "Technical Report", number = "PAM-460", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jul, year = "1989", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @Article{Parlett:1989:TBB, author = "Beresford N. Parlett and Bahram Nour-Omid", title = "Towards a black box {Lanczos} program", journal = j-COMP-PHYS-COMM, volume = "53", number = "1--3", pages = "169--179", month = may, year = "1989", CODEN = "CPHCBZ", DOI = "https://doi.org/10.1016/0010-4655(89)90158-6", ISSN = "0010-4655 (print), 1879-2944 (electronic)", ISSN-L = "0010-4655", bibdate = "Mon Feb 13 10:28:26 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; http://www.sciencedirect.com/science/article/pii/0010465589901586", ZMnumber = "0798.65054", abstract = "The Lanczos algorithm may be used to find a few eigenvalues and eigenvectors of a large matrix. We describe some of the difficulties encountered in trying to make a black box program requiring no judgements from the user.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", fjournal = "Computer Physics Communications", journal-URL = "http://www.sciencedirect.com/science/journal/00104655", keywords = "black box program; eigenvalues; eigenvectors; Lanczos algorithm; large matrix", } @Article{Gao:1990:NCA, author = "Feng Gao and Beresford N. Parlett", title = "A note on communication analysis of parallel sparse {Cholesky} factorization on a hypercube", journal = j-PARALLEL-COMPUTING, volume = "16", number = "1", pages = "59--60", month = nov, year = "1990", CODEN = "PACOEJ", DOI = "https://doi.org/10.1016/0167-8191(90)90158-6", ISSN = "0167-8191 (print), 1872-7336 (electronic)", ISSN-L = "0167-8191", MRclass = "65Y05", MRnumber = "MR1089846 (92a:65361)", bibdate = "Mon Apr 14 12:07:40 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra); C4240 (Programming and algorithm theory)", corpsource = "Dept. of Comput. Sci. British Columbia Univ., Vancouver, BC, Canada", fjournal = "Parallel Computing. Theory and Applications", journal-URL = "http://www.sciencedirect.com/science/journal/01678191", keywords = "communication analysis; factorization; hypercube; linear algebra; nested-dissection method; parallel algorithms; parallel sparse Cholesky", treatment = "P Practical; T Theoretical or Mathematical", } @InProceedings{Parlett:1990:CJH, author = "Beresford N. Parlett", title = "The Contribution of {J. H. Wilkinson} to Numerical Analysis", crossref = "Nash:1990:HSC", pages = "17--30", year = "1990", MRclass = "01A70 (65-03)", MRnumber = "MR1203099", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, mycrossref = "Nash:1990:HSC", } @InProceedings{Parlett:1990:LAI, author = "B. N. Parlett and H. C. Chen", title = "The {Lanczos} algorithm with indefinite inner product", crossref = "Kaashoek:1990:PIS", volume = "5", pages = "393--400", year = "1990", MRclass = "65F15 (15A18 70J10 73K12)", MRnumber = "MR1115469 (92g:65043)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", series = "Progr. Systems Control Theory", ZMnumber = "0719.65026", abstract = "A quadratic eigenvalue problem with symmetric positive definite coefficient matrices may be reduced to linear form while retaining symmetry in the new coefficients but neither of them will be positive definite. Formally the symmetric Lanczos algorithm and subspace iteration may be used to compute some eigenpairs of the linear problem. The trouble is that the basis vectors are orthogonal with respect to an indefinite inner product so there is no assurance that they will be linearly independent. Nevertheless this is an attractive way to solve the original problem and we discuss how to implement it and how it relates to the unsymmetric Lanczos procedures. We discuss complex origin shifts, the Look-Ahead version, reorthogonalization, and error bounds.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", keywords = "complex origin shifts; eigenpairs; error bounds; indefinite inner product; Look-Ahead version; quadratic eigenvalue problem; reorthogonalization; subspace iteration; symmetric Lanczos algorithm", } @InProceedings{Parlett:1990:MLA, author = "Beresford N. Parlett", title = "Misconvergence in the {Lanczos} Algorithm", crossref = "Cox:1990:RNC", pages = "7--24", year = "1990", MRclass = "65F15", MRnumber = "MR1098315 (91m:65110)", bibdate = "Tue Nov 2 19:30:33 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib", ZMnumber = "0726.65032", abstract = "Theoretical and computational tools are developed in this paper that help to understand and predict the apparent misconvergence in Lanczos' method for matrices with clustered eigenvalues. A computable ``point of discovery'' is given that aids with discovering eigenvalues hidden by the misconvergence of the Ritz values in Lanczos' algorithm. The solution hinges on ``Ritz intervals'' and their ``effective spread'', rather than the Ritz values themselves.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F35 Matrix norms, etc. (numerical linear algebra) 15A42 Inequalities involving eigenvalues and eigenvectors", keywords = "convergence; Lanczos' method; matrices with clustered eigenvalues; misconvergence; point of discovery; Ritz intervals; Ritz values", reviewer = "F. Uhlig (Auburn)", } @TechReport{Parlett:1990:RTF, author = "Beresford N. Parlett", title = "Reduction to tridiagonal form and minimal realizations", type = "Technical Report", number = "PAM-486", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jan, year = "1990", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @Article{Parlett:1990:UIP, author = "B. N. Parlett and H. C. Chen", title = "Use of indefinite pencils for computing damped natural modes", journal = j-LINEAR-ALGEBRA-APPL, volume = "140", number = "??", pages = "53--88", year = "1990", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/0024-3795(90)90222-X", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F15 (15A18)", MRnumber = "MR1075543 (92b:65030)", MRreviewer = "M. Tismenetsky", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/linala1990.bib", ZMnumber = "0725.65055", abstract = "A quadratic eigenvalue problem {$ (\lambda \sp 2 \sb i \cdot M + \lambda \sb i C + K) \omega \sb i = 0, $} $ i = 1, ..., 2 n $ is solved where {$M$}, {$C$}, {$K$} are real symmetric and positive definite $ n \times n $ matrices. This problem may be reduced to linear symmetric but not positive definite form. The new problem is {$ (A - 1 / \lambda B)z = 0, $} where {$A$}, {$B$} are symmetric but indefinite matrices.\par The problems are solved by means of the Lanczos algorithm. When {$K$} is singular, then the shifted problem is solved. Real or complex origin shifts, reorthogonalization, and error bounds are discussed. Several methods for solving the reduced problem are mentioned. Some dangers are described, and examples are given comparing the Lanczos algorithm with subspace iteration.", acknowledgement = ack-nhfb, classmath = "*65H17 Eigenvalue and bifurcation problems of nonlinear algebraic equations 65F15 Eigenvalues (numerical linear algebra)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "comparison of methods; error bounds; indefinite pencils; Lanczos algorithm; quadratic eigenvalue problem; reorthogonalization; subspace iteration; symmetric positive definite matrices", reviewer = "L. Boubel{\'\i}kov{\'a} (Praha)", } @Article{Golub:1991:DJW, author = "G. Golub and B. Parlett", title = "Dedication to {J. Wallace Givens}", journal = j-SIAM-J-MAT-ANA-APPL, volume = "12", number = "1", pages = "U1--U1", month = jan, year = "1991", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @TechReport{Hill:1991:RIP, author = "R. O. Hill and Beresford N. Parlett", title = "Refined interlacing properties", type = "Technical Report", number = "PAM-517", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jan, year = "1991", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Parlett:1991:IMR, author = "Beresford N. Parlett and Wee-Liang Heng", title = "Implementation of minimal representation in {$2$D} {Ising} model calculations", type = "Technical Report", number = "PAM-550", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = may, year = "1991", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Longer version (60 pages)(to be published) of \#549", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @InProceedings{Parlett:1991:QFI, author = "Beresford N. Parlett and Jian Le", title = "{QR}; its forward instability and failure to converge", crossref = "Albrecht:1991:NTE", pages = "177--189", year = "1991", MRclass = "65F10 (65F35)", MRnumber = "MR1109104", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", series = "Internat. Ser. Numer. Math.", ZMnumber = "0724.65036", abstract = "The QR factorization of a rectangular matrix {$B$} is known to be backward stable; however, forward instability may occur, i.e., the computed orthogonal transformations are far from the exact ones. On the other hand, if the rank of {$B$} happens to be smaller than the number of columns, then the QR factorization is not unique. The paper shows precisely that forward instability occurs if and only if {$B$} is close to a matrix whose QR factorization is not unique. The analysis is focussed on tridiagonal matrices and upper Hessenberg ones; the implementation of the QR algorithm is the usual one consisting in a shift followed by premultiplication by plane rotation matrices. Several illustrative examples are also discussed.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F25 Orthogonalization (numerical linear algebra)", keywords = "convergence; forward instability; Hessenberg matrices; QR algorithm; QR factorization; rectangular matrix; tridiagonal matrices", reviewer = "J. P. Milaszewicz (Buenos Aires)", } @Article{Parlett:1991:SMP, author = "Beresford N. Parlett", title = "Symmetric matrix pencils", journal = j-J-COMPUT-APPL-MATH, volume = "38", number = "1--3", pages = "373--385", day = "23", month = dec, year = "1991", CODEN = "JCAMDI", DOI = "https://doi.org/10.1016/0377-0427(91)90183-K", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", MRclass = "15A22 (65F15)", MRnumber = "MR1146990 (92m:15011)", MRreviewer = "F. Szidarovszky", bibdate = "Sat Feb 25 13:02:23 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib", note = "Proceedings of the International Symposium on Computational Mathematics (Matsuyama, 1990).", URL = "http://www.sciencedirect.com/science/article/pii/037704279190183K", ZMnumber = "0772.15005", abstract = "Typical matrix eigenvalue problems, quadratic or linear, are best formulated as pencils {$ (A, M) $} in which both {$A$} and {$M$} are real and symmetric. This fact is emphasized in the paper through a set of physical examples. Then, the canonical forms are used to explain the role of the sign characteristic attached to real eigenvalues.\par The Rayleigh quotient is analyzed to describe real eigenvalues and it seems plausible that the class of definite Hermitian pencils is the broadest extension of the class of Hermitian matrices that retains the classical properties. This sheds new light on the class of definite pencils and the stability of their eigenvalues under perturbations. The reduction of indefinite pencils to useful sparse forms is also mentioned.", acknowledgement = ack-nhfb, classmath = "*15A22 Matrix pencils 15A18 Eigenvalues of matrices, etc", fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", keywords = "canonical forms; congruence; definite pencils; equivalence; Hermitian pencils; indefinite pencils; matrix eigenvalue problems; matrix pencils; Rayleigh quotient; rotation transformation; stability; symmetric matrix pencils", reviewer = "M. de la Sen (Bilbao)", } @TechReport{Fernando:1992:ASVa, author = "K. Vince Fernando and Beresford N. Parlett", title = "Accurate Singular Values and Differential qd Algorithms", type = "Technical Report", number = "TR2/92", institution = "NAG Ltd.", address = "Oxford, UK", pages = "????", month = jul, year = "1992", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "To appear in Numer. Math.", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @TechReport{Fernando:1992:ASVb, author = "K. Vince Fernando and Beresford N. Parlett", title = "Accurate singular values and differential qd algorithms", type = "Technical Report", number = "PAM-554", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jul, year = "1992", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @InProceedings{Fernando:1993:ASVc, author = "K. Vince Fernando and Beresford N. Parlett", title = "Accurate singular values and differential qd algorithms", crossref = "Moonen:1993:LAL", pages = "371--374", year = "1993", bibdate = "Thu May 29 18:42:39 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Hill:1992:RIP, author = "R. O. {Hill, Jr.} and B. N. Parlett", title = "Refined Interlacing Properties", journal = j-SIAM-J-MAT-ANA-APPL, volume = "13", number = "1", pages = "239--247", month = jan, year = "1992", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A18 (15A42)", MRnumber = "MR1146664 (92m:15007)", MRreviewer = "Lajos L{\'a}szl{\'o}", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", ZMnumber = "0747.15004", abstract = "Interlacing results and theorems for eigenvalues due to Cauchy, Golub, and Kahan are extended and related to the last component of eigenvectors.", acknowledgement = ack-nhfb, classmath = "*15A42 Inequalities involving eigenvalues and eigenvectors 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 = "Cauchy's interlace theorem; crowded interlacing; eigenvalues; eigenvectors", reviewer = "B. Ruffer-Beedgen (Ladenburg)", } @Article{Hirsch:1992:ERS, author = "Morris W. Hirsch and Richard S. Palais", title = "{Editors}' remarks: {``Some basic information on information-based complexity theory'' [Bull. Amer. Math. Soc. (N.S.) {\bf 26} (1992), no. 1, 3--27; MR1102755 (94e:68077a)] by B. N. Parlett and ``Perspectives on information-based complexity'' [Bull. Amer. Math. Soc. (N.S.) {\bf 26} (1992), no. 1, 29--52; MR1102756 (94e:68077b)] by J. F. Traub and H. Wo{\'z}niakowski}", journal = j-BULL-AMS-N-S, volume = "26", number = "1", pages = "1--2", year = "1992", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0273-0979-1992-00238-0", ISSN = "0273-0979 (print), 1088-9485 (electronic)", MRclass = "68Q30 (00A30 65Y20)", MRnumber = "MR1141473 (94e:68076)", MRreviewer = "Arthur G. Werschulz", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "American Mathematical Society. Bulletin. New Series", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", } @TechReport{Parlett:1992:MES, author = "Beresford N. Parlett and Tzon-Tzer Lu", title = "Minimum eigenvalue separation", type = "Technical Report", number = "PAM-560", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jul, year = "1992", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @TechReport{Parlett:1992:MMR, author = "Beresford N. Parlett and Wee-Liang Heng", title = "The method of minimal representations in {$2$D} {Ising} model calculations", type = "Technical Report", number = "PAM-549", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = may, year = "1992", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Abbreviated version (14 pages) of \#550", acknowledgement = ack-nhfb, } @Article{Parlett:1992:RMS, author = "Beresford N. Parlett", title = "The rewards for maintaining semi-orthogonality among {Lanczos} vectors", journal = j-J-NUM-LIN-ALG-APPL, volume = "1", number = "2", pages = "243--267", year = "1992", CODEN = "NLAAEM", ISSN = "0129-3281", MRclass = "65F15", MRnumber = "MR1182241 (93g:65054)", bibdate = "Thu Jan 23 19:03:25 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Numerical Linear Algebra with Applications", } @Article{Parlett:1992:RTF, author = "Beresford N. Parlett", title = "Reduction to Tridiagonal Form and Minimal Realizations", journal = j-SIAM-J-MAT-ANA-APPL, volume = "13", number = "2", pages = "567--593", month = apr, year = "1992", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/0613036", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F30 (15A57 65F50 93B20)", MRnumber = "MR1152769 (93c:65059)", MRreviewer = "Valeriu Prepeli{\c{t}}{\u{a}}", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", ZMnumber = "0754.65040", acknowledgement = ack-nhfb, classmath = "*65F30 Other matrix algorithms 65F15 Eigenvalues (numerical linear algebra) 65K10 Optimization techniques (numerical methods) 15A21 Canonical forms, etc. 93B10 Canonical structure of systems", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", keywords = "condition number; Gram--Schmidt process; Krylow sequences; Lanczos algorithm; minimal realizations; orthogonal polynomials; reduction to tridiagonal form; three-term recurrence relations; time-invariant; time-invariant linear dynamical systems; tridiagonal matrix", reviewer = "A. Roose (Tallinn)", } @Article{Parlett:1992:SBI, author = "Beresford N. Parlett", title = "Some Basic Information on Information-Based Complexity Theory", journal = j-BULL-AMS-N-S, volume = "26", number = "1", pages = "3--27", year = "1992", CODEN = "BAMOAD", DOI = "https://doi.org/10.1090/S0273-0979-1992-00239-2", ISSN = "0273-0979 (print), 1088-9485 (electronic)", MRclass = "68Q30 (65Y20)", MRnumber = "MR1102755 (94e:68077a)", MRreviewer = "Arthur G. Werschulz", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", ZMnumber = "0765.65042", abstract = "Numerical analysts might be expected to pay close attention to a branch of complexity theory called information-based complexity theory (IBCT), which produces an abundance of impressive results about the quest for approximate solutions to mathematical problems. Why then do most numerical analysts turn a cold shoulder to IBCT? Close analysis of two representative papers reveals a mixture of nice new observations, error bounds repackaged in new language, misdirected examples, and misleading theorems.\par Some elements in the framework of IBCT, erected to support a rigorous yet flexible theory, make it difficult to judge whether a model is off-target or reasonably realistic. For instance, a sharp distinction is made between information and algorithms restricted to this information. Yet the information itself usually comes from an algorithm, so the distinction clouds the issues and can lead to true but misleading inferences. Another troublesome aspect of IBCT is a free parameter {$F$}, the class of admissible problem instances. By overlooking {$F$}'s membership fee, the theory sometimes distorts the economics of problem solving in a way reminiscent of agricultural subsidies.\par The current theory's surprising results only pertain to unnatural situations, and its genuinely new insights might serve us better if expressed in the conventional modes of error analysis and approximation theory.", acknowledgement = ack-nhfb, classmath = "*65F10 Iterative methods for linear systems 68Q25 Analysis of algorithms and problem complexity 65Y20 Complexity and performance of numerical algorithms 65F15 Eigenvalues (numerical linear algebra) 65F20 Overdetermined systems (numerical linear algebra)", fjournal = "American Mathematical Society. Bulletin. New Series", journal-URL = "http://www.ams.org/journals/bull/all_issues.html", keywords = "approximate solutions to mathematical problems; error analysis; information-based complexity; optimal solution of large eigenpair problems; optimal solution of large linear systems", } @Article{Traub:1992:PIB, author = "J. F. Traub and H. Wo{\'z}niakowski", title = "Perspectives on Information-Based Complexity", journal = j-BULL-AMS-N-S, volume = "26", number = "1", pages = "29--52", year = "1992", CODEN = "BAMOAD", ISSN = "0273-0979 (print), 1088-9485 (electronic)", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Reply to \cite{Parlett:1992:SBI}", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, journal-URL = "http://www.ams.org/journals/bull/all_issues.html", } @InProceedings{Fernando:1993:DA, author = "K. Vince Fernando and Beresford N. Parlett", title = "Differential qd algorithms", crossref = "Reichel:1993:NLA", pages = "75--100", year = "1993", MRclass = "65F05", MRnumber = "MR1244154 (94j:65038)", MRreviewer = "I. P{\u{a}}v{\u{a}}loiu", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0794.65023", abstract = "We have discovered a new implementation of the qd algorithm that has a far wider domain of stability than Rutishauser's version. Our algorithm was developed from the examination of the LR-Cholesky transformation and can be adapted to parallel computation in stark contrast to traditional qd. Our algorithm also yields useful a posteriori upper and lower bounds on the smallest singular value of a bidiagonal matrix.\par The zero-shift bidiagonal QR of {\it J. Demmel} and {\it W. Kahan} [SIAM J. Sci. Stat. Comput. 11, No. 5, 873--912 (1990; Zbl 0705.65027)] computes the smallest singular values to maximal relative accuracy and the others to maximal absolute accuracy with little or no degradation in efficiency when compared with the LINPACK code. Our algorithm obtains maximal relative accuracy for all the singular values and runs at least four times faster than the LINPACK code.", acknowledgement = ack-nhfb, classmath = "*65F05 Direct methods for linear systems 65Y05 Parallel computation (numerical methods) 65F15 Eigenvalues (numerical linear algebra) 65B05 Extrapolation to the limit", keywords = "$qd$ algorithm; bidiagonal matrix; LR-Cholesky transformation; parallel computation; quotient-difference algorithm; singular value decomposition", } @TechReport{Fernando:1993:ICA, author = "K. Vince Fernando and Beresford N. Parlett", title = "Implicit {Cholesky} algorithms for singular values and vectors", type = "Technical Report", number = "PAM-587", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = aug, year = "1993", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Paige:1993:ASEa, author = "C. C. Paige and B. N. Parlett and H. A. {Van der Vorst}", title = "Approximate solutions and eigenvalue bounds from {Krylov} subspaces", number = "PAM-579", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = feb, year = "1993", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib", URL = "https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib", acknowledgement = ack-nhfb, notes = "Published in \cite{Paige:1995:ASE}.", } @Article{Parlett:1993:FIT, author = "Beresford N. Parlett and Jian Le", title = "Forward Instability of Tridiagonal {$ Q R $}", journal = j-SIAM-J-MAT-ANA-APPL, volume = "14", number = "1", pages = "279--316", month = jan, year = "1993", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/0614022", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15", MRnumber = "MR1199561 (93k:65033)", MRreviewer = "James Weldon Demmel", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", ZMnumber = "0767.65031", abstract = "In computing eigenvalues only backward stability is required, however, the {$ Q R $} transformation has other uses and then forward stability is needed. This paper gives examples, analyzes the forward instability, and shows that it occurs only when the shift causes ``premature deflation''.\par It is also shown that forward stability is governed by the size of the last entry in normalized eigenvectors of leading principal submatrices, and the extreme values of the derivative of each entry of the transformed matrix as a function of the shift is determined.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", keywords = "$QR$ transformation; eigenvalues; eigenvectors; forward instability; premature deflation; sensitivity analysis; tridiagonal matrices", reviewer = "F. Szidarovszky (Tucson)", } @Article{Berry:1994:CES, author = "M. W. Berry and B. N. Parlett and A. H. Sameh", title = "Computing Extremal Singular Triplets of Sparse Matrices on a Shared-Memory Multiprocessor", journal = j-INT-J-HIGH-SPEED-COMPUTING, volume = "6", number = "2", pages = "239--276", year = "1994", CODEN = "IHSCEZ", DOI = "https://doi.org/10.1142/S0129053394000123", ISSN = "0129-0533", ISSN-L = "0129-0533", bibdate = "Mon Feb 25 11:19:25 MST 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/ijhsc.bib; OCLC Article1st database", URL = "http://www.worldscientific.com/doi/abs/10.1142/S0129053394000123", acknowledgement = ack-nhfb, fjournal = "International Journal of High Speed Computing (IJHSC)", journal-URL = "http://www.worldscientific.com/worldscinet/ijhsc", } @Article{Fernando:1994:ASV, author = "K. Vince Fernando and Beresford N. Parlett", title = "Accurate singular values and differential qd algorithms", journal = j-NUM-MATH, volume = "67", number = "2", pages = "191--229", month = mar, year = "1994", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s002110050024", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F15", MRnumber = "MR1262781 (95a:65071)", MRreviewer = "Roland W. Freund", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://link.springer.de/link/service/journals/00211/bibs/4067002/40670191.htm; http://science.springer.de/nmee/bibs/4067002/40670191.htm; https://www.math.utah.edu/pub/tex/bib/nummath.bib", ZMnumber = "0814.65036", abstract = "An algorithm to compute the singular values of a bidiagonal matrix based on the quotient difference algorithm by {\it H. Rutishauser} [Z. Angew. Math. Phys. 5, 233-251 (1954; Zbl 0055.347)] is studied. It is implemented using neither square roots nor subtractions and gives high relative accuracy for small singular values, is very fast and can be implemented in parallel. Comparisons are made to the recent algorithm by {\it J. Demmel} and {\it W. Kahan} [SIAM J. Sci. Stat. Comput. 11, No. 5, 873-912 (1990; Zbl 0705.65027)].", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); B0290P (Differential equations); C4140 (Linear algebra); C4170 (Differential equations); C7310 (Mathematics)", classmath = "*65F15 Eigenvalues (numerical linear algebra) 65Y05 Parallel computation (numerical methods)", corpsource = "NAG Ltd., Oxford, UK", fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", keywords = "a posteriori upper bounds; algorithm; bidiagonal matrix; Cholesky LR transformation; convergence of numerical methods; differential $qd$ algorithms; differential equations; LINPACK code; lower bounds; mathematics computing; matrix algebra; parallel computation; quotient difference algorithm; singular values; stability; zero-shift bidiagonal QR", reviewer = "A. Ruhe (G{\"o}teborg)", treatment = "P Practical; T Theoretical or Mathematical", } @InProceedings{Parlett:1994:DWF, author = "Beresford N. Parlett", title = "Do We Fully Understand the Symmetric {Lanczos} Algorithm Yet?", crossref = "Brown:1994:PCL", pages = "93--107", year = "1994", MRclass = "65Y20 (65F15)", MRnumber = "MR1298225 (95f:65238)", bibdate = "Sat Mar 4 14:38:48 GMT 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1994:MMR, author = "Beresford N. Parlett and Wee-Liang Heng", title = "The method of minimal representations in {$2$D} {Ising} model calculations", journal = j-J-COMPUT-PHYS, volume = "114", number = "2", pages = "257--264", month = oct, year = "1994", CODEN = "JCTPAH", DOI = "https://doi.org/10.1006/jcph.1994.1164", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", MRclass = "82B20 (82B80)", MRnumber = "MR1294929", bibdate = "Mon Jan 2 07:54:57 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021999184711648", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991", } @InProceedings{Parlett:1994:PDQ, author = "Beresford N. Parlett and K. Vince Fernando", title = "Parallel differential qd for singular vectors", crossref = "Natori:1994:MAP", pages = "242--250", year = "1994", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0807.65035", abstract = "Two qd algorithms (stationary and progressive) to compute singular vectors when accurate singular values are given, are established. The differential forms of these algorithms permit the calculation of accurate and mutually orthogonal singular vectors in an embarrassingly concurrent procedure.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65Y05 Parallel computation (numerical methods)", keywords = "$qd$ algorithms; parallel differential; singular values; singular vectors", reviewer = "W. Heinrichs (D{\"u}sseldorf)", } @InProceedings{Parlett:1994:SVD, author = "Beresford N. Parlett and K. Vince Fernando", title = "Singular vectors via differential qd", crossref = "Lewis:1994:ALA", pages = "161--165", year = "1994", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0819.65050", abstract = "We describe how to use two qd algorithms (stationary and progressive) to compute singular vectors when accurate singular values are given. The differential forms of these algorithms permit the calculation of accurate and mutually orthogonal singular vectors in an embarrassingly concurrent procedure.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", keywords = "$qd$ algorithms; differential $qd$; singular values; singular vectors", } @Article{Edelman:1995:PMN, author = "Alan Edelman and Walter F. Mascarenhas", title = "On {Parlett}'s matrix norm inequality for the {Cholesky} decomposition", journal = j-NUM-LIN-ALG-APPL, volume = "2", number = "3", pages = "243--250", year = "1995", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/nla.1680020306", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", MRclass = "65F05 (65F35)", MRnumber = "96e:65018", MRreviewer = "J. Segethov{\'a}", bibdate = "Thu Jan 23 18:22:28 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib", acknowledgement = ack-nhfb, fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", } @Article{Fernando:1995:ICA, author = "K. Vince Fernando and Beresford N. Parlett", title = "Implicit {Cholesky} algorithms for singular values and vectors of triangular matrices", journal = j-NUM-LIN-ALG-APPL, volume = "2", number = "6", pages = "507--531", year = "1995", CODEN = "NLAAEM", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", MRclass = "65F15", MRnumber = "MR1367058 (96h:65057)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib", ZMnumber = "0841.65022", abstract = "The equivalence of the implicit Cholesky algorithm and a special version of the LP algorithm is proved. Intermediate quantities in the transformation furnish several attractive approximations to the smallest singular value. Shifting combined with the method improves accuracy.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F05 Direct methods for linear systems", fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", keywords = "eigenvalues; factorizations; implicit Cholesky algorithm; Jacobi methods; LP algorithm; noise spaces; null spaces; QR algorithm; singular value; triangular matrices", reviewer = "F. Szidarovszky (Tucson)", } @TechReport{Fernando:1995:WFM, author = "K. Vince Fernando and Beresford N. Parlett and Inderjit Dhillon", title = "A way to find the most redundant equation in a tridiagonal system", type = "Technical Report", number = "PAM-635", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = may, year = "1995", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Paige:1995:ASE, author = "Chris C. Paige and Beresford N. Parlett and Henk A. {van der Vorst}", title = "Approximate solutions and eigenvalue bounds from {Krylov} subspaces", journal = j-NUM-LIN-ALG-APPL, volume = "2", number = "2", pages = "115--133", year = "1995", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/nla.1680020205", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", MRclass = "65F15", MRnumber = "MR1323816 (96a:65054)", MRreviewer = "Colette Lebaud", bibdate = "Thu Jan 23 18:22:28 MST 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib", acknowledgement = ack-nhfb, fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", } @Article{Parlett:1995:NA, author = "Beresford N. Parlett", title = "The new {qd} algorithms", journal = j-ACTA-NUMERICA, volume = "4", pages = "459--491", year = "1995", CODEN = "ANUMFU", DOI = "https://doi.org/10.1017/S0962492900002580", ISBN = "0-521-48255-0", ISBN-13 = "978-0-521-48255-4", ISSN = "0962-4929 (print), 1474-0508 (electronic)", ISSN-L = "0962-4929", MRclass = "65F15", MRnumber = "MR1352476 (96g:65041)", MRreviewer = "Hongyuan Zha", bibdate = "Sat Sep 24 10:23:33 MDT 2011", bibsource = "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/UIA.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/actanumerica.bib", ZMnumber = "0835.65059", acknowledgement = ack-nhfb, ajournal = "Acta Numer.", classmath = "*65F15 Eigenvalues (numerical linear algebra) 65Y05 Parallel computation (numerical methods)", fjournal = "Acta Numerica", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU", keywords = "$qd$-algorithms; CFR; eigenvalues; eigenvectors; Gram--Schmidt orthogonalization; LR-algorithms; parallel computation; quotient-difference algorithm; singular values; tridiagonal matrices", onlinedate = "07 November 2008", reviewer = "H. Matthies (Hamburg)", } @InProceedings{Parlett:1995:SVD, author = "Beresford N. Parlett and K. Vince Fernando", title = "Singular vectors via differential qd", crossref = "Bailey:1995:PSS", pages = "564--568", year = "1995", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0836.65059", abstract = "We describe how to use two qd algorithms (stationary and progressive) to compute singular vectors when accurate singular values are given. The differential forms of these algorithms permit the calculation of accurate and mutually orthogonal singular vectors in an embarrassingly concurrent procedure.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65B05 Extrapolation to the limit", keywords = "$qd$ algorithms; inverse iteration; singular values; singular vectors", } @TechReport{Parlett:1996:COE, author = "Beresford N. Parlett", title = "The construction of orthogonal eigenvectors for tight clusters by use of submatrices", type = "Technical Report", number = "PAM-664", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = jan, year = "1996", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Article{Parlett:1996:FRP, author = "B. N. Parlett and J. He", title = "Frequency response plots: New approaches", journal = j-Z-ANGE-MATH-MECH, volume = "76", number = "Supplement 3", pages = "78--80", year = "1996", CODEN = "ZAMMAX", ISSN = "0044-2267 (print), 1521-4001 (electronic)", ISSN-L = "0044-2267", MRclass = "93C80", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "0925.93610", acknowledgement = ack-nhfb, classmath = "*93C80 Frequency-response methods", fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001", } @Article{Parlett:1996:IST, author = "B. N. Parlett", title = "Invariant subspaces for tightly clustered eigenvalues of tridiagonals", journal = j-BIT-NUM-MATH, volume = "36", number = "3", pages = "542--562", month = sep, year = "1996", CODEN = "BITTEL, NBITAB", DOI = "https://doi.org/10.1007/BF01731933", ISSN = "0006-3835 (print), 1572-9125 (electronic)", MRclass = "65F15", MRnumber = "MR1410097 (97j:65065)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "International Linear Algebra Year (Toulouse, 1995).", URL = "http://www.mai.liu.se/BIT/contents/bit36.html; https://www.math.utah.edu/pub/tex/bib/bit.bib", ZMnumber = "0856.15009", abstract = "The invariant subspace of a real symmetric tridiagonal matrix {$T$} associated with a tight cluster of $m$ eigenvalues has a special structure. This structure is revealed by the defined envelope of the subspace having $m$ high hills separated by $ m - 1 $ low valleys. This paper describes a long technical report that shows the existence of $m$ submatrices of {$T$} each one having a single eigenvalue in the cluster interval whose normalized eigenvector has small entries in the first and last positions. These little eigenvectors determine a distinguished basis for an approximating subspace whose overlap matrix is tridiagonal and close to the identity. The only communication needed among the submatrices to make an orthogonal basis is between nearest neighbors. A variety of examples illustrate the theory.", acknowledgement = ack-nhfb, classmath = "*15A18 Eigenvalues of matrices, etc. 15A57 Other types of matrices", fjournal = "BIT. Numerical Mathematics", journal-URL = "http://link.springer.com/journal/10543", keywords = "eigenvectors; invariant subspace; real symmetric tridiagonal matrix; tightly clustered eigenvalues", reviewer = "K. Burian (Hav{\'\i}rov)", } @InProceedings{Parlett:1996:OEG, author = "B. N. Parlett", title = "Orthogonal eigenvectors without {Gram--Schmidt}", crossref = "Watson:1996:NA", pages = "140--153", year = "1996", MRclass = "65F15", MRnumber = "MR1405621 (97d:65019)", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @TechReport{Parlett:1996:WHM, author = "Beresford N. Parlett", title = "What {Hadamard} missed", type = "Technical Report", number = "PAM-671", institution = inst-CPAM-UCB, address = inst-CPAM-UCB:adr, month = mar, year = "1996", bibdate = "Fri Nov 11 09:09:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, xxnote = "Check author list??", } @InProceedings{Shub:1996:PDD, author = "M. Shub and Alexandre Chorin and Arieh Iserles and Beresford Parlett and Steve Smale and Shmuel Winograd", title = "Panel discussion: {Does} numerical analysis need a model of computation?", crossref = "Renegar:1996:MNA", volume = "32", pages = "1--18", year = "1996", bibdate = "Tue Nov 2 18:47:44 MST 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "https://www.math.utah.edu/pub/tex/bib/numana1990.bib", acknowledgement = ack-nhfb, annote = "Described as proceedings", keywords = "AMS; applied mathematics; numerical analysis; SIAM", } @Article{Bakkaloglu:1997:PPA, author = "B. Bakkalo{\u{g}}lu and K. Erciye{\c{s}} and {\c{C}}. K. Ko{\c{c}}", title = "A parallelization of {Parlett}'s algorithm for functions of triangular matrices", journal = j-PARALLEL-ALGORITHMS-APPL, volume = "11", number = "1--2", pages = "61--69", month = may, year = "1997", CODEN = "PAAPEC", DOI = "https://doi.org/10.1080/10637199708915587", ISSN = "1063-7192", ISSN-L = "1026-7689", MRclass = "65Y05 (65F30)", MRnumber = "MR1462307 (98c:65208)", bibdate = "Tue Dec 23 19:03:42 MST 2003", bibsource = "http://www.gbhap-us.com/journals/728/728-top.htm; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; MathSciNet database", URL = "https://www.math.utah.edu/pub/tex/bib/parallelalgorithmsappl.bib", acknowledgement = ack-nhfb, fjournal = "Parallel Algorithms and Applications", journal-URL = "http://www.tandfonline.com/loi/gpaa20", remark = "Also cited as v12 n8 pp 61--69 1998.", } @Article{Kandic:1997:ECH, author = "Dragan B. Kandi{\'c} and Beresford Parlett and Branimir D. Reljin and Petar M. Vasi{\'c}", title = "Explicit Construction of Hyperdominant Symmetric Matrices With Assigned Spectrum", journal = j-LINEAR-ALGEBRA-APPL, volume = "258", number = "1--3", pages = "41--51", month = jun, year = "1997", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(96)00161-9", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A18; 15-XX", MRnumber = "MR1444093 (97m:15011)", MRreviewer = "F. Szidarovszky", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1997&volume=258&issue=1-3&aid=9600161; https://www.math.utah.edu/pub/tex/bib/linala1990.bib", ZMnumber = "0878.15004", abstract = "A matrix {$ A = (a_{ij}) $} is upper (lower) Hessenberg if $ a_{ij} = 0 $ whenever $ i & g t; j + 1 $ $ (j & g t; i + 1) $. Orthogonal Hessenberg matrices have a unique representation in the form {$ \prod_{i = 1}^n P_i $}, where the {$ P_i $} are plane rotators (Lemma 2). A real matrix is called hyperdominant if it has nonnegative diagonals and nonpositive off diagonals and all row sums are nonnegative. It is shown (Theorem 2) that for any set of $ n & g t; 1 $ numbers $ 0 \leq \lambda_1 \leq \lambda_2 \leq \dots \leq \lambda_n $ there exists a nontrivial hyperdominant matrix with spectrum $ \{ \lambda_1, \dots, \lambda_n \} $", acknowledgement = ack-nhfb, classmath = "*15A18 Eigenvalues of matrices, etc. 15A57 Other types of matrices", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "hyperdominant symmetric matrices; inverse eigenvalue problem", reviewer = "W. Wieslaw (Wroclaw)", } @Article{Parlett:1997:FSW, author = "Beresford N. Parlett and Inderjit S. Dhillon", title = "{Fernando}'s Solution to {Wilkinson}'s Problem: An Application of Double Factorization", journal = j-LINEAR-ALGEBRA-APPL, volume = "267", number = "1--3", pages = "247--279", month = dec, year = "1997", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(97)80053-5", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A23", MRnumber = "MR1479123 (99f:15018)", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.cs.utexas.edu/users/inderjit/public_papers/pdonfer.pdf; http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1997&volume=267&issue=1-3&aid=9700022; https://www.math.utah.edu/pub/tex/bib/linala1990.bib", ZMnumber = "0886.65033", abstract = "An algorithm for the computation of eigenvectors to a real symmetric tridiagonal matrix, when eigenvalues are already computed, is studied. It is built up on a recursion, used already by {\it W. Givens} (J. Assoc. Comput. Mach. 4, 298--307 (1957); MR 19.10806). Following a suggestion by {\it K. V. Fernando} [On computing an eigenvector of a tridiagonal matrix. I: Basic results, SIAM J. Matrix Anal. Appl. 18, No. 4, 1013--1034 (1997)], it is shown at which coordinate this recursion should be started, in order to be stable and yield orthogonal eigenvectors, also when the eigenvalue approximations are multiple to the accuracy used. These starting coordinates are found by running Gaussian elimination both forwards and backwards. Several numerical examples are included.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "algorithm; double factorization; eigenvalues; eigenvectors; Gaussian elimination; numerical examples; symmetric tridiagonal matrix", reviewer = "A. Ruhe (G{\"o}teborg)", } @InProceedings{Parlett:1997:NMR, author = "Beresford N. Parlett and Jianxun He", booktitle = "{Proceedings of the 36th IEEE Conference on Decision and Control, 1997}", title = "Nearly minimal reduced order systems", volume = "4", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "3867--3872", year = "1997", DOI = "https://doi.org/10.1109/CDC.1997.652465", bibdate = "Tue Mar 5 09:03:06 MST 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=652465", acknowledgement = ack-nhfb, journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5239", } @InProceedings{Parlett:1997:NVP, author = "Beresford N. Parlett", title = "New versions of $ q d $ for products of bidiagonals", crossref = "Buhmann:1997:ATO", pages = "183--200", year = "1997", MRclass = "65F15", MRnumber = "MR1601711", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "1031.65044", acknowledgement = ack-nhfb, classmath = "*65F05 Direct methods for linear systems 65F50 Sparse matrices", keywords = "$qd$-algorithm; Gram--Schmidt process; LR algorithm; product of two bidiagonal matrices; triangular factorization; tridiagonal matrix", } @Book{Parlett:1998:SEP, author = "Beresford N. Parlett", title = "The Symmetric Eigenvalue Problem", volume = "20", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xxiv + 398", year = "1998", DOI = "https://doi.org/10.1137/1.9781611971163", ISBN = "0-89871-402-8 (paperback), 1-61197-116-0 (e-book)", ISBN-13 = "978-0-89871-402-9 (paperback), 978-1-61197-116-3 (e-book)", LCCN = "QA188 .P37 1998", MRclass = "65F15 (15A18)", MRnumber = "MR1490034 (99c:65072)", MRreviewer = "F. Szidarovszky", bibdate = "Fri Nov 21 06:49:56 2014", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib; https://www.math.utah.edu/pub/tex/bib/master.bib", note = "Corrected reprint \cite{Parlett:1980:SEP}.", series = "Classics in Applied Mathematics", URL = "http://www.loc.gov/catdir/enhancements/fy0708/97040623-d.html", ZMnumber = "0885.65039", abstract = "According to Parlett, ``Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts''. Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in 1980). In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse. The first nine chapters are based on a matrix on which it is possible to make similarity transformations explicitly. The only source of error is inexact arithmetic. The last five chapters turn to large sparse matrices and the task of making approximations and judging them.", acknowledgement = ack-nhfb, acknowledgement = ack-njh # " and " # ack-nhfb # " and " # ack-rah, classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18 Eigenvalues of matrices, etc. 15A23 Factorization of matrices 15A57 Other types of matrices 15-02 Research monographs (linear algebra) 65-02 Research monographs (numerical analysis) 65F25 Orthogonalization (numerical linear algebra)", keywords = "bandmatrices; bounds for eigenvalues; eigenvalues; generalized eigenvalue problem; Krylov sequences; localization of eigenvalues; orthogonal transformations; tridiagonal matrices; vector iteration", libnote = "Not yet in my library.", remark = "Unabridged, corrected republication of the original edition (1980; Zbl 0431.65017)", tableofcontents = "Convergence theory for the Rayleigh quotient iteration \\ Eigenvectors of tridiagonals \\ Convergence theory, simpler than Wilkinson's, for Wilkinson's shift strategy in $Q L$ and $Q R$ \\ New proofs and sharper results for error bounds \\ Optimal properties of Rayleigh--Ritz approximations \\ Approximation theory from Krylov subspaces, Paige's theorem for noisy Lanczos algorithms, and semiorthogonality among Lanczos vectors \\ Four flavors of subspace iteration", } @Article{Parlett:1998:SSP, author = "Beresford N. Parlett", title = "Spectral sensitivity of products of bidiagonals", journal = j-LINEAR-ALGEBRA-APPL, volume = "275/276", number = "1--3", pages = "417--431", day = "15", month = may, year = "1998", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F15 (15A18)", MRnumber = "MR1628402 (99e:65063)", MRreviewer = "Yao Zhang", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Proceedings of the Sixth Conference of the International Linear Algebra Society (Chemnitz, 1996).", URL = "http://www.elsevier.com/cas/tree/store/laa/sub/1998/275-276/1-3/6055.pdf; http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1998&volume=275-276&issue=1-3&aid=6055; https://www.math.utah.edu/pub/tex/bib/linala1990.bib", ZMnumber = "0933.15010", abstract = "Simple formulae are derived for certain relative condition numbers. Tridiagonal matrices may be represented as products of bidiagonals in various ways depending on properties such as symmetry and positive definiteness. The condition numbers give the amplification factor for relative changes in a nonzero eigenvalue caused by relative changes in an entry of a bidiagonal factor. The formulae show that in many, but not all cases these condition numbers are of modest size. Several examples illustrate the results and raise new questions.", acknowledgement = ack-nhfb, classmath = "*15A12 Conditioning of matrices", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "condition numbers; eigenvalue; products of bidiagonals; spectral sensitivity; tridiagonal matrices", } @Article{Barlow:2000:ASE, author = "J. L. Barlow and Beresford N. Parlett and Kre{\v{s}}imir Veseli{\'c}", title = "The accurate solution of eigenvalue problems", journal = j-LINEAR-ALGEBRA-APPL, volume = "309", number = "1--3", pages = "1--2", day = "15", month = apr, year = "2000", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(00)00059-8", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Mon Oct 9 10:54:41 MDT 2000", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/25/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/126/25/25/article.pdf; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Parlett:2000:A, author = "Beresford N. Parlett", title = "The {$ Q R $} Algorithm", journal = j-COMPUT-SCI-ENG, volume = "2", number = "1", pages = "38--42", month = jan # "\slash " # feb, year = "2000", CODEN = "CSENFA", DOI = "https://doi.org/10.1109/5992.814656", ISSN = "1521-9615 (print), 1558-366X (electronic)", ISSN-L = "1521-9615", bibdate = "Fri Oct 13 14:31:09 2000", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://dlib.computer.org/cs/books/cs2000/pdf/c1038.pdf; http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=814656; http://www.computer.org/cse/cs1999/c1038abs.htm; https://www.math.utah.edu/pub/tex/bib/computscieng.bib", acknowledgement = ack-nhfb, fjournal = "Computing in Science and Engineering", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992", } @Article{Parlett:2000:IAP, author = "Beresford N. Parlett and Osni A. Marques", title = "An implementation of the $ d q d s $ algorithm (positive case)", journal = j-LINEAR-ALGEBRA-APPL, volume = "309", number = "1--3", pages = "217--259", day = "15", month = apr, year = "2000", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(00)00010-0", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F15", MRnumber = "MR1758369 (2001d:65048)", bibdate = "Mon Oct 9 10:54:41 MDT 2000", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "See original LAPACK Working note in \cite{Parlett:2002:IDA}.", URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/37/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/126/25/37/article.pdf; https://www.math.utah.edu/pub/tex/bib/lawn.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", ZMnumber = "0952.65031", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra)", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "differential quotient-difference algorithm with shifts; dqds algorithm; IEEE arithmetic; shifting; smallest eigenvalue; splitting", remark = "Proceedings of the International Workshop on Accurate Solution of Eigenvalue Problems (University Park, PA, 1998)", reviewer = "F. Szidarovszky (Tucson)", } @Article{Parlett:2000:PSP, author = "Beresford N. Parlett", title = "Problems and Solutions: {Problems}: 10839", journal = j-AMER-MATH-MONTHLY, volume = "107", number = "10", pages = "950", year = "2000", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", MRclass = "Contributed Item", MRnumber = "MR1543775", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "The American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Parlett:2000:RRR, author = "Beresford N. Parlett and Inderjit S. Dhillon", title = "Relatively Robust Representations of Symmetric Tridiagonals", journal = j-LINEAR-ALGEBRA-APPL, volume = "309", number = "1--3", pages = "121--151", day = "15", month = apr, year = "2000", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(99)00262-1", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F15", MRnumber = "MR1758365 (2001e:65064)", MRreviewer = "Raffaella Pavani", bibdate = "Mon Oct 9 10:54:41 MDT 2000", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/33/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/126/25/33/article.pdf; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", ZMnumber = "0948.65026", abstract = "The triangular factorization of an unreduced symmetric tridiagonal matrix is considered with respect to relative changes in the nontrivial entries of the lower left matrix and the diagonal part. The effect of these changes is modeled by diagonal scaling matrices. Relative changes in the eigenvalues of the tridiagonal matrix are studied in detail with respect to the inner perturbations induced by the scaling matrix. Furthermore, an algorithm for computing numerically orthogonal eigenvectors is sketched. This algorithm does not rely on the Gram--Schmidt process but requires conditions on the locus of eigenvalues.", acknowledgement = ack-nhfb, classmath = "*65F05 Direct methods for linear systems 65F35 Matrix norms, etc. (numerical linear algebra) 65F50 Sparse matrices", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "algorithm; diagonal scaling matrices; eigenvalues; error analysis; orthogonal eigenvectors; symmetric tridiagonal matrix; triangular factorization", remark = "Proceedings of the International Workshop on Accurate Solution of Eigenvalue Problems (University Park, PA, 1998)", reviewer = "Thomas Sonar (Braunschweig)", } @Article{Parlett:2000:TR, author = "Beresford N. Parlett", title = "For tridiagonals {$T$} replace {$T$} with {$ L D L^t $}", journal = j-J-COMPUT-APPL-MATH, volume = "123", number = "1--2", pages = "117--130", day = "1", month = nov, year = "2000", CODEN = "JCAMDI", DOI = "https://doi.org/10.1016/S0377-0427(00)00394-0", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", MRclass = "65F10 (65F35)", MRnumber = "MR1798522 (2001j:65055)", bibdate = "Sat Feb 25 12:43:37 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib", note = "Numerical analysis 2000, Vol. III. Linear algebra", URL = "http://www.sciencedirect.com/science/article/pii/S0377042700003940", ZMnumber = "0970.65032", abstract = "The author discusses two of the ideas needed to compute eigenvectors that are orthogonal without making use of the Gram--Schmidt procedure when some of the eigenvalues are tightly clustered. In the first of the new schemes, the radical new goal is to compute an approximate eigenvector for a given approximate eigenvalue with a relative residual property. In the second scheme, due to the relative gaps in the spectrum the origin is shifted and the triangular factorization is used. In the development, the recently discovered differential stationary QD algorithms are used. Examples of both ideas, using four by four systems, are given", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F05 Direct methods for linear systems", fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", keywords = "clustered eigenvalues; eigenvalue; LDU factorization; numerical examples; orthogonal eigenvectores; QD algorithm; triangular factorization", reviewer = "R. P. Tewarson (Stony Brook)", } @TechReport{Dhillon:2002:OER, author = "Inderjit S. Dhillon and Beresford N. Parlett", title = "Orthogonal Eigenvectors and Relative Gaps", type = "LAPACK Working Note", number = "154", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = aug, year = "2002", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "UT-CS-02-474, August 2002 Published in \cite{Dhillon:2004:OER}.", URL = "https://www.math.utah.edu/pub/tex/bib/lawn.bib; http://www.netlib.org/lapack/lawns/lawn154.ps; http://www.netlib.org/lapack/lawnspdf/lawn154.pdf", acknowledgement = ack-nhfb, } @TechReport{Parlett:2002:IDA, author = "Beresford N. Parlett and Osni A. Marques", title = "An implementation of the $ d q d s $ algorithm positive case", type = "LAPACK Working Note", number = "155", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = aug, year = "2002", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "LBNL-43726, UT-CS-02-475, August 2002. Published in \cite{Parlett:2000:IDA}.", URL = "https://www.math.utah.edu/pub/tex/bib/lawn.bib; http://www.netlib.org/lapack/lawns/lawn155.ps; http://www.netlib.org/lapack/lawnspdf/lawn155.pdf", acknowledgement = ack-nhfb, } @Article{Parlett:2002:LEP, author = "Beresford N. Parlett and Olaf Krafft and Martin Schaefer", title = "The Largest Eigenvalue of a Positive Definite Symmetric Matrix: 10839", journal = j-AMER-MATH-MONTHLY, volume = "109", number = "10", pages = "922--923", month = dec, year = "2002", CODEN = "AMMYAE", ISSN = "0002-9890 (print), 1930-0972 (electronic)", ISSN-L = "0002-9890", bibdate = "Mon Jan 30 12:00:15 MST 2012", bibsource = "http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/i355032; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib", URL = "http://www.jstor.org/stable/3072468", acknowledgement = ack-nhfb, fjournal = "American Mathematical Monthly", journal-URL = "https://www.jstor.org/journals/00029890.htm", } @Article{Parlett:2002:MDD, author = "Beresford N. Parlett", title = "The (matrix) discriminant as a determinant", journal = j-LINEAR-ALGEBRA-APPL, volume = "355", number = "1--3", pages = "85--101", day = "1", month = nov, year = "2002", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/S0024-3795(02)00335-X", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A15 (15A57)", MRnumber = "MR1930139 (2003i:15008)", MRreviewer = "Jorma Kaarlo Merikoski", bibdate = "Mon Apr 28 07:27:18 MDT 2003", bibsource = "http://www.elsevier.com/locate/laa; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.elsevier.nl/gej-ng/10/30/19/201/27/33/abstract.html; https://www.math.utah.edu/pub/tex/bib/linala2000.bib", ZMnumber = "1018.15006", acknowledgement = ack-nhfb, classmath = "*15A15 Special matrix functions 15A21 Canonical forms, etc. 15A63 Bilinear forms, etc", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "inner product space; matrix determinant; matrix discriminant; similarity transformations", reviewer = "V{\'a}clav Burjan (Praha)", } @Misc{Parlett:2002:QA, author = "Beresford N. Parlett", title = "The {QR} Algorithm", howpublished = "World-Wide Web document", pages = "15", day = "22", month = apr, year = "2002", bibdate = "Mon Apr 25 18:25:57 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Lecture notes for Math 128.", URL = "http://www.cs.berkeley.edu/~wkahan/Math128/Parlett.pdf; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib", acknowledgement = ack-nhfb, } @Book{Barlow:2003:SIA, editor = "Jesse L. Barlow and Beresford N. Parlett", title = "Special issue on accurate solution of eigenvalue problems", publisher = pub-ELSEVIER-SCIENCE, address = pub-ELSEVIER-SCIENCE:adr, pages = "iv + 425", year = "2003", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", MRclass = "15-06 (65F15)", MRnumber = "MR1903024", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Including papers from the 3rd International Workshop (IWASEP) held in Hagen, July 3--6, 2000, Linear Algebra Appl. {\bf 358} (2003).", acknowledgement = ack-nhfb, } @Article{Dhillon:2003:OER, author = "Inderjit S. Dhillon and Beresford N. Parlett", title = "Orthogonal Eigenvectors and Relative Gaps", journal = j-SIAM-J-MAT-ANA-APPL, volume = "25", number = "3", pages = "858--899", month = jul, year = "2003", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479800370111", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15 (15A18 15A23)", MRnumber = "MR2081239 (2005k:65078)", MRreviewer = "Daniel Kressner", bibdate = "Sat Apr 16 10:32:32 MDT 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/3; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "See original LAPACK Working note in \cite{Dhillon:2002:OER}.", URL = "http://epubs.siam.org/sam-bin/dbq/article/37011; https://www.math.utah.edu/pub/tex/bib/lawn.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Parlett:2003:PEF, author = "Beresford N. Parlett", title = "Perturbation of eigenpairs of factored symmetric tridiagonal matrices", journal = j-FOUND-COMPUT-MATH, volume = "3", number = "2", pages = "207--223", year = "2003", DOI = "https://doi.org/10.1007/s10208-001-0051-5", ISSN = "1615-3375 (print), 1615-3383 (electronic)", ISSN-L = "1615-3375", MRclass = "65F15", MRnumber = "MR1966300 (2004f:65044)", MRreviewer = "Mei-Qin Chen", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "1028.65027", abstract = "The solution of the tridiagonal eigenproblem is discussed for an indefinite symmetric matrix allowing a triangular factorization {$ T = L D L^t $}, where {$D$} is a diagonal matrix and {$L$} has $1$'s on the diagonal and is lower bidiagonal, {$ L = I + \tilde {L} $}. From the study of the behaviour of the eigenvalues and eigenvectors under small changes in the nonzero entries of {$D$} and {$ \tilde {L} $} the condition numbers are obtained. For the element growth in the factorization, it is shown that some eigenpairs are robust and others are sensitive. A $ 4 \times 4 $ example with huge element growth for which the standard multiplicative perturbation theory fails to predict that the two very small eigenvalues are determined to high relative accuracy is given. This example shows the advantage of the new method.", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F50 Sparse matrices 65F35 Matrix norms, etc. (numerical linear algebra)", fjournal = "Foundations of Computational Mathematics. The Journal of the Society for the Foundations of Computational Mathematics", journal-URL = "http://link.springer.com/journal/10208", keywords = "condition number; eigenvalues; eigenvectors; perturbation; triangular factorization; tridiagonal eigenproblem", reviewer = "V{\'a}clav Burjan (Praha)", } @Article{Parlett:2003:SDF, author = "Beresford N. Parlett", title = "The spectral diameter as a function of the diagonal entries", journal = j-NUM-LIN-ALG-APPL, volume = "10", number = "7", pages = "595--602", month = oct # "\slash " # nov, year = "2003", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/nla.338", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", MRclass = "15A42 (05C50 15A57)", MRnumber = "MR2030625 (2004m:15028)", MRreviewer = "Jorma Kaarlo Merikoski", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "http://www.interscience.wiley.com/jpages/1070-5325; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; http://www3.interscience.wiley.com/journalfinder.html", note = "Dedicated to the 70th birthday of Ivo Marek.", URL = "https://www.math.utah.edu/pub/tex/bib/numlinaa.bib", ZMnumber = "02206752", abstract = "For certain specified real symmetric matrices {$A$} the spectral diameter of {$ A - \operatorname {diag}(A) $} is less than or equal to the spectral diameter of {$A$}. Included are irreducible matrices whose undirected graphs have no cycles.", acknowledgement = ack-nhfb, classmath = "*65F99 Numerical linear algebra 65F15 Eigenvalues (numerical linear algebra)", fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", keywords = "acyclic; spectral diameter; tridiagonal matrices", onlinedate = "8 Oct 2003", } @TechReport{Dhillon:2004:DIM, author = "Inderjit S. Dhillon and Beresford N. Parlett and Christof V{\"o}mel", title = "The Design and Implementation of the {MRRR} Algorithm", type = "LAPACK Working Note", number = "162", institution = inst-UTK-CS, address = inst-UTK-CS:adr, month = feb, year = "2004", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "UT-CS-04-541, December, 2004.", URL = "https://www.math.utah.edu/pub/tex/bib/lawn.bib; http://www.netlib.org/lapack/lawns/lawn162.ps; http://www.netlib.org/lapack/lawnspdf/lawn162.pdf", acknowledgement = ack-nhfb, } @Article{Dhillon:2004:MRC, author = "Inderjit S. Dhillon and Beresford N. Parlett", title = "Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices", journal = j-LINEAR-ALGEBRA-APPL, volume = "387", number = "1", pages = "1--28", day = "1", month = aug, year = "2004", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2003.12.028", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65F15 (15A18)", MRnumber = "MR2069265 (2005d:65055)", MRreviewer = "Daniel Kressner", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; http://www.sciencedirect.com/science/journal/00243795", URL = "https://www.math.utah.edu/pub/tex/bib/linala2000.bib", ZMnumber = "1055.65048", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 15A18 Eigenvalues of matrices, etc. 15A23 Factorization of matrices", fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", keywords = "clustered eigenvalues; eigenvectors; high relative accuracy; orthogonality; relatively robust representations; symmetric tridiagonal matrix", reviewer = "Alan L.Andrew (Bundoora)", } @Article{Dhillon:2004:OER, author = "Inderjit S. Dhillon and Beresford N. Parlett", title = "Orthogonal Eigenvectors and Relative Gaps", journal = j-SIAM-J-MAT-ANA-APPL, volume = "25", number = "3", pages = "858--899", month = jul, year = "2004", CODEN = "SJMAEL", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/3; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "See original LAPACK Working note in \cite{Dhillon:2002:OER}.", URL = "http://epubs.siam.org/sam-bin/dbq/article/37011", ZMnumber = "1068.65046", acknowledgement = ack-nhfb, classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F25 Orthogonalization (numerical linear algebra) 15A23 Factorization of matrices", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", keywords = "$qd$-type algorithm; algorithm GETvec; bidiagonal factorization; comparison of methods; eigenvectors; inverse iteration; numerical examples; orthogonality; symmetric tridiagonal matrix", reviewer = "Juan Ramon Torregrosa Sanchez (Valencia)", } @TechReport{Parlett:2004:HMA, author = "Beresford N. Parlett and Christof V{\"o}mel", title = "How the {MRRR} Algorithm Can Fail on Tight Eigenvalue Clusters", type = "LAPACK Working Note", number = "163", institution = inst-UTK-CS, address = inst-UTK-CS:adr, pages = "15", month = dec, year = "2004", bibdate = "Fri Apr 22 17:06:37 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "UT-CS-04-542, December, 2004.", URL = "http://www.eecs.berkeley.edu/Pubs/TechRpts/2004/CSD-04-1367.pdf; https://www.math.utah.edu/pub/tex/bib/lawn.bib; http://www.netlib.org/lapack/lawns/lawn163.ps; http://www.netlib.org/lapack/lawnspdf/lawn163.pdf", acknowledgement = ack-nhfb, } @Article{Bai:2005:GSO, author = "Zhong-Zhi Bai and Beresford N. Parlett and Zeng-Qi Wang", title = "On generalized successive overrelaxation methods for augmented linear systems", journal = j-NUM-MATH, volume = "102", number = "1", pages = "1--38", month = nov, year = "2005", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s00211-005-0643-0", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F10", MRnumber = "MR2206670 (2006j:65077)", MRreviewer = "Heike Fa{\ss}bender", bibdate = "Sat Nov 26 18:13:08 MST 2005", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=102&issue=1; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=102&issue=1&spage=1", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", } @Article{Dhillon:2005:GMM, author = "Inderjit S. Dhillon and Beresford N. Parlett and Christof V{\"o}mel", title = "Glued Matrices and the {MRRR} Algorithm", journal = j-SIAM-J-SCI-COMP, volume = "27", number = "2", pages = "496--510", month = mar, year = "2005", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/040620746", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F15", MRnumber = "MR2202231 (2006k:65098)", MRreviewer = "Cristina Tablino Possio", bibdate = "Mon Nov 21 14:52:52 MST 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/27/2; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/62074", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @TechReport{Marques:2005:SCM, author = "Osni A. Marques and Beresford N. Parlett and Christof V{\"o}mel", title = "Subset Computations with the {MRRR} Algorithm", type = "LAPACK Working Note", number = "167", institution = "Computer Science Division, University of California, Berkeley", address = "Berkeley, CA, USA", pages = "9", day = "26", month = sep, year = "2005", bibdate = "Mon Mar 20 12:30:00 2006", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Also issued as Technical Report UCB//CSD-05-1392", URL = "http://www.netlib.org/lapack/lawnspdf/lawn167.pdf", abstract = "The main advantage of inverse iteration over the QR algorithm and Divide \& Conquer for the symmetric tridiagonal eigenproblem is that subsets of eigenpairs can be computed at reduced cost. The MRRR algorithm (MRRR = Multiple Relatively Robust Representations) is a clever variant of inverse iteration without the need for reorthogonalization. {\tt stegr}, the current version of MRRR in LAPACK 3.0, does not allow for subset computations. The next release of {\tt stegr} is designed to compute a (sub-)set of $k$ eigenpairs with {$ O(k n) $} operations. Because of the special way in which eigenvectors are computed, MRRR subset computations are more complicated than when using inverse iteration. Unlike the latter, MRRR sometimes cannot ignore the unwanted part of the spectrum. We describe the problems with what we call false singletons. These are eigenvalues that appear to be isolated with respect to the wanted eigenvalues but in fact belong to a tight cluster of unwanted eigenvalues. This paper analyzes these complications and ways to deal with them.", acknowledgement = ack-nhfb, keywords = "false singleton; Multiple relatively robust representations; numerically orthogonal eigenvectors; subset computation; symmetric tridiagonal matrix", } @Article{Parlett:2005:BMD, author = "Beresford N. Parlett", title = "A bidiagonal matrix determines its hyperbolic {SVD} to varied relative accuracy", journal = j-SIAM-J-MAT-ANA-APPL, volume = "26", number = "4", pages = "1022--1057", year = "2005", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479803424980", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A18 (15A23 65F15)", MRnumber = "MR2178210 (2006k:15033)", MRreviewer = "Alan L. Andrew", bibdate = "Fri Nov 11 06:36:51 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", ZMnumber = "02206316", abstract = "Let {$ T = L \Omega L^t $} be an invertible, unreduced, indefinite tridiagonal symmetric matrix with {$ \Omega $} a diagonal signature matrix. We provide error bounds on the (relative) change in an eigenvalue and the angular change in its eigenvector when the entries in {$L$} suffer small relative changes. Our results extend those of Demmel and Kahan for {$ \Omega = I $}. The relative condition number for an eigenvalue exceeds by 1 its absolute condition number as an eigenvalue of {$ \Omega L^t L $}. The condition number of an eigenvector is a weighted sum of the relative separations of the eigenvalue from each of the others.\par A small example shows that very small eigenpairs can be robust even when the large eigenvalues are extremely sensitive. When {$L$} is well conditioned for inversion, then all eigenvalues are robust and the eigenvectors depend only on the relative separations.", acknowledgement = ack-nhfb, classmath = "*15A18 Eigenvalues of matrices, etc. 15A23 Factorization of matrices", fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", keywords = "bidiagonal; condition number; eigenvector; hyperbolic SVD", } @Article{Zheng:2005:TLT, author = "Xiaoqiang Zheng and Beresford N. Parlett and Alex Pang", title = "Topological Lines in {$3$D} Tensor Fields and Discriminant {Hessian} Factorization", journal = j-IEEE-TRANS-VIS-COMPUT-GRAPH, volume = "11", number = "4", pages = "395--407", month = jul # "\slash " # aug, year = "2005", CODEN = "ITVGEA", DOI = "https://doi.org/10.1109/TVCG.2005.67", ISSN = "1077-2626 (print), 1941-0506 (electronic), 2160-9306", ISSN-L = "1077-2626", bibdate = "Thu Nov 10 07:58:55 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Visualization and Computer Graphics", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945", } @InProceedings{Zheng:2005:TST, author = "Xiaoqiang Zheng and Beresford N. Parlett and Alex T. Pang", booktitle = "{IEEE Visualization, 2005. VIS 05}", title = "Topological structures of {$3$D} tensor fields", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "551--558", year = "2005", DOI = "https://doi.org/10.1109/VISUAL.2005.1532841", bibdate = "Tue Mar 5 09:03:06 MST 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1532841", acknowledgement = ack-nhfb, journal-URL = "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=10269", } @Article{Barlow:2006:PSI, author = "Jesse L. Barlow and Beresford N. Parlett and Kresimir Veseli{\'c}", title = "Preface [Special issue on accurate solutions of eigenvalue problems]", journal = j-LINEAR-ALGEBRA-APPL, volume = "417", number = "2--3", pages = "381--381", year = "2006", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2006.03.020", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "65-06 (15A18 65F15)", MRnumber = "MR2250319", bibdate = "Fri May 14 12:29:46 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; http://www.sciencedirect.com/science/journal/00243795", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Dhillon:2006:DIM, author = "Inderjit S. Dhillon and Beresford N. Parlett and Christof V{\"o}mel", title = "The design and implementation of the {MRRR} algorithm", journal = j-TOMS, volume = "32", number = "4", pages = "533--560", month = dec, year = "2006", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1186785.1186788", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F15 (65Y20)", MRnumber = "MR2290445", bibdate = "Sat Apr 14 09:48:57 MDT 2007", bibsource = "http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", abstract = "In the 1990's, Dhillon and Parlett devised the algorithm of multiple relatively robust representations (MRRR) for computing numerically orthogonal eigenvectors of a symmetric tridiagonal matrix {$T$} with {$ O(n^2) $} cost. While previous publications related to MRRR focused on theoretical aspects of the algorithm, a documentation of software issues has been missing. In this article, we discuss the design and implementation of the new MRRR version STEGR that will be included in the next LAPACK release. By giving an algorithmic description of MRRR and identifying governing parameters, we hope to make STEGR more easily accessible and suitable for future performance tuning. Furthermore, this should help users understand design choices and tradeoffs when using the code.", acknowledgement = ack-nhfb, fjournal = "ACM Transactions on Mathematical Software", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", } @Article{Marques:2006:CES, author = "Osni A. Marques and Beresford N. Parlett and Christof V{\"o}mel", title = "Computations of eigenpair subsets with the {MRRR} algorithm", journal = j-NUM-LIN-ALG-APPL, volume = "13", number = "8", pages = "643--653", year = "2006", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/nla.493", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", MRclass = "65F15", MRnumber = "MR2259547 (2007h:65033)", MRreviewer = "Marc Van Barel", bibdate = "Fri May 14 12:30:20 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", } @Article{Parlett:2006:AOM, author = "B. N. Parlett and E. Barszcz", title = "Another orthogonal matrix", journal = j-LINEAR-ALGEBRA-APPL, volume = "417", number = "2-3", pages = "342--346", year = "2006", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2005.03.032", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A57 (15A23)", MRnumber = "MR2250316 (2007e:15020)", MRreviewer = "Zhongxiao Jia", bibdate = "Fri May 14 12:30:52 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @TechReport{Demmel:2007:PAL, author = "James W. Demmel and Osni A. Marques and Beresford N. Parlett and Christof V{\"o}mel", title = "Performance and Accuracy of {LAPACK}'s Symmetric Tridiagonal Eigensolvers", type = "LAPACK Working Note", number = "183", institution = inst-UCB-EECS, address = inst-UCB-EECS:adr, month = apr, year = "2007", MRclass = "15A18, 15A23", bibdate = "Fri Apr 24 12:25:43 2009", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.netlib.org/lapack/lawnspdf/lawn183.pdf", abstract = "We compare four algorithms from the latest LAPACK 3.1 release for computing eigenpairs of a symmetric tridiagonal matrix. These include QR iteration, bisection and inverse iteration (BI), the Divide-and-Conquer method (DC), and the method of Multiple Relatively Robust Representations (MR).\par Our evaluation considers speed and accuracy when computing all eigenpairs, and additionally subset computations. Using a variety of carefully selected test problems, our study includes a variety of today's computer architectures.\par Our conclusions can be summarized as follows. (1) DC and MR are generally much faster than QR and BI on large matrices. (2) MR almost always does the fewest floating point operations, but at a lower MFlop rate than all the other algorithms. (3) The exact performance of MR and DC strongly depends on the matrix at hand. (4) DC and QR are the most accurate algorithms with observed accuracy {$ O(\sqrt {n} \epsilon) $}. The accuracy of BI and MR is generally {$ O(n \epsilon) $}. (5) MR is preferable to BI for subset computations.", acknowledgement = ack-nhfb, } @TechReport{Demmel:2007:PNL, author = "James W. Demmel and Jack J. Dongarra and Beresford N. Parlett and William Kahan and Ming Gu and David S. Bindel and Yozo Hida and Xiaoye S. Li and Osni A. Marques and E. Jason Riedy and Christof V{\"o}mel and Julien Langou and Piotr Luszczek and Jakub Kurzak and Alfredo Buttari and Julie Langou and Stanimire Tomov", title = "Prospectus for the Next {LAPACK} and {ScaLAPACK} Libraries", type = "LAPACK Working Note", number = "181", institution = inst-UTK-CS, address = inst-UTK-CS:adr, day = "11", month = mar, year = "2007", bibdate = "Fri Apr 24 12:25:43 2009", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.netlib.org/lapack/lawnspdf/lawn181.pdf", acknowledgement = ack-nhfb, utknumber = "UT-CS-07-592", } @TechReport{Demmel:2007:TIL, author = "James W. Demmel and Osni A. Marques and Beresford N. Parlett and Christof V{\"o}mel", title = "A Testing Infrastructure for {LAPACK}'s Symmetric Eigensolvers", type = "LAPACK Working Note", number = "182", institution = inst-UCB-EECS, address = inst-UCB-EECS:adr, month = apr, year = "2007", MRclass = "15A18, 15A23", bibdate = "Fri Apr 24 12:25:43 2009", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.netlib.org/lapack/lawnspdf/lawn182.pdf", abstract = "LAPACK is often mentioned as a positive example of a software library that encapsulates complex, robust, and widely used numerical algorithms for a wide range of applications. At installation time, the user has the option of running a (limited) number of test cases to verify the integrity of the installation process. On the algorithm developer's side, however, more exhaustive tests are usually performed to study algorithm behavior on a variety of problem settings and also computer architectures. In this process, difficult test cases need to be found that reflect particular challenges of an application or push algorithms to extreme behavior. These tests are then assembled into a comprehensive collection, therefore making it possible for any new or competing algorithm to be stressed in a similar way. This note describes such an infrastructure for exhaustively testing the symmetric tridiagonal eigensolvers implemented in LAPACK. It consists of two parts: a selection of carefully chosen test matrices with particular idiosyncrasies and a portable testing framework that allows easy testing and data processing. The tester facilitates experiments with algorithmic choices, parameter and threshold studies, and performance comparisons on different architectures.", acknowledgement = ack-nhfb, } @Article{Parlett:2007:WHM, author = "Beresford N. Parlett", title = "What {Hadamard} missed", journal = "Internat. J. Appl. Sci. Comput.", volume = "14", number = "3", pages = "116--136", year = "2007", ISSN = "1089-0025", MRclass = "65F15", MRnumber = "MR2374179 (2008j:65060)", bibdate = "Fri May 14 12:31:28 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Applied Science and Computations", } @Article{Demmel:2008:PAL, author = "James W. Demmel and Osni A. Marques and Beresford N. Parlett and Christof V{\"o}mel", title = "Performance and accuracy of {LAPACK}'s symmetric tridiagonal eigensolvers", journal = j-SIAM-J-SCI-COMP, volume = "30", number = "3", pages = "1508--1526", year = "2008", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/070688778", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F15 (65Y20)", MRnumber = "MR2398876 (2008m:65116)", MRreviewer = "Ross A. Lippert", bibdate = "Fri May 14 12:31:44 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Liesen:2008:NSP, author = "J{\"o}rg Liesen and Beresford N. Parlett", title = "On nonsymmetric saddle point matrices that allow conjugate gradient iterations", journal = j-NUM-MATH, volume = "108", number = "4", pages = "605--624", month = feb, year = "2008", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s00211-007-0131-9", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F10", MRnumber = "MR2369206 (2009c:65076)", MRreviewer = "Rafael J. Villanueva", bibdate = "Tue Jul 8 09:49:13 MDT 2008", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", } @Article{Parlett:2008:MPR, author = "Beresford Parlett and Gilbert Strang", title = "Matrices with prescribed {Ritz} values", journal = j-LINEAR-ALGEBRA-APPL, volume = "428", number = "7", pages = "1725--1739", year = "2008", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2007.10.040", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A18 (15A29)", MRnumber = "MR2388652 (2009c:15015)", MRreviewer = "Claude M. Vall{\'e}e", bibdate = "Fri May 14 12:33:07 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Misc{Parlett:2008:RDE, author = "Beresford N. Parlett", title = "Recollections (designed to entertain or enlighten)", howpublished = "Web document", day = "30", month = mar, year = "2008", bibdate = "Mon Mar 31 16:55:05 2008", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "The Bay Area Scientific Computing Day, BASCD08, honoring Profs. Kahan and Parlett, 29--30 March, 2008.", URL = "http://math.berkeley.edu/bascd08", acknowledgement = ack-nhfb, } @Article{Ferreira:2009:CAO, author = "Carla Ferreira and Beresford Parlett", title = "Convergence of {$ L R $} algorithm for a one-point spectrum tridiagonal matrix", journal = j-NUM-MATH, volume = "113", number = "3", pages = "417--431", month = sep, year = "2009", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s00211-009-0238-2", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "65F15", MRnumber = "MR2534131", bibdate = "Fri May 14 08:10:17 MDT 2010", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=????&volume=113&issue=3; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=????&volume=113&issue=3&spage=417", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", } @Article{Marques:2009:ATI, author = "Osni A. Marques and Christof V{\"o}mel and James W. Demmel and Beresford N. Parlett", title = "{Algorithm 880}: a testing infrastructure for symmetric tridiagonal eigensolvers", journal = j-TOMS, volume = "35", number = "1", pages = "8:1--8:13", month = jul, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1377603.1377611", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65F15 (65Y20)", MRnumber = "MR2501873", bibdate = "Tue Aug 5 18:12:48 MDT 2008", bibsource = "http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "LAPACK is often mentioned as a positive example of a software library that encapsulates complex, robust, and widely used numerical algorithms for a wide range of applications. At installation time, the user has the option of running a (limited) number of test cases to verify the integrity of the installation process. On the algorithm developer's side, however, more exhaustive tests are usually performed to study algorithm behavior on a variety of problem settings and also computer architectures. In this process, difficult test cases need to be found that reflect particular challenges of an application or push algorithms to extreme behavior. These tests are then assembled into a comprehensive collection, therefore making it possible for any new or competing algorithm to be stressed in a similar way. This article describes an infrastructure for exhaustively testing the symmetric tridiagonal eigensolvers implemented in LAPACK. It consists of two parts: a selection of carefully chosen test matrices with particular idiosyncrasies and a portable testing framework that allows for easy testing and data processing. The tester facilitates experiments with algorithmic choices, parameter and threshold studies, and performance comparisons on different architectures.", acknowledgement = ack-nhfb, articleno = "8", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "accuracy; design; eigenvalues; eigenvectors; implementation; LAPACK; numerical software; performance; symmetric matrix; test matrices; testing", } @Article{Parlett:2009:RCG, author = "Beresford N. Parlett", title = "A result complementary to {Gersgorin}'s {Circle Theorem}", journal = j-LINEAR-ALGEBRA-APPL, volume = "431", number = "1-2", pages = "20--27", year = "2009", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2009.01.030", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A18 (15A42)", MRnumber = "MR2522553 (2010e:15009)", MRreviewer = "Fuad Kittaneh", bibdate = "Fri May 14 12:36:11 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Parlett:2009:RFM, author = "Beresford N. Parlett", title = "Review of {{\em Functions of Matrices: Theory and Computation}, Nicholas J. Higham. SIAM, Philadelphia, PA (2008), xx + 425 pp}", journal = j-LINEAR-ALGEBRA-APPL, volume = "430", number = "11--12", pages = "3139--3140", day = "1", month = jun, year = "2009", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Wed Mar 30 14:20:44 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; http://www.sciencedirect.com/science/journal/00243795", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Parlett:2009:SGM, author = "Beresford N. Parlett and Christof V{\"o}mel", title = "The spectrum of a glued matrix", journal = j-SIAM-J-MAT-ANA-APPL, volume = "31", number = "1", pages = "114--132", year = "2009", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/070687062", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A18 (15A23)", MRnumber = "MR2487053", MRreviewer = "Ion Zaballa", bibdate = "Fri May 14 12:36:19 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Shomron:2009:LAM, author = "Noam Shomron and Beresford N. Parlett", title = "Linear algebra meets {Lie} algebra: the {Kostant--Wallach} theory", journal = j-LINEAR-ALGEBRA-APPL, volume = "431", number = "10", pages = "1745--1767", year = "2009", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2009.06.007", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", MRclass = "15A18 (14R20 17Bxx)", MRnumber = "MR2567787", bibdate = "Fri May 14 12:40:55 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", } @Article{Dubrulle:2010:RTM, author = "A. A. Dubrulle and B. N. Parlett", title = "Revelations of a transposition matrix", journal = j-J-COMPUT-APPL-MATH, volume = "233", number = "5", pages = "1217--1219", day = "1", month = jan, year = "2010", CODEN = "JCAMDI", DOI = "https://doi.org/10.1016/j.cam.2008.11.018", ISSN = "0377-0427 (print), 1879-1778 (electronic)", ISSN-L = "0377-0427", MRclass = "65F15 (15A18)", MRnumber = "MR2559358", bibdate = "Sat Feb 25 13:24:20 MST 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0377042709001745", ZMnumber = "1179.15003", abstract = "Matrix transposition, which is most commonly thought of as a simple exchange of the entries of a matrix, is a similarity transformation. While this transformation is not unique, its composition is determined by the spectral configuration of the matrix to which it applies. We use this relationship here to show that, conversely, certain properties of the spectrum of a matrix can be inferred from some knowledge of its transposition matrices.\par The paper is organised as follows. Section 2 is a detailed analysis of the relationship between the spectrum of a matrix and the constituents of an associated transposition matrix. In Section 3, we discuss the spectral properties revealed by transposition matrices and an application to the product of two skew-symmetric matrices.", acknowledgement = ack-nhfb, fjournal = "Journal of Computational and Applied Mathematics", journal-URL = "http://www.sciencedirect.com/science/journal/03770427", } @Article{Parlett:2010:BRB, author = "Beresford Parlett", title = "Book Review: {{\booktitle{The matrix eigenvalue problem: GR and Krylov subspace methods}} [book review of MR2383888]; \booktitle{Numerical methods for general and structured eigenvalue problems} [book review of MR2164298]}", journal = j-SIAM-REVIEW, volume = "52", number = "4", pages = "771--774", month = "????", year = "2010", CODEN = "SIREAD", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "00A17", MRnumber = "2743241", bibdate = "Fri Jun 21 11:25:02 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", journal-URL = "http://epubs.siam.org/sirev", } @Article{Gutknecht:2011:HWA, author = "Martin H. Gutknecht and Beresford N. Parlett", title = "From qd to {$ L R $}, or, how were the qd and {$ L R $} algorithms discovered?", journal = j-IMA-J-NUMER-ANAL, volume = "31", number = "3", pages = "741--754", month = jul, year = "2011", CODEN = "IJNADH", DOI = "https://doi.org/10.1093/imanum/drq003", ISSN = "0272-4979 (print), 1464-3642 (electronic)", ISSN-L = "0272-4979", MRclass = "65-03 (01A60 15A21 65F15 65H04)", MRnumber = "2832778", MRreviewer = "Fabio Di Benedetto", bibdate = "Fri Jul 15 12:37:42 MDT 2011", bibsource = "http://imanum.oxfordjournals.org/content/31/3.toc; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://imajna.oxfordjournals.org/content/31/3/741.full.pdf+html", ZMnumber = "1222.65032", abstract = "Perhaps, the most astonishing idea in eigenvalue computation is Rutishauser's idea of applying the {$ L R $} transform to a matrix for generating a sequence of similar matrices that become more and more triangular. The same idea is the foundation of the ubiquitous {$ Q R $} algorithm. It is well known that this idea originated in Rutishauser's qd algorithm, which precedes the {$ L R $} algorithm and can be understood as applying {$ L R $} to a tridiagonal matrix. But how did Rutishauser discover qd and when did he find the qd-{$ L R $} connection? We checked some of the early sources and have come up with an explanation.", acknowledgement = ack-nhfb, fjournal = "IMA Journal of Numerical Analysis", journal-URL = "http://imajna.oxfordjournals.org/content/by/year", onlinedate = "May 27, 2010", } @Article{Morzfeld:2011:TSO, author = "Matthias Morzfeld and Fai Ma and Beresford N. Parlett", title = "The Transformation of Second-Order Linear Systems into Independent Equations", journal = j-SIAM-J-APPL-MATH, volume = "71", number = "4", pages = "1026--1043", month = "????", year = "2011", CODEN = "SMJMAP", DOI = "https://doi.org/10.1137/100818637", ISSN = "0036-1399 (print), 1095-712X (electronic)", ISSN-L = "0036-1399", MRclass = "34C20 (34A30 70J10)", MRnumber = "2819506", MRreviewer = "O. A. Sebakhy", bibdate = "Fri Jul 22 09:01:56 MDT 2011", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIAP/71/4; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", URL = "http://epubs.siam.org/siap/resource/1/smjmap/v71/i4/p1026_s1", ZMnumber = "1232.34060", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Applied Mathematics", journal-URL = "http://epubs.siam.org/siap", onlinedate = "July 07, 2011", } @Article{Vomel:2011:DLI, author = "Christof V{\"o}mel and Beresford N. Parlett", title = "Detecting Localization in an Invariant Subspace", journal = j-SIAM-J-SCI-COMP, volume = "33", number = "6", pages = "3447--3467", month = "????", year = "2011", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/09077624X", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F15 (15A18)", MRnumber = "2862021", MRreviewer = "Fabio Di Benedetto", bibdate = "Thu Feb 9 06:05:59 MST 2012", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/33/6; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", URL = "http://epubs.siam.org/sisc/resource/1/sjoce3/v33/i6/p3447_s1", ZMnumber = "1232.15011", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "December 13, 2011", } @Article{Ferreira:2012:SEU, author = "Carla Ferreira and Beresford Parlett and Froil{\'a}n M. Dopico", title = "Sensitivity of eigenvalues of an unsymmetric tridiagonal matrix", journal = j-NUM-MATH, volume = "122", number = "3", pages = "527--555", month = nov, year = "2012", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s00211-012-0470-z", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", MRclass = "15A42 (15A12 65F15)", MRnumber = "2983090", MRreviewer = "Chun-Hua Guo", bibdate = "Tue Nov 6 10:54:38 MST 2012", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=122&issue=3; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/nummath2010.bib", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=122&issue=3&spage=527", ZMnumber = "06134329", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", } @Article{Li:2014:IDA, author = "Shengguo Li and Ming Gu and Beresford N. Parlett", title = "An Improved {DQDS} Algorithm", journal = j-SIAM-J-SCI-COMP, volume = "36", number = "3", pages = "C290--C308", month = "????", year = "2014", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/120881087", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65F15", MRnumber = "3224580", MRreviewer = "Heike Fa\ss bender", bibdate = "Sat Sep 13 12:24:04 MDT 2014", bibsource = "http://epubs.siam.org/toc/sjoce3/36/3; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", ZMnumber = "06340661", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2014", } @Article{Parlett:2016:IEP, author = "Beresford Parlett and Froil{\'a}n M. Dopico and Carla Ferreira", title = "The Inverse Eigenvector Problem for Real Tridiagonal Matrices", journal = j-SIAM-J-MAT-ANA-APPL, volume = "37", number = "2", pages = "577--597", month = "????", year = "2016", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/15M1025293", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "15A29 (15A18 65F15 65F18)", MRnumber = "3490889", MRreviewer = "Hua Dai", bibdate = "Fri Sep 23 08:21:42 MDT 2016", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/2; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2016", } @Article{Ferreira:2020:EWM, author = "Carla Ferreira and Beresford Parlett", title = "Eigenpairs of {Wilkinson} Matrices", journal = j-SIAM-J-MAT-ANA-APPL, volume = "41", number = "3", pages = "1388--1415", month = "????", year = "2020", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/20M1327343", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F15 (15A18)", MRnumber = "4151476", MRreviewer = "Jin Yun Yuan", bibdate = "Fri Mar 12 10:18:03 MST 2021", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/41/3; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", onlinedate = "January 2020", } @Article{Ferreira:2022:RTD, author = "Carla Ferreira and Beresford Parlett", title = "A real triple dqds algorithm for the nonsymmetric tridiagonal eigenvalue problem", journal = j-NUM-MATH, volume = "150", number = "2", pages = "373--422", month = feb, year = "2022", CODEN = "NUMMA7", DOI = "https://doi.org/10.1007/s00211-021-01254-z", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Thu Feb 10 08:03:50 MST 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/nummath2020.bib", URL = "http://link.springer.com/article/10.1007/s00211-021-01254-z", acknowledgement = ack-nhfb, fjournal = "Numerische Mathematik", journal-URL = "http://link.springer.com/journal/211", }

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

@Article{Bunch:1995:EDB, author = "James R. Bunch", title = "Editorial: Dedicated to {Beresford Parlett} and {William Kahan}", journal = j-NUM-LIN-ALG-APPL, volume = "2", number = "2", pages = "85--85", year = "1995", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/nla.1680020202", ISSN = "1070-5325 (print), 1099-1506 (electronic)", bibdate = "Sat Jan 20 06:15:41 2018", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/numlinaa.bib", acknowledgement = ack-nhfb, fjournal = "Numerical Linear Algebra with Applications", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506", } @Article{Davies:2003:SPA, author = "P. I. Davies and N. J. Higham", title = "A {Schur--Parlett} algorithm for computing matrix functions", journal = j-SIAM-J-MAT-ANA-APPL, volume = "25", number = "2", pages = "464--485", month = "????", year = "2003", CODEN = "SJMAEL", DOI = "https://doi.org/10.1137/S0895479802410815", ISSN = "0895-4798 (print), 1095-7162 (electronic)", ISSN-L = "0895-4798", MRclass = "65F30", MRnumber = "2047429", bibdate = "Thu Jun 6 12:11:59 MDT 2013", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", journal-URL = "http://epubs.siam.org/simax", } @Article{Koikari:2009:ABS, author = "Souji Koikari", title = "{Algorithm 894}: {On} a block {Schur--Parlett} algorithm for $ \varphi $-functions based on the sep-inverse estimate", journal = j-TOMS, volume = "36", number = "2", pages = "12:1--12:20", month = mar, year = "2009", CODEN = "ACMSCU", DOI = "https://doi.org/10.1145/1499096.1499101", ISSN = "0098-3500 (print), 1557-7295 (electronic)", ISSN-L = "0098-3500", MRclass = "65P10", MRnumber = "2738193", bibdate = "Fri Apr 3 17:44:12 MDT 2009", bibsource = "http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib", abstract = "FORTRAN 95 software is provided for computing the matrix values of $ \varphi $-functions required in exponential integrators. The subroutines in the library accept as their argument a full, diagonal, or upper quasitriangular matrix with real or complex entries in one of four precisions. Two different algorithms are implemented, one is the scaling and squaring method, and the other is a modified block Schur--Parlett algorithm. In the latter algorithm, a recursive three-by-three blocking is applied to the argument based on an estimate of the sep-inverse function. The estimation of the sep-inverse function is carried out by Hager--Higham estimator implemented as the subroutine xLACON in LAPACK. Our modifications to the block Schur--Parlett algorithm are described together with the results of numerical experiments.", acknowledgement = ack-nhfb, articleno = "12", fjournal = "ACM Transactions on Mathematical Software (TOMS)", journal-URL = "http://portal.acm.org/toc.cfm?idx=J782", keywords = "$\varphi$-functions; block Schur--Parlett algorithm; exponential integrators; matrix functions", } @Article{Schulman:2017:ACM, author = "Leonard J. Schulman and Alistair Sinclair", title = "Analysis of a Classical Matrix Preconditioning Algorithm", journal = j-J-ACM, volume = "64", number = "2", pages = "9:1--9:23", month = jun, year = "2017", CODEN = "JACOAH", DOI = "https://doi.org/10.1145/2988227", ISSN = "0004-5411 (print), 1557-735X (electronic)", bibdate = "Fri Sep 8 08:45:18 MDT 2017", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/jacm.bib", abstract = "We study a classical iterative algorithm for balancing matrices in the $ L_\infty $ norm via a scaling transformation. This algorithm, which goes back to Osborne and Parlett 8 Reinsch in the 1960s, is implemented as a standard preconditioner in many numerical linear algebra packages. Surprisingly, despite its widespread use over several decades, no bounds were known on its rate of convergence. In this article, we prove that, for any irreducible $ n \times n $ (real or complex) input matrix $A$, a natural variant of the algorithm converges in $ O(n^3 \log (n \rho / \epsilon))$ elementary balancing operations, where $ \rho $ measures the initial imbalance of $A$ and $ \epsilon $ is the target imbalance of the output matrix. (The imbalance of $A$ is $ | \log (a_i^{\rm out} / a_i^{\rm in})|$, where $ a_i^{\rm out}$, $ a_i^{\rm in}$ are the maximum entries in magnitude in the $i$ th row and column, respectively.) This bound is tight up to the $ \log n$ factor. A balancing operation scales the $i$ th row and column so that their maximum entries are equal, and requires $ O(m / n)$ arithmetic operations on average, where $m$ is the number of nonzero elements in $A$. Thus, the running time of the iterative algorithm is $ {\tilde {O}}(n^2 m)$. This is the first time bound of any kind on any variant of the Osborne--Parlett--Reinsch algorithm. We also prove a conjecture of Chen that characterizes those matrices for which the limit of the balancing process is independent of the order in which balancing operations are performed.", acknowledgement = ack-nhfb, articleno = "9", fjournal = "Journal of the ACM", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401", } @Article{Wang:2020:KPJ, author = "Yunjie Wang and Gang Wu", title = "On the {Kahan--Parlett--Jiang} theorem --- a globally optimal backward perturbation error for two-sided invariant subspaces", journal = j-LINEAR-ALGEBRA-APPL, volume = "602", number = "??", pages = "73--92", day = "1", month = oct, year = "2020", CODEN = "LAAPAW", DOI = "https://doi.org/10.1016/j.laa.2020.05.003", ISSN = "0024-3795 (print), 1873-1856 (electronic)", ISSN-L = "0024-3795", bibdate = "Fri Mar 12 08:38:22 MST 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/linala2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0024379520302342", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", journal-URL = "http://www.sciencedirect.com/science/journal/00243795", }

%%% ==================================================================== %%% Cross-referenced entries must come last:

@Proceedings{Ralston:1967:MMD, editor = "Anthony Ralston and Herbert S. Wilf", booktitle = "Mathematical Methods for Digital Computers", title = "Mathematical Methods for Digital Computers", volume = "II", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "x + 287", year = "1967", ISBN = "0-471-70686-8 (vol. 1), 0-471-70689-2 (vol. 2), 0-471-70690-6 (vol. 3)", ISBN-13 = "978-0-471-70686-1 (vol. 1), 978-0-471-70689-2 (vol. 2), 978-0-471-70690-8 (vol. 3)", LCCN = "????", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Proceedings{Morrell:1969:IPP, editor = "A. J. H. Morrell", booktitle = "{Information processing 68: proceedings of IFIP congress 1968, organized by the International Federation for Information Processing, Edinburgh, 5--10 August 1968}", title = "{Information processing 68: proceedings of IFIP congress 1968, organized by the International Federation for Information Processing, Edinburgh, 5--10 August 1968}", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "????", year = "1969", ISBN = "0-7204-2032-6", ISBN-13 = "978-0-7204-2032-6", LCCN = "QA76 .I578", bibdate = "Fri Nov 11 07:22:32 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; melvyl.cdlib.org:210/CDL90", acknowledgement = ack-nhfb, remark = "Volume 1. Mathematics, software. Volume 2. Hardware, applications.", subject = "Electronic data processing; Congresses; Electronic digital computers; Congresses; Machine theory; Congresses", } @Book{Wilkinson:1971:LA, editor = "James H. Wilkinson and Christian Reinsch", booktitle = "Linear Algebra", title = "Linear Algebra", volume = "II", publisher = pub-SV, address = pub-SV:adr, pages = "viii + 439", year = "1971", ISBN = "0-387-05414-6, 3-540-05414-6", ISBN-13 = "978-0-387-05414-8, 978-3-540-05414-6", LCCN = "QA251 .W67", bibdate = "Wed Dec 15 18:44:50 1993", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib", series = "Handbook for Automatic Computation, Editors: {F. L. Bauer, A. S. Householder, F. W. J. Olver, H. Rutishauser, K. Samelson and E. Stiefel}", acknowledgement = ack-nhfb, author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022); James H. Wilkinson (27 September 1919--5 October 1986)", tableofcontents = "Part I: Linear systems, least squares and linear programming \\ J. H. Wilkinson / Introduction to Part I / 1--8 \\ 1. Introduction \\ 2. List of procedures \\ 3. Positive definite symmetric matrices \\ 4. Non-positive definite symmetric matrices \\ 5. Non-Hermitian matrices \\ 6. Least squares and related problems \\ 7. The linear programming problem \\ R. S. Martin, G. Peters and J. H. Wilkinson / Symmetric decomposition of a positive definite matrix / 9--30 \\ Martin, Peters and Wilkinson / Iterative refinement of the solution of a positive definite system of equations / 31--44 \\ F. L. Bauer and C. Reinsch / Inversion of positive definite matrices by the Gauss-Jordan method / 45--49 \\ Martin and Wilkinson / Symmetric decomposition of positive definite band matrices / 50--56 \\ T. Ginsburg / The conjugate gradient method / 57--69 \\ Martin and Wilkinson / Solution of symmetric and unsymmetric band equations and the calculation of eigenvectors of band matrices / 70--92 \\ H. J. Bowdler, Martin, Peters and Wilkinson / Solution of real and complex systems of linear equations / 93--110 \\ P. Businger and G. H. Golub / Linear least squares solutions by Householder transformations / 111--118 \\ Bauer / Elimination with weighted row combinations for solving linear equations and least squares problems / 119--133 \\ Golub and Reinsch / Singular value decomposition and least squares solutions / 134--151 \\ R. H. Bartels, J. Stoer and Ch. Zenger / A realization of the simplex method based on triangular decompositions / 152--190 \\ Part II: The algebraic eigenvalue problem \\ Wilkinson / Introduction to Part II / 191--201 \\ 1. Introduction \\ 2. List of procedures \\ 3. Real, dense, symmetric matrices \\ 4. Symmetric band matrices \\ 5. Simultaneous determination of dominant eigenvalues and eigenvectors of a symmetric sparse matrix \\ 6. The generalized symmetric eigenvalue problems $A x = \lambda B x$ and $A B x = \lambda x$ \\ 7. Hermitian matrices \\ 8. Real dense unsymmetric matrices \\ 9. Unsymmetric band matrices \\ 10. Dense unsymmetric matrices with complex elements, H. Rutishauser / The Jacobi method for real symmetric matrices / 202--211 \\ Martin, Reinsch and Wilkinson / Householder's tridiagonalization of a symmetric matrix / 212--226 \\ H. Bowdler, Martin, Reinsch and Wilkinson / The $QR$ and $QL$ algorithms for symmetric matrices / 227--240 \\ A. Dubrulle, Martin and Wilkinson / The implicit $QL$ algorithm / 241--248 \\ W. Barth, Martin, and Wilkinson / Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection / 249--256 \\ Reinsch and Bauer / Rational $QR$ transformation with Newton shift for symmetric tridiagonal matrices / 257--265 \\ Martin, Reinsch and Wilkinson / The $QR$ algorithm for band symmetric matrices / 266--272 \\ H. R. Schwarz / Tridiagonalization of a symmetric band matrix / 273--283 \\ Rutishauser / Simultaneous iteration method for symmetric matrices / 284--302 \\ Martin and Wilkinson / Reduction of the symmetric eigenproblem $A x = \lambda B x$ and related problems to standard form / 303--314 \\ B. N. Parlett and Reinsch / Balancing a matrix for calculation of eigenvalues and eigenvectors / 315--326 \\ P. J. Eberlein and J. Boothroyd / Solution to the eigenproblem by a norm reducing Jacobi type method / 327--338 \\ Martin and Wilkinson / Similarity reduction of a general matrix to Hessenberg form / 339--358 \\ Martin, Peters and Wilkinson / The $QR$ algorithm for real Hessenberg matrices / 359--371 \\ Peters and Wilkinson / Eigenvectors of real and complex matrices by $LR$ and $QR$ triangularizations / 372--395 \\ Martin and Wilkinson / The modified $LR$ algorithm for complex Hessenberg matrices / 396--403 \\ Eberlein / Solution to the complex eigenproblem by a norm reducing Jacobi type method / 404--417 \\ Peters and Wilkinson / The calculation of specified eigenvectors by inverse iteration / 418--439", } @Proceedings{Greville:1972:PDP, editor = "T. N. E. (Thomas Nall Eden) Greville", booktitle = "{Population dynamics: proceedings of a symposium conducted by the Mathematics Research Center, the University of Wisconsin, Madison, June 19--21, 1972}", title = "{Population dynamics: proceedings of a symposium conducted by the Mathematics Research Center, the University of Wisconsin, Madison, June 19--21, 1972}", volume = "29", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "ix + 445", year = "1972", ISBN = "0-12-302940-6", ISBN-13 = "978-0-12-302940-9", bibdate = "Fri Nov 11 07:27:17 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; melvyl.cdlib.org:210/CDL90", note = "Some catalogs show ISBN 0-12-302940-1 with invalid checksum.", series = "Mathematics Research Center Publications", acknowledgement = ack-nhfb, meetingname = "Symposium on Population Dynamics (1972 : Mathematics Research Center, University of Wisconsin)", subject = "Population; Congresses; Mathematics; Congresses; Models, Theoretical; Congresses", } @Proceedings{Bunch:1976:SMC, editor = "James R. Bunch and Donald J. Rose", booktitle = "{Sparse Matrix Computations: Proceedings of the Symposium on Sparse Matrix Computations at Argonne National Laboratory on September 9--11, 1975}", title = "{Sparse Matrix Computations: Proceedings of the Symposium on Sparse Matrix Computations at Argonne National Laboratory on September 9--11, 1975}", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xi + 453", year = "1976", ISBN = "0-12-141050-1", ISBN-13 = "978-0-12-141050-6", LCCN = "QA188 .S989 1975", bibdate = "Sat Oct 22 18:13:05 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", acknowledgement = ack-nhfb, tableofcontents = "Contributors / / ix \\ Preface / / xi \\ I. Design and Analysis of Elimination Algorithms / / 1 \\ 1. Graph Theory and Gaussian Elimination / Robert Endre Tarjan / 3 \\ 2. Partitioning Using PAQ / Thomas D. Howell / 23 \\ 3. Block Methods for Solving Sparse Linear Systems / James R. Bunch / 39 \\ 4. A Recursive Analysis of Dissection Strategies / Donald J. Rose and Gregory F. Whitten / 59 \\ 5. Applications of an Element Model for Gaussian Elimination / S. C. Eisenstat, M. H. Schultz, and 4. H. Sherman / 85 \\ 6. An Optimization Problem Arising from Tearing Methods / Alberto Sangiovanni-Vincentelli / 97 \\ II. Eigenvalue Problems . / / 111 \\ 1. A Bibliographical Tour of the Large, Sparse Generalized Eigenvalue Problem / G. W. Stewart / 113 \\ 2. How Far Should You Go With the Lanczos Process? / W. Kahan and B. N. Parlett / 131 \\ III. Optimization, Least Squares and Linear Programming / / 145 \\ 1. Optimization for Sparse Systems / T. L. Magnanti / 147 \\ 2. Methods for Sparse Linear Least Squares Problems / {AA}ke Bj{\"o}rck / 177 \\ 3. The Orthogonal Factorization of a Large Sparse Matrix / Philip E. Gill and Walter Murray / 201 \\ 4. A Fast, Stable Implementation of the Simplex Method Using Bartels-Golub Updating / Michael A. Saunders / 213 \\ 5. Using the Steepest-edge Simplex Algorithm to Solve Sparse Linear Programs / D. Goldfarb / 227 \\ IV. Mathematical Software / / 241 \\ 1. Sparse Matrix Software / W. Morven Gentleman and Alan George / 243 \\ 2. Considerations in the Design of Software for Sparse Gaussian Elimination / S. C. Eisenstat, M. H. Schultz, and A. H. Sherman / 263 \\ 3. Finding the Block Lower Triangular Form of a Sparse Matrix / Fred Gustavson / 275 \\ V. Matrix Methods for Partial Difference Equations / / 291 \\ 1. Marching Algorithms and Block Gaussian Elimination / Randolph E. Bank / 293 \\ 2. A Generalized Conjugate Gradient Method for the Numerical Solution of Elliptic Partial Differential Equations / Paul Concus, Gene H. Golub, and Dianne P. O'Leary / 309 \\ 3. Preconditioned Conjugate Gradient Iteration Applied to Galerkin Methods for a Mildly-Nonlinear Dirichlet Problem / Jim Douglas, Jr. and Todd Dupont / 333 \\ 4. The Sparse Tableau Approach to Finite Element Assembly / Gary Hachtel / 349 \\ 5. A Capacitance Matrix Technique / B. L. Buzbee / 365 \\ 6. M-Matrix Theory and Recent Results in Numerical Linear Algebra / Richard S. Varga / 375 \\ VI. Applications / / 389 \\ 1. Sparse Matrix Problems in a Finite Element Open Ocean Model / Joel E. Hirsh and William L. Briggs / 391 \\ 2. Calculation of Normal Modes of Oceans Using a Lanczos Method / Alan K. Cline, Gene H. Golub, and George W. Platzman / 409 \\ 3. Application of Sparse Matrix Techniques to Reservoir Simulation / P. T. Woo, S. C. Eisenstat, M. H. Schultz, and A. H. Sherman / 427 \\ 4. On the Origins and Numerical Solution of Some Sparse Nonlinear Systems / T. A. Porsching / 439", } @Proceedings{Bathe:1977:FCA, editor = "Klaus-J{\"u}rgen Bathe and J. Tinsley (John Tinsley) Oden and Edward L. Wilson", booktitle = "{Formulations and computational algorithms in finite element analysis: U.S.--Germany symposium}", title = "{Formulations and computational algorithms in finite element analysis: U.S.--Germany symposium}", publisher = pub-MIT, address = pub-MIT:adr, pages = "xvi + 1091", year = "1977", ISBN = "0-262-02127-7", ISBN-13 = "978-0-262-02127-2", LCCN = "TA347.F5 F67; TA347.F5 F67", bibdate = "Fri Nov 11 07:31:16 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; melvyl.cdlib.org:210/CDL90", acknowledgement = ack-nhfb, remark = "This book contains the papers presented at the U.S.--German symposium on finite element methods, held at MIT, August, 1976.", subject = "Finite element method; Congresses", } @Proceedings{Absi:1980:NME, editor = "{\'E}lie Absi", booktitle = "Numerical methods for engineering: 2nd International Congress = {M{\'e}thodes num{\'e}riques dans les sciences de l'ing{\'e}nieur: 2e Congr{\`e}s international}", title = "Numerical methods for engineering: 2nd International Congress = {M{\'e}thodes num{\'e}riques dans les sciences de l'ing{\'e}nieur: 2e Congr{\`e}s international}", publisher = pub-DUNOD, address = pub-DUNOD:adr, pages = "????", year = "1980", ISBN = "2-04-012165-X (vol. 1), 2-04-012194-3 (vol. 2)", ISBN-13 = "978-2-04-012165-5 (vol. 1), 978-2-04-012194-5 (vol. 2)", LCCN = "TA329 .C64 1980; TA329 .C64 1980", bibdate = "Fri Nov 11 07:42:06 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; umlibr.library.umass.edu:210/INNOPAC", acknowledgement = ack-nhfb, meetingname = "Colloque international sur les m{\'e}thodes num{\'e}riques dans les sciences de l'ing{\'e}nieur (2nd: 1980: Paris)", remark = "English or French. Organized by the Groupe pour l'avancement des m{{\'e}}thodes num{\'e}riques dans les sciences de l'ing{\'e}nieur.", subject = "Engineering mathematics; Congresses; Numerical analysis; Congresses", } @Book{Arden:1980:WCA, editor = "Bruce W. Arden", booktitle = "What can be automated?: The computer science and engineering research study ({COSERS})", title = "What can be automated?: The computer science and engineering research study ({COSERS})", volume = "3", publisher = pub-MIT, address = pub-MIT:adr, pages = "934", year = "1980", ISBN = "0-262-01060-7", ISBN-13 = "978-0-262-01060-3", LCCN = "QA76 .W49", bibdate = "Sun Dec 30 00:09:10 MST 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gear-c-w.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/tex/bib/signum.bib; z3950.loc.gov:7090/Voyager", series = "The MIT Press series in computer science", acknowledgement = ack-nhfb, subject = "Computers; Electronic data processing", } @Proceedings{Glowinski:1982:CMA, editor = "R. Glowinski and Jacques Louis Lions", booktitle = "{Computing methods in applied sciences and engineering, V: proceedings of the Fifth International Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, France, December 14--18, 1981}", title = "{Computing methods in applied sciences and engineering, V: proceedings of the Fifth International Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, France, December 14--18, 1981}", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "x + 668", year = "1982", ISBN = "0-444-86450-4", ISBN-13 = "978-0-444-86450-5", LCCN = "QA297 .E53 1981", bibdate = "Fri Nov 11 07:52:56 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib1; melvyl.cdlib.org:210/CDL90", acknowledgement = ack-nhfb, meetingname = "International Symposium on Computing Methods in Applied Sciences and Engineering (5th : 1981 : Versailles, France)", remark = "Organized by Institut national de recherche en informatique et en automatique.. English or French.", subject = "Numerical analysis; Data processing; Congresses; Science; Data processing; Congresses; Engineering; Data processing; Congresses", } @Proceedings{Glowinski:1984: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-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "xiii + 728", year = "1984", ISBN = "0-444-87597-2", ISBN-13 = "978-0-444-87597-6", LCCN = "QA297 .I57 1983", bibdate = "Mon Jan 15 11:05:19 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Proceedings{Numrich:1985:SA, editor = "Robert W. Numrich", booktitle = "Supercomputer applications", title = "Supercomputer applications", publisher = pub-PLENUM, address = pub-PLENUM:adr, pages = "viii + 307", year = "1985", ISBN = "0-306-42013-9", ISBN-13 = "978-0-306-42013-9", LCCN = "QA76.5.S8944 1984a", bibdate = "Fri Aug 30 08:01:51 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; University of California MELVYL catalog.", note = "Proceedings of the Supercomputer Applications Symposium cosponsored by the Purdue University Computing Center, the Purdue Center for Parallel and Vector Computing, and Control Data, held October 31--November 1, 1984, in West Lafayette, Indiana.", acknowledgement = ack-nhfb, annote = "Published in Proceedings of the Supercomputer Applications Symposium cosponsored by the Purdue University Computing Center, the Purdue Center for Parallel and Vector Computing, and Control Data, held October 31--November 1, 1984, in West Lafayette, Indiana.", keywords = "CYBER 205 (Computer) --- Congresses; Supercomputer systems --- Applications; Supercomputers --- Congresses", } @Proceedings{Glowinski:1986:CMA, editor = "R. (Roland) Glowinski and Jacques Louis Lions", booktitle = "{Computing methods in applied sciences and engineering, VII: proceedings of the Seventh International Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, France, December 9--13, 1985}", title = "{Computing methods in applied sciences and engineering, VII: proceedings of the Seventh International Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, France, December 9--13, 1985}", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "xii + 648", year = "1986", ISBN = "0-444-70059-5", ISBN-13 = "978-0-444-70059-9", LCCN = "TA345", bibdate = "Fri Nov 11 08:21:06 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; library.ox.ac.uk:210/ADVANCE", acknowledgement = ack-nhfb, meetingname = "International Symposium on Computing Methods in Applied Sciences and Engineering 1985 : Versailles, France, 7th.", remark = "Includes 1 chapter in French.. There are English and French forewords.", subject = "Engineering; Data processing; Congresses; Technology; Data processing; Congresses", } @Proceedings{Crane:1987:HAC, editor = "G. E. Crane", booktitle = "{HSNC'87: ACM Conference on the History of Scientific and Numeric Computation, conference proceedings: papers presented at the Conference, Princeton, New Jersey, May 13-15, 1987}", title = "{HSNC'87: ACM Conference on the History of Scientific and Numeric Computation, conference proceedings: papers presented at the Conference, Princeton, New Jersey, May 13-15, 1987}", publisher = pub-ACM, address = pub-ACM:adr, pages = "viii + 150", month = oct, year = "1987", ISBN = "0-89791-229-2", ISBN-13 = "978-0-89791-229-7", LCCN = "QA76 .A25 1987", bibdate = "Tue Nov 14 13:59:59 MST 2023", bibsource = "fsz3950.oclc.org:210/WorldCat; http://portal.acm.org/proceedings/hsnc/; https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib; https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib; https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib", acknowledgement = ack-nhfb, author-dates = "David M. Young, Jr. (October 20, 1923--December 21, 2008); George Elmer Forsythe (8 January 1917--9 April 1972); John Todd (16 May 1911--21 June 2007); John W. Tukey (16 June 1915--26 July 2000); Leslie Fox (30 September 1918--1 August 1992); Magnus Rudolph Hestenes (13 February 1906--31 May 1991)", remark = "Sponsored by the Allegheny Region of the Association for Computing Machinery in cooperation with ACM SIGNUM and the Society for Industrial and Applied Mathematics.", subject = "Electronic data processing; Congresses; Electronic digital computers; Ordinateurs; Congr{\`e}s; Electronic data processing.; Electronic digital computers.", subject-dates = "George Elmer Forsythe (8 January 1917--9 April 1972); James H. Wilkinson (27 September 1919--5 October 1986); John W. Tukey (16 June 1915--26 July 2000)", tableofcontents = "H. H. Goldstine / Keynote address --- Remembrance of things past / https://doi.org/10.1145/41579.41580 / 1--16 \\ L. Fox / Early numerical analysis in the United Kingdom / https://doi.org/10.1145/41579.41581 / 21--39 \\ J. Todd / The prehistory and ancient history of computation at the U.S. National Bureau of Standards / https://doi.org/10.1145/41579.41582 / 47--51 \\ D. J. Wheeler / Programmed computing at the Universities of Cambridge and Illinois in the early fifties / https://doi.org/10.1145/41579.41583 / 53--58 \\ The development of methods of using computers for calculations in the early fifties at Cambridge and Illinois Universities. They are the recollections of a participant. \\ J. R. Rice / Mathematical software and ACM Publications / https://doi.org/10.1145/41579.41584 / 59--62 \\ M. Gutknecht / The pioneer days of scientific computing in Switzerland / https://doi.org/10.1145/41579.41585 / 63--69 \\ M. R. Hestenes / Conjugacy and gradients in variational theory and analysis / https://doi.org/10.1145/41579.41586 / 71--90 \\ C.-E. Fr{\"o}berg / {B I T} --- a child of the computer / https://doi.org/10.1145/41579.41587 / 91--93 \\ I. Babuska / Comments on postwar development of computational mathematics in some countries of Eastern Europe / https://doi.org/10.1145/41579.41588 / 95--96 \\ J. W. Cooley / How the FFT gained acceptance / https://doi.org/10.1145/41579.41589 / 97--100 \\ C. W. Gear, R. Skeel / The development of ODE methods: a symbiosis between hardware and numerical analysis / https://doi.org/10.1145/41579.41590 / 105--115 \\ D. M. Young / An historical review of iterative methods / https://doi.org/10.1145/41579.41591 / 117--123 \\ T. Oden / Some historic comments on finite elements / https://doi.org/10.1145/41579.41592 / 125--130 \\ B. N. Parlett / J. H. Wilkinson's work and influence on matrix computations / https://doi.org/10.1145/41579.41593 / 133--138 \\ J. Varah / The work of George Forsythe and his students / https://doi.org/10.1145/41579.41594 / 139--150", } @Proceedings{Glowinski:1988:FIS, editor = "Roland Glowinski and Gene H. Golub and G{\'e}rard Meurant and Jacques P{\'e}riaux", booktitle = "{First International Symposium on Domain Decomposition Methods for Partial Differential Equations: Proceedings of the First International Symposium on Domain Decomposition Methods for Partial Differential Equations, Ecole Nationale des Ponts et Chauss{\'e}es, Paris, France, January 7--9, 1987}", title = "{First International Symposium on Domain Decomposition Methods for Partial Differential Equations: Proceedings of the First International Symposium on Domain Decomposition Methods for Partial Differential Equations, Ecole Nationale des Ponts et Chauss{\'e}es, Paris, France, January 7--9, 1987}", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "x + 431", year = "1988", ISBN = "0-89871-220-3", ISBN-13 = "978-0-89871-220-9", LCCN = "QA402.2 .I571 1987", MRclass = "65-06 (76-06)", MRnumber = "89f:65005", bibdate = "Sun Jan 14 09:19:15 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Proceedings{Cox:1990:RNC, editor = "M. G. Cox and S. Hammarling", booktitle = "Reliable numerical computation", title = "Reliable numerical computation", publisher = pub-OXFORD, address = pub-OXFORD:adr, pages = "xvi + 339", year = "1990", ISBN = "0-19-853564-3", ISBN-13 = "978-0-19-853564-5", LCCN = "QA297 .R435 1990", MRclass = "65-06", MRnumber = "91k:65011", bibdate = "Fri Dec 20 18:34:52 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib; https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", note = "Based on papers from a conference in honour of the late James Hardy Wilkinson (died Sunday 5th October 1986) held at National Physical Laboratory, Teddington, Middlesex, UK, 8th--10th July 1987.", price = "US\$75.00", abstract = "Published to honor the late Jim Wilkinson, the respected pioneer in numerical analysis, this book includes contributions from his colleagues and collaborators, leading experts in their own right. The breadth of Wilkinson's research is reflected in the topics covered, which include linear algebra, error analysis and computer arithmetic algorithms, and mathematical software. An invaluable reference, the book is completely up-to-date with the latest developments on the Lanczos algorithm, QR-factorizations, error propagation models, parameter estimation problems, sparse systems, and shape-preserving splines. Reflecting the current growth and vitality of this field, the volume is an essential reference for all numerical analysts.", acknowledgement = ack-nhfb, author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)", tableofcontents = "List of contributors / / xv \\ Prologue. Reflections on Jim Wilkinson / Gene Golub / 1 \\ 1. Misconvergence in the Lanczos algorithm / Beresford Parlett / 7 \\ 2. The Lanczos algorithm for a pure imaginary Hermitian matrix / Charles L. Lawson and Kajal K. Gupta / 25 \\ 3. Nearest defective matrices and the geometry of ill-conditioning / James Demmel / 35 \\ 4. Computational aspects of the Jordan canonical form / Theo Beelen and Paul Van Dooren / 57 \\ 5. Some aspects of generalized QR factorizations / C. C. Paige / 73 \\ 6. The multifrontal method in a parallel environment / I. S. Duff, N. I. M. Gould, M. Lescrenier, and J. K. Reid / 93 \\ 7. A Schur-complement method for sparse quadratic programming / Philip E. Gill, Walter Murray, Michael A. Saunders, and Margaret H. Wright / 113 \\ 8. A probabilistic round-off error propagation model. Application to the eigenvalue problem / Fran{\c{c}}oise Chatelin and Marie Christine Brunet / 139 \\ 9. Analysis of the Cholesky decomposition of a semi-definite matrix / Nicholas J. Higham / 161 \\ 10. On the conditioning of parameter estimation problems / James M. Varah / 187 \\ 11. Rounding errors in algebraic process-in level-index arithmetic / F. W J. Olver / 197 \\ 12. Experiments in tearing large sparse systems / Mario Arioli and lain S. Duff / 207 \\ 13. The least-squares solution of linear equations with block-angular observation matrix / M. G. Cox / 227 \\ 14. An iterative method for solving linear inequalities / G. W Stewart / 241 \\ 15. Iterative refinement and reliable computing / Ake Bjorck / 249 \\ 16. Software for shape-preserving spline interpolation / Christian H. Reinsch / 267 \\ 17. Experiences with some software engineering practices in numerical software / D. A. H. Jacobs and G. Markham / 277 \\ 18. Evolution of numerical software for dense linear algebra / Jack Dongarra and Sven Hammarling / 297 \\ Epilogue. Jim Wilkinson: some after-dinner sentiments / L. Fox / 329", } @Proceedings{Kaashoek:1990:PIS, editor = "M. A. Kaashoek and J. H. van Schuppen and A. C. M. Ran", booktitle = "{Proceedings of the International Symposium MTNS-89}", title = "{Proceedings of the International Symposium MTNS-89}", volume = "3--5", publisher = pub-BIRKHAUSER-BOSTON, address = pub-BIRKHAUSER-BOSTON:adr, pages = "????", year = "1990", ISBN = "0-8176-3469-X (vol 1), 0-8176-3470-3 (vol. 2), 0-8176-3471-1 (vol. 3), 0-8176-3468-1 (set)", ISBN-13 = "978-0-8176-3469-8 (vol 1), 978-0-8176-3470-4 (vol. 2), 978-0-8176-3471-1 (vol. 3), 978-0-8176-3468-1 (set)", LCCN = "QA402 .P766 1989", bibdate = "Fri Nov 11 07:56:03 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; melvyl.cdlib.org:210/CDL90", series = "Progress in systems and control theory", acknowledgement = ack-nhfb, meetingname = "International Symposium on the Mathematical Theory of Networks and Systems (9th : 1989 : Amsterdam, Netherlands)", remark = "The 1989 International Symposium on the Mathematical Theory of Networks and Systems (MTNS) \ldots{} held in Amsterdam, The Netherlands, June 19-23, 1989. Vol. 1. Realization and modelling in system theory. Vol. 2. Robust control of linear systems and nonlinear control. Vol. 3. Signal processing, scattering and operator theory, and numerical methods.", subject = "System analysis; Congresses; Control theory; Congresses", } @Book{Nash:1990:HSC, editor = "Stephen G. Nash", booktitle = "A History of Scientific Computing", title = "A History of Scientific Computing", publisher = pub-AW # " and " # pub-ACM, address = pub-AW # " and " # pub-ACM:adr, pages = "xix + 359", year = "1990", ISBN = "0-201-50814-1", ISBN-13 = "978-0-201-50814-7", LCCN = "QA76.17 .H59 1990", bibdate = "Wed Dec 15 10:39:57 1993", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/birkhoff-garrett.bib; https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib; https://www.math.utah.edu/pub/bibnet/authors/g/gear-c-w.bib; https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib; https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib; https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;; https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib; https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/numana1990.bib; z3950.loc.gov:7090/Voyager", series = "ACM Press history series", acknowledgement = ack-nhfb, author-dates = "Charles William ``Bill'' Gear (1 February 1935--15 March 2022); Garrett Birkhoff (19 January 1911--22 November 1996); Magnus Rudolph Hestenes (13 February 1906--31 May 1991)", remark = "Based on papers presented at the Conference on the History of Scientific and Numeric Computation, held in Princeton, NJ, 1987. A few brief mentions of Alston Householder are indexed in the book, with photographs of him on pages xvi and 344.", subject = "Electronic data processing; History; Science; Data processing", tableofcontents = "Remembrance of things past / Herman H. Goldstine / 5--16 \\ The contribution of J. H. Wilkinson to numerical analysis / B. N. Parlett / 17--30 \\ The influence of George Forsythe and his students / James Varah / 31--40 \\ Howard H. Aiken and the computer / I. Bernard Cohen / 41--52 \\ Particles in their self-consistent field: from Hartree's differential analyzer to Cray machines / Oscar Buneman / 57--62 \\ Fluid dynamics, reactor computations, and surface representation / Garrett Birkhoff / 63--87 \\ The development of ODE methods: a symbiosis between hardware and numerical analysis / C. W. Gear and R. D. Skeel / 88--105 \\ A personal retrospection of reservoir simulation / Donald W. Peaceman / 106--129 \\ How the FFT gained acceptance / James W. Cooley / 133--140 \\ Origins of the simplex method / George B. Dantzig / 141--151 \\ Historical comments on finite elements / J. Tinsley Oden / 152--166 \\ Conjugacy and gradients / Magnus R. Hestenes / 167--179 \\ A historical review of iterative methods / David M. Young / 180--194 \\ Shaping the evolution of numerical analysis in the computer age: the SIAM thrust / I. Edward Block / 199--205 \\ Reminiscences on the University of Michigan summer schools, the Gatlinburg Symposia, and Numerische Mathematik / Richard S. Varga / 206--210 \\ The origin of mathematics of computation and some personal recollections / Eugene Isaacson / 211--216 \\ Mathematical software and ACM publications / John R. Rice / 217--227 \\ BIT --- a child of the computer / Carl-Erik Fr{\"o}berg / 228--233 \\ The Los Alamos experience, 1943--1954 / N. Metropolis / 237--250 \\ The prehistory and early history of computation at the U.S. National Bureau of Standards / John Todd / 251--268 \\ Programmed computing at the Universities of Cambridge and Illinois in the early fifties / David J. Wheeler / 269--279 \\ Early numerical analysis in the United Kingdom / L. Fox / 280--300 \\ The pioneer days of scientific computing in Switzerland / Martin H. Gutknecht / 301--313 \\ The development of computational mathematics in Czechoslovakia and the USSR / I. Babuska / 314--328 \\ The contribution of Leningrad mathematicians to the development of numerical linear algebra, 1950--1986 / V. N. Kublanovskaya / 329--338", } @Proceedings{Albrecht:1991:NTE, editor = "J. (Julius) Albrecht", booktitle = "{Numerical treatment of eigenvalue problems: Workshop in Oberwolfach, February 25-March 3, 1990 = Numerische Behandlung von Eigenwertaufgaben: Tagung in Oberwolfach, 25. Februar--3. M{\"a}rz 1990}", title = "{Numerical treatment of eigenvalue problems: Workshop in Oberwolfach, February 25-March 3, 1990 = Numerische Behandlung von Eigenwertaufgaben: Tagung in Oberwolfach, 25. Februar--3. M{\"a}rz 1990}", volume = "96", publisher = pub-BIRKHAUSER, address = pub-BIRKHAUSER:adr, pages = "ix + 243", year = "1991", ISBN = "3-7643-2575-5", ISBN-13 = "978-3-7643-2575-6", bibdate = "Fri Nov 11 08:23:50 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; melvyl.cdlib.org:210/CDL90", series = "International series of numerical mathematics; Numerical treatment of eigenvalue problems", acknowledgement = ack-nhfb, remark = "English and German.", subject = "Differential equations; Numerical solutions; Data processing; Congresses; Matrices; Data processing; Congresses; Eigenvalues; Data processing; Congresses", } @Proceedings{Moonen:1993:LAL, editor = "Marc S. Moonen and Gene H. Golub and Bart L. R. {De Moor}", booktitle = "{Linear Algebra for Large Scale and Real-Time Applications: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3--14, 1992}", title = "{Linear Algebra for Large Scale and Real-Time Applications: Proceedings of the NATO Advanced Study Institute, Leuven, Belgium, August 3--14, 1992}", volume = "232", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "ix + 435", year = "1993", ISBN = "0-7923-2151-0", ISBN-13 = "978-0-7923-2151-4", LCCN = "QA185.D37 L56 1993", MRclass = "65-06 (65Fxx 65Y05)", MRnumber = "94e:65009", bibdate = "Mon Jan 15 17:53:04 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib", series = "NATO ASI series. Series E, Applied sciences", URL = "http://catdir.loc.gov/catdir/enhancements/fy0823/92046135-d.html; http://www.gbv.de/dms/hbz/toc/ht004938330.pdf; http://zbmath.org/?q=an:0810.00029", ZMnumber = "0810.00029", abstract = "In recent years there has been great interest in large scale and real-time matrix computations; these computations arise in a variety of fields, such as computer graphics, imaging, speech and image processing, telecommunication, biomedical signal processing, optimization and so on. This volume, which is an outgrowth of a NATO ASI, held at Leuven, Belgium, August 1992, gives an account of recent research advances in numerical techniques used in large scale and real-time computations and their implementation on high performance computers.", acknowledgement = ack-nhfb, 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{Reichel:1993:NLA, editor = "Lothar Reichel and Arden Ruttan and Richard S. Varga", booktitle = "{Numerical linear algebra: proceedings of the Conference in Numerical Linear Algebra and Scientific Computation, Kent (Ohio), USA, March 13--14, 1992}", title = "{Numerical linear algebra: proceedings of the Conference in Numerical Linear Algebra and Scientific Computation, Kent (Ohio), USA, March 13--14, 1992}", publisher = pub-GRUYTER, address = pub-GRUYTER:adr, pages = "vii + 199", year = "1993", ISBN = "3-11-013784-4", ISBN-13 = "978-3-11-013784-2", LCCN = "QA184.C655 1993", bibdate = "Fri Nov 11 08:28:39 MST 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; melvyl.cdlib.org:210/CDL90", acknowledgement = ack-nhfb, meetingname = "Conference in Numerical Linear Algebra and Scientific Computation (1992 : Kent, Ohio)", subject = "Algebras, Linear; Congresses; Numerical analysis; Congresses", } @Proceedings{Brown:1994:PCL, editor = "J. David Brown and Moody T. Chu and Donald C. Ellison and Robert J. Plemmons", booktitle = "{Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh, North Carolina, December 12--17, 1993}", title = "{Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh, North Carolina, December 12--17, 1993}", volume = "73", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "lxv + 644", year = "1994", ISBN = "0-89871-339-0", ISBN-13 = "978-0-89871-339-8", LCCN = "QC19.2 .C67 1993", bibdate = "Wed Jun 8 14:42:43 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/einstein.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager", series = "Proceedings in Applied Mathematics", acknowledgement = ack-nhfb, meetingname = "Cornelius Lanczos International Centenary Conference (1993:Raleigh, NC)", subject = "Mathematical physics; Congresses; Astrophysics; Mathematics; Lanczos, Cornelius; Physicists; Hungary; Biography; Mathematicians", subject-dates = "1893--1974", tableofcontents = "The Life and Works of Cornelius Lanczos \\ \\ A Photographic Essay / / xvii \\ Cornelius Lanczos: A Biographical Essay / Barbara Gellai / xxi \\ Cornelius Lanczos (1893-1974), and the Hungarian Phenomenon in Science and Mathematics / Peter D. Lax / xlix \\ The Roots of Cornelius Lanczos / George Marx / liii \\ Reminiscences of Cornelius Lanczos / Jon Todd / lviii \\ Published Papers and Books of Cornelius Lanczos / / lx \\ \\ Plenary Presentations: Computational Mathematics \\ \\ Lanczos and the FFT: A Discovery Before its Time / James W. Cooley / 3 \\ Lanczos Algorithms for Large Scale Symmetric and Nonsymmetric Matrix Eigenvalue Problems / Jane K. Cullum / 11 \\ The Look-Ahead Lanczos Process for Nonsymmetric Matrices and its Applications / Roland W Freund / 33 \\ The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic / Anne Greenbaum / 49 \\ The Lanczos Process and Pade Approximation / Martin H. Gutknecht / 61 \\ The Tau Method and the Numerical Solution of Differential Equations: Past Research and Recent Research / Eduardo L. Ortiz / 77 \\ Krylov Subspace Processes, Krylov Subspace Methods, and Iteration Polynomials / C. C. Paige / 83 \\ Do We Fully Understand the Symmetric Lanczos Algorithm Yet? / Beresford N. Parlett / 93 \\ On Generalized Band Matrices and Their Inverses / P{\'a}l R{\'o}sa, Francesco Romani, and Roberto Bevilacqua / 109 \\ Theoretical Error Bounds and General Analysis of a Few Lanczos-Type Algorithms / Youcef Saad / 123 \\ Lanczos and Linear Systems / G. W. Stewart / 135 \\ \\ Plenary Presentations: Theoretical Physics and Astrophysics \\ \\ Integration on the Space of Connections Modulo Gauge Transformations / Abbay Ashtekar, Donald Marolf, and Jose Mourdo / 143 \\ Quasiclassical Domains in a Quantum Universe / James B. Hartle / 161 \\ Gauge Invariant Energy-Momentum Tensor in Spinar Electrodynamics / D. Petiot and Y. Takahashi / 173 \\ $\gamma$-Ray Bursts and Neutron Star Mergers / Tsvi Piran / 187 \\ Lanczos's Early Contributions to Relativity and His Relationship with Einstein / John Stachel / 201 \\ Topological Roots of Black Hole Entropy / Claudio Teitelboim / 223 \\ Variational Principles, Local Symmetries, and Black Hole Entropy / Robert M. Wald / 231 \\ \\ Mathematics Minisymposia \\ \\ Eigenvalue Computations: Theory and Algorithms / / 241 \\ Eigenvalue Computations: Applications / / 249 \\ Moments in Numerical Analysis / / 265 \\ Iterative Methods for Linear Systems / / 277 \\ Least Squares / / 301 \\ Software for Lanczos-based Algorithms / / 311 \\ Tau Method / / 335 \\ Chebyshev Polynomials / / 357 \\ Lanczos Methods in Control and Signal Processing / / 375 \\ Development of the FFT / / 393 \\ The FFT in Signal Processing / / 399 \\ Wavelets / / 411 \\ \\ Physics Minisymposia \\ \\ Computational Magnetohydrodynamics in Astrophysics / / 431 \\ Numerical Simulations of Collisionless Space Plasmas / / 453 \\ Detection of Gravitational Radiation from Astrophysical Sources / / 477 \\ Lanczos $H$-tensor / / 489 \\ Cosmic Censorship / / 513 \\ Cauchy Problem of General Relativity / / 527 \\ Black Hole Evaporation and Thermodynamics / / 543 \\ The Problem of Time in Quantum Gravity / / 555 \\ New Variables and Loop Quantization / / 571 \\ Decoherence and the Foundations of Quantum Mechanics / / 589 \\ Open Questions in Particle Theory / / 603 \\ Supercollider Physics / / 621 \\ Symplectic Methods in Physics / / 633", } @Proceedings{Lewis:1994:ALA, editor = "John G. Lewis", booktitle = "Applied Linear Algebra: Proceedings of the Fifth {SIAM} Conference on Applied Linear Algebra, Snowbird, Utah, June 15--18, 1994", title = "Applied Linear Algebra: Proceedings of the Fifth {SIAM} Conference on Applied Linear Algebra, Snowbird, Utah, June 15--18, 1994", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "x + 578", year = "1994", ISBN = "0-89871-336-6", ISBN-13 = "978-0-89871-336-7", LCCN = "QA184.S58 1994", bibdate = "Fri May 14 12:41:12 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/i/ipsen-ilse-c-f.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Proceedings{Natori:1994:MAP, editor = "M. Natori and T. Nodera", booktitle = "Matrix analysis and parallel computing", title = "Matrix analysis and parallel computing", volume = "10", publisher = "Keio University", address = "Yokohama, Japan", pages = "276", year = "1994", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Nov 11 08:31:31 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", series = "Adv. Numer. Methods Large Sparse Sets Linear Equations", acknowledgement = ack-nhfb, remark = "Papers presented at the 10th PCG symposium, held at Keio University, Tokyo, Japan, March 14-16, 1994.", } @Proceedings{Bailey:1995:PSS, editor = "D. H. Bailey and P. E. Bjorstad and J. R. Gilbert and M. V. Mascagni and R. S. Schreiber and H. D. Simon and V. J. Torczon and L. T. Watson", booktitle = "{Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing (February 15--17, 1995, San Francisco, CA)}", title = "{Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing (February 15--17, 1995, San Francisco, CA)}", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xviii + 875", year = "1995", ISBN = "0-89871-344-7", ISBN-13 = "978-0-89871-344-2", LCCN = "QA76.58.S55 1995", bibdate = "Tue Sep 3 12:52:10 MDT 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, sponsor = "Society for Industrial and Applied Mathematics.", } @Book{Iserles:1995:AN, editor = "A. Iserles", booktitle = "{Acta Numerica 1995}", title = "{Acta Numerica 1995}", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "491", year = "1995", ISBN = "0-521-48255-0", ISBN-13 = "978-0-521-48255-4", LCCN = "", bibdate = "Fri Nov 11 07:13:56 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, } @Proceedings{Renegar:1996:MNA, editor = "James Renegar and Michael Shub and Steve Smale", booktitle = "{The mathematics of numerical analysis: 1995 AMS--SIAM Summer Seminar in Applied Mathematics, July 17--August 11, 1995, Park City, Utah}", title = "{The mathematics of numerical analysis: 1995 AMS--SIAM Summer Seminar in Applied Mathematics, July 17--August 11, 1995, Park City, Utah}", volume = "32", publisher = pub-AMS, address = pub-AMS:adr, pages = "xi + 927 + [1]", year = "1996", ISBN = "0-8218-0530-4", ISBN-13 = "978-0-8218-0530-5", ISSN = "0075-8485", LCCN = "QA297 .A57 1995", bibdate = "Tue Oct 27 18:18:33 MST 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", series = "Lectures in Applied Mathematics --- American Mathematical Society", acknowledgement = ack-nhfb, keywords = "numerical analysis -- congresses", sponsor = "American Mathematical Society. Society for Industrial and Applied Mathematics.", } @Proceedings{Watson:1996:NA, editor = "G. A. Watson and D. F. Griffiths", booktitle = "Numerical analysis 1995", title = "Numerical analysis 1995", volume = "344", publisher = pub-LONGMAN, address = pub-LONGMAN:adr, pages = "237", year = "1996", ISBN = "0-582-27633-0 (paperback)", ISBN-13 = "978-0-582-27633-8 (paperback)", ISSN = "0269-3674", LCCN = "QA297.N854 1996", bibdate = "Wed Nov 3 09:30:14 MST 1999", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Proceedings of the 16th Dundee Biennial Conference on Numerical Analysis, University of Dundee, June 27--30, 1995.", series = "Pitman research notes in mathematics series", acknowledgement = ack-nhfb, keywords = "numerical analysis -- research", } @Proceedings{Watson:1982:NAP, editor = "George Alistair Watson", booktitle = "{Numerical Analysis: Proceedings of the 9th Biennial Conference, held at Dundee, Scotland, June 23--26, 1981}", title = "{Numerical Analysis: Proceedings of the 9th Biennial Conference, held at Dundee, Scotland, June 23--26, 1981}", volume = "912", publisher = pub-SV, address = pub-SV:adr, bookpages = "xi + 245", pages = "xi + 245", year = "1982", CODEN = "LNMAA2", DOI = "https://doi.org/10.1007/BFb0093144", ISBN = "0-387-11199-9 (softcover), 3-540-11199-9 (softcover), 3-540-39009-X (e-book)", ISBN-13 = "978-0-387-11199-5 (softcover), 978-3-540-11199-3 (softcover), 978-3-540-39009-1 (e-book)", ISSN = "0075-8434 (print), 1617-9692 (electronic)", ISSN-L = "0075-8434", LCCN = "QA3 .L28 no. 912; QA1 .L471; QA297 .D915n 1981", bibdate = "Sat Oct 29 15:16:39 1994", bibsource = "fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/m/more-jorge.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/lnm1980.bib; library.ox.ac.uk:210/ADVANCE; melvyl.cdlib.org:210/CDL90", series = ser-LECT-NOTES-MATH, URL = "http://www.springerlink.com/content/978-3-540-39009-1", acknowledgement = ack-nhfb, subject = "Analisi numerica; Congressi; 1981; Dundee; Numerical analysis; Congresses", tableofcontents = "P. H. Calamai and A. R. Conn / A second-order method for solving the continuous multifacility location problem / 1--25 \\ M. P. Cullinan and M. J. D. Powell / Data smoothing by divided differences / 26--37 \\ G. Dahlquist / On the control of the global error in stiff initial value problems / 38--49 \\ L. M. Delves / Chebyshev methods for integral and differential equations / 50--63 \\ J. Douglas, Jr. / Simulation of miscible displacement in porous media by a modified method of characteristic procedure / 64--70 \\ I. S. Duff / Full matrix techniques in sparse Gaussian elimination / 71--84 \\ R. Fletcher / Second order corrections for non-differentiable optimization / 85--114 \\ C. W. Gear and K. A. Gallivan / Automatic methods for highly oscillatory ordinary differential equations / 115--124 \\ G. H. Golub and M. L. Overton / Convergence of a two-stage Richardson iterative procedure for solving systems of linear equations / 125--139 \\ J. G. Hayes: Curved knot lines and surfaces with ruled segments / 140--156 \\ P. J. van der Houwen / On the time integration of parabolic differential equations / 157--168 \\ T. E. Hull / Precision control, exception handling and a choice of numerical algorithms / 169--178 \\ P. Lancaster / Generalized Hermitian matrices: a new frontier for numerical analysis? / 179--189 \\ R. J. Y. McLeod / Some applications of geometry in numerical analysis / 190--229 \\ L. B. Wahlbin / A quasioptimal estimate in piecewise polynomial Galerkin approximation of parabolic problems / 230 --245 \\ Back matter / 249--251", } @Proceedings{Buhmann:1997:ATO, editor = "Martin D. Buhmann and Arieh Iserles", booktitle = "Approximation Theory and Optimization: tributes to {M. J. D. Powell} [{Conference on Numerical Mathematics in Cambridge, on 27--30 July 1996}]", title = "Approximation Theory and Optimization: tributes to {M. J. D. Powell} [{Conference on Numerical Mathematics in Cambridge, on 27--30 July 1996}]", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, pages = "xiii + 220", year = "1997", ISBN = "0-521-58190-7 (hardcover)", ISBN-13 = "978-0-521-58190-5 (hardcover)", LCCN = "QA221 .A655 1997", MRclass = "90-04 (90C30)", MRnumber = "1601707", bibdate = "Tue Nov 28 17:36:07 2023", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/m/more-jorge.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib", acknowledgement = ack-nhfb, remark = "This volume comprises ten invited papers, presented at the Conference on Numerical Mathematics in Cambridge, on 27--30 July 1996, the occasion being the sixtieth birthday of Professor M. J. D. Powell FRS.", tableofcontents = "Preface / vii \\ Submitted Talks / ix \\ M. D. Buhmann and R. Fletcher / M. J. D. Powell's contributions to numerical mathematics / 1 \\ M. D. Buhmann and R. Fletcher / A brief review of M. J. D. Powell's work in univariate and multivariate approximation theory / 1 \\ M. D. Buhmann and R. Fletcher / The contributions of Mike Powell to optimization / 13 \\ M. D. Buhmann and R. Fletcher / M. J. D. Powell's publications / 19 \\ I. Barrodale and Zala / MJDP-BCS industrial liaison: Applications to defence science / 31 \\ C. de Boor / On the Meir\slash Sharma\slash Hall\slash Meyer analysis of the spline interpolation error / 47 \\ M. D. Buhmann, C. A. Micchelli and A. Ron / Asymptotically optimal approximation and numerical solutions of differential equations / 59 \\ A. R. Conn, K. Scheinberg and Ph. L. Toint / On the convergence of derivative-free methods for unconstrained optimization / 83 \\ I. C. Demetriou and M. J. D. Powell / Least squares fitting to univariate data subject to restrictions on the signs of the second differences / 109 \\ N. Dyn, F. J. Narcowich and J. D. Ward / A framework for interpolation and approximation on Riemannian manifolds / 133 \\ R. Fletcher / Dense factors of sparse matrices / 145 \\ W. Gropp and J. J. Mor{\'e} / Optimization environments and the NEOS Server / 167 \\ B. N. Parlett / New versions of $ q d $ for products of bidiagonals / 183 \\ M. J. Todd / On adjusting parameters in homotopy methods for linear programming / 201", } @Proceedings{Barlow:2000:PIW, editor = "Jesse L. Barlow and Beresford N. Parlett", booktitle = "{Proceedings of the International Workshop on Accurate Solution of Eigenvalue Problems}", title = "{Proceedings of the International Workshop on Accurate Solution of Eigenvalue Problems}", publisher = pub-ELSEVIER, address = pub-ELSEVIER:adr, pages = "iii + 361", year = "2000", CODEN = "LAAPAW", ISSN = "0024-3795 (print), 1873-1856 (electronic)", MRclass = "65-06 (15-06 65F15 65L15 65N25)", MRnumber = "MR1758357 (2000m:65010)", bibdate = "Thu Nov 10 18:37:11 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", note = "Held at Pennsylvania State University, University Park, PA, July 20--23, 1998, Linear Algebra Appl. {\bf 309} (2000), no. 1--3.", series = j-LINEAR-ALGEBRA-APPL, acknowledgement = ack-nhfb, }

%%% Last MathSciNet search: Thu Feb 10 08:11:55 2022