%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author = "Nelson H. F. Beebe",
%%% version = "1.99",
%%% date = "30 September 2024",
%%% time = "11:50:43 MDT",
%%% filename = "lanczos-cornelius.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 = "08577 23942 100543 1054498",
%%% email = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "bibliography; BibTeX; Cornel Lanczos;
%%% Cornelius Lanczos; Kornel Lancius; Kornel
%%% Lanczos; L{\a}nczos Korn{\'e}l",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "This is a bibliography of the publications
%%% of Cornelius Lanczos (2 February 1893--25
%%% June 1974). The family name was originally
%%% the German--Jewish L{\"o}wy, but was changed
%%% to the Hungarian L{\'a}nczos in 1906, when
%%% Cornelius was then still in school.
%%%
%%% Lanczos wrote in Hungarian, French, German,
%%% and English, and under five author names:
%%%
%%% (1) Hungarian form: L{\'a}nczos Korn{\'e}l
%%% (2) German form: Kornel Lancius
%%% (3) German form: Kornel Lanczos
%%% (1922--July 29, 1927)
%%% (4) German form: Cornel Lanczos
%%% (mid-1927--1935)
%%% (5) English form: Cornelius Lanczos or
%%% C. Lanczos (1931--1998)
%%%
%%% At version 1.07, coverage is believed to be
%%% COMPLETE (the bibliography includes
%%% everything listed in Anonymous:1994:PPB, and
%%% more), although it is likely that entries are
%%% missing for some translations of Lanczos's
%%% books into other languages.
%%%
%%% At version 1.99, the year coverage looked
%%% like this:
%%%
%%% 1921 ( 1) 1956 ( 4) 1991 ( 12)
%%% 1922 ( 2) 1957 ( 5) 1992 ( 16)
%%% 1923 ( 5) 1958 ( 8) 1993 ( 23)
%%% 1924 ( 2) 1959 ( 1) 1994 ( 169)
%%% 1925 ( 7) 1960 ( 3) 1995 ( 21)
%%% 1926 ( 5) 1961 ( 5) 1996 ( 27)
%%% 1927 ( 2) 1962 ( 9) 1997 ( 28)
%%% 1928 ( 0) 1963 ( 4) 1998 ( 27)
%%% 1929 ( 4) 1964 ( 10) 1999 ( 25)
%%% 1930 ( 5) 1965 ( 7) 2000 ( 21)
%%% 1931 ( 6) 1966 ( 13) 2001 ( 19)
%%% 1932 ( 7) 1967 ( 11) 2002 ( 15)
%%% 1933 ( 3) 1968 ( 4) 2003 ( 14)
%%% 1934 ( 2) 1969 ( 5) 2004 ( 9)
%%% 1935 ( 2) 1970 ( 11) 2005 ( 16)
%%% 1936 ( 2) 1971 ( 6) 2006 ( 12)
%%% 1937 ( 1) 1972 ( 9) 2007 ( 15)
%%% 1938 ( 3) 1973 ( 7) 2008 ( 11)
%%% 1939 ( 1) 1974 ( 17) 2009 ( 9)
%%% 1940 ( 1) 1975 ( 16) 2010 ( 13)
%%% 1941 ( 2) 1976 ( 8) 2011 ( 7)
%%% 1942 ( 5) 1977 ( 4) 2012 ( 0)
%%% 1943 ( 0) 1978 ( 6) 2013 ( 1)
%%% 1944 ( 0) 1979 ( 3) 2014 ( 1)
%%% 1945 ( 0) 1980 ( 5) 2015 ( 0)
%%% 1946 ( 0) 1981 ( 7) 2016 ( 2)
%%% 1947 ( 0) 1982 ( 9) 2017 ( 0)
%%% 1948 ( 1) 1983 ( 6) 2018 ( 2)
%%% 1949 ( 2) 1984 ( 15) 2019 ( 1)
%%% 1950 ( 1) 1985 ( 9) 2020 ( 1)
%%% 1951 ( 6) 1986 ( 8) 2021 ( 0)
%%% 1952 ( 5) 1987 ( 18) 2022 ( 1)
%%% 1953 ( 2) 1988 ( 6) 2023 ( 2)
%%% 1954 ( 0) 1989 ( 13) 2024 ( 1)
%%% 1955 ( 5) 1990 ( 13)
%%%
%%% Article: 522
%%% Book: 76
%%% InBook: 5
%%% InCollection: 26
%%% InProceedings: 188
%%% MastersThesis: 2
%%% Misc: 1
%%% PhdThesis: 7
%%% Proceedings: 31
%%% TechReport: 34
%%% Unpublished: 4
%%%
%%% Total entries: 896
%%%
%%% This bibliography consists of two main parts:
%%%
%%% * publications of Lanczos
%%% * publications about Lanczos or his works
%%%
%%% The second part is only a sampling: the name
%%% Lanczos appears in countless article titles
%%% in the engineering, mathematics, and science
%%% literature.
%%%
%%% The final (third) part contains entries that
%%% are cross referenced by earlier entries.
%%%
%%% While Lanczos worked primarily in theoretical
%%% physics and applied mathematics, his work has
%%% had wide influence, with use in chemical
%%% physics, cryptography, crystallography,
%%% engineering, geology, geophysics, nuclear
%%% physics, quantum chemistry, and quantum
%%% physics.
%%%
%%% Lanczos wrote 14 books, with several
%%% appearing in more than one edition, or from
%%% more than one publisher. Most have URL links
%%% to the Hathi Trust Digital Library: a few are
%%% available for online viewing in their
%%% entirety (though not downloadable), while
%%% most others permit only severely-limited
%%% searching due to copyright restrictions.
%%%
%%% It is considered an honor in mathematics and
%%% science to have one's name attached to
%%% concepts, such as algorithms, conjectures,
%%% equations, hypotheses, methods, propositions,
%%% theorems, and so on. It is an even greater
%%% honor to be connected with some of the
%%% greatest mathematicians or scientists in
%%% history. Here are about three dozen examples
%%% from this bibliography:
%%%
%%% * Bach--Lanczos identity
%%% * block Lanczos method (or procedure)
%%% * Invert--Lanczos process
%%% * Krylov--Lanczos method
%%% * Lanczos algorithm (for eigensolutions)
%%% * Lanczos approximation
%%% * Lanczos basis
%%% * Lanczos bidiagonalization
%%% * Lanczos coordinates
%%% * Lanczos decomposition
%%% * Lanczos iteration
%%% * Lanczos phenomena
%%% * Lanczos potential
%%% * Lanczos potential spinor
%%% * Lanczos process (subspace iteration)
%%% * Lanczos representation
%%% * Lanczos tau method (for function interpolation)
%%% * Lanczos technique
%%% * Lanczos transformation
%%% * Lanczos tridiagonalization
%%% * Lanczos vectors
%%% * Lanczos--Arnoldi algorithm
%%% * Lanczos--Chebyshev reduction method
%%% * Lanczos--Legendre reduction method
%%% * Lanczos--Ortiz theory of canonical polynomials
%%% * Lanczos--Pad{\'e} spectral solution
%%% * Lanczos-hybrid regularization
%%% * Liouville--Lanczos approach
%%% * look-ahead Lanczos algorithm
%%% * Newton--Lanczos method (for solution of
%%% nonlinear finite-element equations)
%%% * Pad{\'}e-via-Lanczos algorithm (or method)
%%% * Riemann--Lanczos equations (or problems)
%%% * Schwinger--Lanczos algorithm
%%% * Shift-and-Invert Lanczos method
%%% * Spectral Lanczos Decomposition Method (SLDM)
%%% * Unsymmetric Lanczos Reduction method
%%% * Weyl--Lanczos equations (or relations)
%%%
%%% A search in mid-2011 of http://scholar.google.com/
%%% found these important Lanczos works (ordered by
%%% descending reference counts):
%%%
%%% Lanczos:1950:IMS 2224
%%% Lanczos:1961:AA 1561
%%% Lanczos:1970:VPM 1534
%%% Lanczos:1952:SSL 647
%%% Lanczos:1996:LDO 618
%%% Lanczos:1938:RPR 231
%%% Lanczos:1938:TIE 221
%%% Lanczos:1966:DFSa,b 204
%%% Lanczos:1962:SRT 155
%%% Lanczos:1988:AA 147
%%% Lancius:1922:BSW 93
%%% Lanczos:1930:ISL 90
%%% Lanczos:1964:PAG 78
%%% Lanczos:1958:LSS 46
%%% Lanczos:1957:EGR 41
%%% Lanczos:1961:PMP 29
%%% Lanczos:1973:LVC 26
%%% Rosser:1951:SCE 25
%%% Lanczos:1953:CPS 21
%%% Lanczos:1965:AEC 20
%%%
%%% Those numbers are suggestive of the relative
%%% importance of some of Lanczos' books and
%%% papers. That Web site includes links to the
%%% citing documents, allowing researchers to
%%% find more recent works that build on that of
%%% Lanczos.
%%%
%%% Lanczos was born about 30km southwest of
%%% Budapest in the city of
%%% Sz{\'e}kesfeh{\'e}rv{\'a}r, the first capital
%%% of Hungary (ca. 1000--1250 CE). He attended
%%% the Budapest University of Science where the
%%% famous Roland E{\"o}tv{\"o}s (E{\"o}tv{\"o}s
%%% Lor{\'a}nd in Hungarian) (1848--1919) was one
%%% of his professors. One of E{\"o}tv{\"o}s'
%%% most important contributions was the
%%% demonstration (to 8 decimal digits) of the
%%% equivalence between inertial mass and
%%% gravitational mass, and accurate measurement
%%% of Newton's gravitational constant, $G$:
%%%
%%% http://en.wikipedia.org/wiki/E%C3%B6tv%C3%B6s_experiment
%%% http://www.kfki.hu/eotvos/onehund.html
%%%
%%% His torsion balance was later improved and
%%% the equivalence has now been confirmed with
%%% an accuracy of 1 part in $10^{11}$. The
%%% demonstrated equivalence was fundamental
%%% evidence for Albert Einstein's Principle of
%%% Equivalence in the Theory of Relativity,
%%% although in 1912, Einstein was still unaware
%%% of that work.
%%%
%%% Lanczos's graduate supervisor was nominally
%%% Rudolf Ortvay, but Lanczos worked largely
%%% independently on his thesis work.
%%%
%%% Although Lanczos' thesis work on General
%%% Relativity was completed in 1919, it was not
%%% published until 1921 because of the political
%%% turmoil in Hungary after the collapse of the
%%% Austro-Hungarian Empire after World War I.
%%% At Lanczos' request of 3 December 1919,
%%% Albert Einstein read Lanczos' thesis, and on
%%% 22 January 1920, wrote to him that the work
%%% was worthy of a Ph.D. degree, and accepted
%%% Lanczos' request to dedicate his thesis to
%%% Einstein.
%%%
%%% Lanczos had a fellowship at the Budapest
%%% Institute of Technology until 1921, when he
%%% moved to Freiburg, Germany, then in 1924 to
%%% the University of Frankfurt, Germany.
%%%
%%% In 1924, Lanczos discovered an exact solution
%%% of the Einstein field equation for a
%%% symmetric rigidly-rotating cylinder of dust
%%% particles. At the recommendation of Leo
%%% Szil{\'a}rd, Lanczos moved to Berlin to serve
%%% as Albert Einstein's assistant in 1928--1929.
%%% No joint publications of Lanczos and Einstein
%%% came from that work, but the two remained
%%% friends, and exchanged letters for more than
%%% three decades, until Einstein's death in
%%% 1955.
%%%
%%% Lanczos left Hungary in 1931 for the USA,
%%% taking a temporary annual post at the
%%% Department of Mathematics, Purdue University,
%%% but spending the next several years split
%%% between Budapest and Purdue. At Purdue, he
%%% became Professor of Mathematical Physics, and
%%% by 1942, was also Professor in the
%%% Experimental Curriculum for Women, and
%%% Research Professor of Aeronautical
%%% Engineering.
%%%
%%% Lanczos briefly returned to Hungary in 1939
%%% to try to rescue family members, but
%%% fortunately managed to catch the last ship
%%% back to the US before World War II began in
%%% September 1939, and was soon back at Purdue
%%% University. He lost several family members
%%% in the Holocaust.
%%%
%%% In 1939--1942, Lanczos worked with Gordon
%%% Danielson at Purdue on the analysis of
%%% crystallographic X-ray diffraction data, and
%%% invented (prior to electronic computers) what
%%% later became famous as the Fast Fourier
%%% Transform. For more on the important history
%%% of that discovery, and its relation to
%%% Lanczos, and earlier work in France, Germany,
%%% and England extending back to 1759, see the
%%% bibliography of John Wilder Tukey in the file
%%% tukey-john-w.bib in this collection.
%%%
%%% Lanczos spent a year during 1943--1944 on
%%% leave from Purdue University, working on the
%%% Mathematical Tables Project at the National
%%% Bureau of Standards. That Project ultimately
%%% led to the famous Handbook of Mathematical
%%% Functions (NBS #55, 1964), edited by Milton
%%% Abramowitz and Irene Stegun. However,
%%% Lanczos is not listed in it as a chapter
%%% author.
%%%
%%% In 1944, and after World War II, from 1946 to
%%% 1948, Lanczos worked at Boeing Airplane
%%% Company, Seattle, Washington.
%%%
%%% In early 1949, Lanczos joined the Institute
%%% for Numerical Analysis (INA) of the US
%%% National Bureau of Standards, located on the
%%% campus of the University of California at Los
%%% Angeles, and remained there until 1952.
%%%
%%% Unfortunately, members of the INA were
%%% persecuted during the anti-communist
%%% witchhunts of the infamous McCarthy era
%%% during the early 1950s in the US.
%%% Consequently, in October 1952, Lanczos moved
%%% to Ireland, to succeed first, Walter Heitler,
%%% and later, Erwin Schr{\"o}dinger, at the
%%% Dublin Institute for Advanced Studies. He
%%% spent part of 1953--1954 back in the US at
%%% North American Aviation. Otherwise, he
%%% worked in Dublin until 1974, except for
%%% several excursions as visiting professor at
%%% several US universities and companies. His
%%% first permanent job was that in Dublin,
%%% obtained at the age of 61.
%%%
%%% Lanczos died in Budapest, Hungary, in 1974
%%% during a visit there, and is buried in that
%%% city in the Jewish cemetery of Farkasr{\'e}t.
%%%
%%% In 1993, in Sz{\'e}kesfeh{\'e}rv{\'a}r, a
%%% two-block street branching from the Neumann
%%% J{\'a}nos utca was named L{\'a}nczos
%%% Korn{\'e}l utca.
%%%
%%% There is a small photo gallery of pictures
%%% of Lanczos in his later years at
%%%
%%% http://www.maths.manchester.ac.uk/~higham/photos/lanczos/
%%%
%%% There is an archive of Lanczos papers,
%%% letters, and writing, with commentaries, at
%%%
%%% http://www.physics.ncsu.edu/lanczos/
%%%
%%% That site includes English translations of
%%% his works that were written in French,
%%% German, and Hungarian. It also includes 36
%%% years of letters between Lanczos and
%%% Einstein. The collected works prepared at
%%% that institution are documented in entry
%%% Davis:1998:CLC. That source contains an
%%% extensive list of Lanczos publications.
%%%
%%% 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
%%%
%%% * the Karlsruhe virtual catalog at
%%% http://www.ubka.uni-karlsruhe.de/kvk_en.html
%%%
%%% * the US Library of Congress catalog at
%%% http://catalog.loc.gov/
%%%
%%% * the author's cattobib utility, which
%%% provides Z39.50 interfaces to many
%%% large libraries around the world, at
%%% https://www.math.utah.edu/pub/cattobib/
%%%
%%% * the American Institute of Physics
%%% Scitation database at
%%% http://scitation.aip.org/search_scitation
%%%
%%% * the American Physical Society PROLA
%%% database at
%%% http://publish.aps.org/search
%%%
%%% * the American Mathematical Society
%%% MathSciNet database at
%%% http://ams.rice.edu/mathscinet/search.html
%%%
%%% * the Canadian Journal of Physics
%%% database at
%%% http://www.nrcresearchpress.com/search/advanced
%%%
%%% * the European Mathematical Society
%%% Zentralblatt fuer Mathematik database
%%% at http://zb.msri.org/ZMATH/zmath/en/
%%%
%%% * the Europhysics journal archive at
%%% http://www.europhysicsnews.org/
%%%
%%% * the JSTOR database at
%%% http://www.jstor.org/
%%%
%%% * the Nature journal archive at
%%% http://www.nature.com/search/
%%%
%%% * the journal archives of the National
%%% Academy of Science at
%%% http://www.pnas.org/
%%%
%%% * the SAO/NASA Astrophysics Data System at
%%% http://adsabs.harvard.edu/
%%%
%%% * the Science journal archive at
%%% http://www.sciencemag.org/search
%%%
%%% * the SPIRES high-energy physics
%%% literature database at the Stanford
%%% Linear Accelerator at Stanford
%%% University at
%%% http://www.slac.stanford.edu/spires/hep/search/
%%%
%%% * the Springer journal database at
%%% http://www.springer.com/?SGWID=0-102-13-0-0
%%%
%%% * the Wiley journal database at
%%% http://onlinelibrary.wiley.com/
%%%
%%% * many online library catalogs, including
%%% those of the British Library, the
%%% Karlsruhe Virtual Library catalog, the
%%% Oxford University Library, the University of
%%% California library system, and the US
%%% Library of Congress.
%%%
%%% 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{
"\let \k = \c" #
"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi" #
"\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}}\fi" #
"\ifx \undefined \mathbf \def \mathbf #1{{\bf #1}}\fi" #
"\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}} \fi"
}
%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
%%% ====================================================================
%%% Institution abbreviations:
@String{BCS = "Boeing Computer Services"}
@String{BCS:adr = "Seattle, WA, USA"}
@String{inst-CERFACS = "CERFACS"}
@String{inst-CERFACS:adr = "Toulouse, France"}
@String{inst-CPAM-UCB = "Center for Pure and Applied Mathematics,
University of California, Berkeley"}
@String{inst-CPAM-UCB:adr = "Berkeley, CA, USA"}
@String{inst-MCCM = "Manchester Centre for Computational
Mathematics"}
@String{inst-MCCM:adr = "Manchester, England"}
@String{inst-U-MARYLAND-CS = "Department of Computer Science,
University of Maryland"}
@String{inst-U-MARYLAND-CS:adr = "College Park, MD, 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-ADV-QUANTUM-CHEM = "Advances in quantum chemistry"}
@String{j-AM-SCI = "American Scientist"}
@String{j-AMER-J-PHYSICS = "American Journal of Physics"}
@String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"}
@String{j-ANN-MATH-2 = "Annals of Mathematics (2)"}
@String{j-ANN-PHYS-1900 = "Annalen der Physik (1900)"}
@String{j-ANN-PHYS-5 = "Annalen der Physik 5 (Berlin, Germany)"}
@String{j-APPL-MATH-COMP = "Applied Mathematics and Computation"}
@String{j-APPL-MATH-LETT = "Applied Mathematics Letters"}
@String{j-APPL-NUM-MATH = "Applied Numerical Mathematics"}
@String{j-ARCH-APPL-MECH = "Archive of Applied Mechanics =
Ingenieur-Archiv"}
@String{j-BIOMETRIKA = "Biometrika"}
@String{j-BIT = "BIT"}
@String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"}
@String{j-BULL-AMS = "Bulletin of the American Mathematical
Society"}
@String{j-BULL-INST-MATH-APPL = "Bulletin of the Institute of Mathematics and
its Applications"}
@String{j-CAH-PHYS = "Cahiers de Physique"}
@String{j-CAN-J-PHYS = "Canadian Journal of Physics = Journal
canadien de physique"}
@String{j-CHEM-PHYS-LETT = "Chemical Physics Letters"}
@String{j-COMM-NUMER-METHODS-ENGRG = "Communications in Numerical Methods in
Engineering"}
@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-AIDED-CIVIL-INFRASTRUCT-ENG = "Computer-Aided Civil and Infrastructure Engineering"}
@String{j-COMPUT-MATER-SCI = "Computational Materials Science"}
@String{j-COMPUT-MATH-APPL = "Computers and Mathematics with Applications"}
@String{j-COMPUT-METH-APPL-MECH-ENG = "Computer Methods in Applied Mechanics and
Engineering"}
@String{j-COMPUT-PHYS = "Computers in Physics"}
@String{j-COMPUTING = "Computing"}
@String{j-EARTHQUAKE-ENG-STRUCT-DYN = "Earthquake engineering \& structural
dynamics"}
@String{j-ELECTRON-COMMUN-JPN-PART-1-COMMUN = "Electronics and Communications in
Japan (Part I: Communications)"}
@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
Analysis"}
@String{j-ERGEB-EXAKTEN-NATURWISS = "Ergebnisse der Exakten
Naturwissenschaften"}
@String{j-EUROPHYS-NEWS = "Europhysics News"}
@String{j-FIZ-SZ = "Fizikai Szemle (Budapest)"}
@String{j-FOUND-PHYS = "Foundations of Physics"}
@String{j-GEN-RELATIVITY-GRAV = "General relativity and gravitation"}
@String{j-GEOPHYS-J-INT = "Geophysical journal international"}
@String{j-HIST-MATH = "Historia Mathematica"}
@String{j-IEEE-TRANS-KNOWL-DATA-ENG = "IEEE Transactions on Knowledge and Data
Engineering"}
@String{j-IJQC = "International Journal of Quantum Chemistry"}
@String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"}
@String{j-INT-J-NUMER-ANAL-METHODS-GEOMECH = "International Journal for
Numerical and Analytical Methods in
Geomechanics"}
@String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical
Methods in Engineering"}
@String{j-J-APPROX-THEORY = "Journal of Approximation Theory"}
@String{j-J-CHEM-PHYS = "Journal of Chemical Physics"}
@String{j-J-CHEMOM = "Journal of Chemometrics"}
@String{j-J-COMPUT-APPL-MATH = "Journal of Computational and Applied
Mathematics"}
@String{j-J-COMPUT-CHEM = "Journal of Computational Chemistry"}
@String{j-J-COMPUT-PHYS = "Journal of Computational Physics"}
@String{j-J-FRANKLIN-INST = "Journal of {The Franklin Institute}"}
@String{j-J-INST-ELECTR-ENG = "Journal of the Institution of Electrical
Engineers"}
@String{j-J-INST-MATH-APPL = "Journal of the Institute of Mathematics and
its Applications"}
@String{j-J-MATH-CHEM = "Journal of Mathematical Chemistry"}
@String{j-J-MATH-PHYS = "Journal of Mathematical Physics"}
@String{j-J-MATH-PHYS-MIT = "Journal of mathematics and physics /
Massachusetts Institute of Technology"}
@String{j-J-NUM-LIN-ALG-APPL = "Journal of Numerical linear algebra with
applications"}
@String{j-J-PAR-DIST-COMP = "Journal of Parallel and Distributed
Computing"}
@String{j-J-PHYS-C = "Journal of Physics C: Solid State Physics"}
@String{j-J-RES-NATL-BUR-STAND-1934 = "Journal of Research of the National
Bureau of Standards (1934)"}
@String{j-J-RES-NATL-BUR-STAND-1977 = "Journal of Research of the National
Bureau of Standards (1977)"}
@String{j-J-SCI-COMPUT = "Journal of Scientific Computing"}
@String{j-J-SIAM = "Journal of the Society for Industrial and
Applied Mathematics"}
@String{j-J-WASH-ACAD-SCI = "Journal of the Washington Academy of
Sciences"}
@String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"}
@String{j-LINEAR-ALGEBRA-APPL = "Linear Algebra and its Applications"}
@String{j-MAGN-MAGN-MATER = "Journal of Magnetism and Magnetic Materials"}
@String{j-MATH-ANN = "Mathematische Annalen"}
@String{j-MATH-COMPUT = "Mathematics of Computation"}
@String{j-MATH-GAZ = "Mathematical Gazette"}
@String{j-MATH-MAG = "Mathematics Magazine"}
@String{j-MATH-NACHR = "Mathematische Nachrichten"}
@String{j-MICROW-OPT-TECHNOL-LETT = "Microwave and Optical Technology Letters"}
@String{j-NASA-CONF-PUBL = "NASA conference publication"}
@String{j-NATURWISSENSCHAFTEN = "Naturwissenschaften"}
@String{j-NUCL-PHYS-A = "Nuclear Physics A"}
@String{j-NUCL-PHYS-B-PROC-SUPPL = "Nuclear Physics B, Proceedings Supplements"}
@String{j-NUM-LIN-ALG-APPL = "Numerical Linear Algebra with Applications"}
@String{j-NUM-MATH = "Numerische Mathematik"}
@String{j-NUMER-ALGORITHMS = "Numerical Algorithms"}
@String{j-NUMER-METHODS-PARTIAL-DIFFER-EQU = "Numerical Methods for Partial
Differential Equations"}
@String{j-NUOVO-CIMENTO-10 = "Il Nuovo Cimento (10)"}
@String{j-PAC-J-MATH = "Pacific Journal of Mathematics"}
@String{j-PAMM = "Proceedings in Applied Mathematics and
Mechanics"}
@String{j-PARALLEL-ALGORITHMS-APPL = "Parallel Algorithms and Applications"}
@String{j-PARALLEL-COMPUTING = "Parallel Computing"}
@String{j-PHYS-LET-A = "Physics Letters A"}
@String{j-PHYS-REV = "Physical Review"}
@String{j-PHYS-REV-2 = "Physical Review (2)"}
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%%% ====================================================================
%%% Series abbreviations:
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%%% ====================================================================
%%% Series abbreviations:
@String{ser-BOSTON-STUD-PHILOS-SCI = "Boston Studies in the Philosophy of
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%%% ====================================================================
%%% Part 1 (of 2): publications by Cornelius Lanczos
%%%
%%% Bibliography entries, sort by ascending year, and then by citation
%%% key with ``bibsort -byyear'.
%%%
%%% NB: See http://nektar1.oszk.hu/librivision_eng.html for an English
%%% interface into the Hungarian library catalog used to locate several
%%% entries in this bibliography.
@PhdThesis{Lanczos:1921:FBM,
author = "Cornelius Lanczos",
title = "{Die funktionentheoretischen Beziehungen der
Maxwellsche Aethergleichungen --- Ein Beitrag zur
Relativit{\"a}ts und Elektronentheorie}. ({German})
[{The} function-theoretical relationships of the
{Maxwellian} aether-equations --- {A} contribution to
the theory of relativity and electrons]",
type = "{Ph.D.} thesis",
school = "University of Szeged",
address = "Szeged, Hungary",
year = "1921",
bibdate = "Wed Jun 08 16:18:48 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Dedicated, with permission, to Albert Einstein.",
acknowledgement = ack-nhfb,
advisor = "Rudolf Ortvay",
keywords = "Relativity and gravitational theory",
language = "German",
}
@Article{Lanczos:1922:BSW,
author = "Kornel Lanczos",
title = "{Bemerkung zur de Sitterschen Welt} ({German})
[{Remark} on the {de Sitter} universe]",
journal = j-PHYSIKAL-Z,
volume = "23",
number = "24",
pages = "539--543",
day = "15",
month = dec,
year = "1922",
CODEN = "PHZTAO",
ISSN = "0369-982X",
bibdate = "Thu Jun 09 18:07:54 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://hdl.handle.net/2027/mdp.39015086723239?urlappend=%3Bseq=627",
acknowledgement = ack-nhfb,
fjournal = "Physikalische Zeitschrift",
journal-URL = "http://catalog.hathitrust.org/Record/000541302",
language = "German",
}
@Article{Lanczos:1922:VKE,
author = "Kornel Lanczos",
title = "{Ein vereinfchendes Koordinatensystem f{\"u}r die
Einsteinschen Gravitationsgleichungen} ({German}) [{A}
simplifying coordinate system for {Einstein}'s
equations of gravity]",
journal = j-PHYSIKAL-Z,
volume = "22",
number = "24",
pages = "537--539",
day = "15",
month = dec,
year = "1922",
CODEN = "PHZTAO",
ISSN = "0369-982X",
bibdate = "Thu Jun 09 18:05:37 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://hdl.handle.net/2027/mdp.39015086723239?urlappend=%3Bseq=625",
acknowledgement = ack-nhfb,
fjournal = "Physikalische Zeitschrift",
journal-URL = "http://catalog.hathitrust.org/Record/000541302",
language = "German",
}
@Article{Lancius:1923:TEG,
author = "Kornel Lancius",
title = "{Zur Theorie der Einsteinschen
Gravitationsgleichungen}. ({German}) [{On} the theory
of {Einstein}'s Gravitational Equations]",
journal = j-Z-PHYSIK,
volume = "13",
number = "1",
pages = "7--16",
month = "????",
year = "1923",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01328197",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:46:23 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Published with family name ``Lancius'' (for Lanczos),
possibly a typographical, or audio transcription,
error.",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1923:BTM,
author = "Kornel Lanczos",
title = "{Bemerkung zur Theorie der Merkurperihelverschiebung}.
({German}) [{Remark} on the perihelion advance of
{Mercury}]",
journal = j-NATURWISSENSCHAFTEN,
volume = "11",
number = "45",
pages = "910--911",
month = "????",
year = "1923",
CODEN = "NATWAY",
DOI = "https://doi.org/10.1007/BF01551516",
ISSN = "0028-1042 (print), 1432-1904 (electronic)",
ISSN-L = "0028-1042",
bibdate = "Wed Jun 08 17:42:18 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Naturwissenschaften",
journal-URL = "http://link.springer.com/journal/114",
language = "German",
}
@Article{Lanczos:1923:RAR,
author = "Kornel Lanczos",
title = "{Zum Rotationsproblem der allgemeinen
Relativit{\"a}tstheorie }. ({German}) [{On} the
rotation problem in the {Theory of General
Relativity}]",
journal = j-Z-PHYSIK,
volume = "14",
number = "1",
pages = "204--219",
month = "????",
year = "1923",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01340041",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:46:23 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1923:RSW,
author = "Kornel Lanczos",
title = "{{\"U}ber die Rotverschiebung in der de Sitterschen
Welt}. ({German}) [{On} the red shift in the {de
Sitter} universe]",
journal = j-Z-PHYSIK,
volume = "17",
number = "1",
pages = "168--189",
month = "????",
year = "1923",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01328677",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:26:52 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1924:FVM,
author = "Kornel Lanczos",
title = "{Fl{\"a}chenhafte Verteilung der Materie in der
Einsteinschen Gravitationstheorie}. ({German})
[{Surface} Distribution of Matter in {Einstein}'
{Theory of Gravity}]",
journal = j-ANN-PHYS-1900,
volume = "74",
number = "5",
pages = "518--540",
month = "????",
year = "1924",
DOI = "https://doi.org/10.1002/andp.19243791403",
ISSN = "1521-3889",
bibdate = "Thu Jun 09 14:09:51 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Annalen der Physik (1900)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-3889",
language = "German",
wiley-volume = "379",
}
@Article{Lanczos:1924:SKI,
author = "Kornel Lanczos",
title = "{{\"U}ber eine station{\"a}re Kosmologie im Sinne der
Einsteinischen Gravitationstheorie}. ({German}) [{On} a
stationary cosmology in the sense of {Einstein}'s
{Theory of Gravitation}]",
journal = j-Z-PHYSIK,
volume = "21",
number = "1",
pages = "73--110",
month = "????",
year = "1924",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01328251",
ISSN = "0044-3328",
bibdate = "Wed Jun 08 14:25:20 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "English translation in \cite{Lanczos:1997:SCS}.",
URL = "http://adsabs.harvard.edu/abs/1924ZPhy...21...73L",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lancius:1925:AVA,
author = "Kornel Lancius",
title = "{Zum Anwendung des Variationsprinzip in der
allgemeinen Relativit{\"a}tstheorie}. ({German}) [{On}
the application of a variational principle in {General
Relativity}]",
journal = "Acta Litt. Adac. Scient. Regiae Univ. Hung.
Francisco-Josephina",
volume = "1--2",
number = "??",
pages = "182--192",
month = "????",
year = "1925",
bibdate = "Thu Jun 09 18:12:25 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
language = "German",
}
@Article{Lanczos:1925:PAR,
author = "Kornel Lanczos",
title = "{Zum Problem der {\"A}therstrahlung in einer
r{\"a}umlich geschossenen Welt}. ({German}) [{On} the
Problem of Aether Radiation in a Spatially-Closed
Universe]",
journal = j-Z-PHYSIK,
volume = "32",
number = "1",
pages = "135--149",
month = "????",
year = "1925",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01331654",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 14:14:49 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1925:PUS,
author = "Kornel Lanczos",
title = "{Zum Problem der unendlich schwachen Felder in der
Einsteinschen Gravitationstheorie}. ({German}) [{On}
the problem of the infinitely weak fields in the
{Einstein} {Theory of Gravitation}]",
journal = j-Z-PHYSIK,
volume = "31",
number = "1",
pages = "112--132",
month = "????",
year = "1925",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF02980566",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:24:51 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1925:QUK,
author = "Kornel Lanczos",
title = "{{\"U}ber die quantentheoretische Umdeutung
kinematischer und meckanischer Beziehungen}. ({German})
[{Quantum}-theoretical Reinterpretation of Kinematics
and Mechanical Relations]",
journal = j-Z-PHYSIK,
volume = "33",
number = "12",
pages = "879--893",
day = "18",
month = sep,
year = "1925",
CODEN = "ZEPYAA",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 14:14:49 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1925:SEM,
author = "Kornel Lanczos",
title = "{Station{\"a}re Elektronenbahnen und die Methode der
Eigenfunktionen}. ({German}) [{Stationary} Electron
Trajectories and the Method of Eigenfunctions]",
journal = j-Z-PHYSIK,
volume = "33",
number = "1",
pages = "128--143",
month = "????",
year = "1925",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01328297",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 14:14:49 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1925:WAR,
author = "Kornel Lanczos",
title = "{Zum Wirkungsprinzip der allgemeinen
Relativit{\"a}tstheorie}. ({German}) [{On} the action
principle of the {Theory of General Relativity}]",
journal = j-Z-PHYSIK,
volume = "32",
number = "1",
pages = "163--172",
month = "????",
year = "1925",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01331657",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:37:02 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1925:ZPW,
author = "Kornel Lanczos",
title = "{{\"U}ber eine zeitlich periodische Welt und eine neue
Behandlung des Problems der {\"A}therstrahlung}.
({German}) [{On} a Universe Periodic in Time and a New
Treatment of the Problem of Aether Radiation]",
journal = j-Z-PHYSIK,
volume = "32",
number = "1",
pages = "56--80",
month = "????",
year = "1925",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01331648",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 14:12:15 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1926:FDN,
author = "Kornel Lanczos",
title = "{{\"U}ber eine feldm{\"a}{\ss}ige Darstellung der
neuen Quantenmechanik}. ({German}) [{On} a
Field-Theoretical Representation of the New Quantum
Mechanics]",
journal = j-Z-PHYSIK,
volume = "35",
number = "11--12",
pages = "812--830",
day = "26",
month = feb,
year = "1926",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01379857",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 14:14:49 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
received = "22 December 1925",
}
@Article{Lanczos:1926:KBQ,
author = "Kornel Lanczos",
title = "{{\"U}ber die komplexe Beschaffenheit der
quantenmechanischen Matrizen}. ({German}) [{On} the
complex nature of the matrices in quantum mechanics]",
journal = j-Z-PHYSIK,
volume = "37",
number = "6",
pages = "405--413",
month = "????",
year = "1926",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01397612",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:39:33 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1926:TIG,
author = "Kornel Lanczos",
title = "{{\"U}ber tensorielle Integralgleichungen}. ({German})
[{On} tensorial integral equations]",
journal = j-MATH-ANN,
volume = "95",
number = "1",
pages = "143--153",
year = "1926",
CODEN = "MAANA3",
DOI = "https://doi.org/10.1007/BF01206603",
ISSN = "0025-5831 (print), 1432-1807 (electronic)",
ISSN-L = "0025-5831",
bibdate = "Thu Jun 09 17:01:14 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Annalen",
journal-URL = "http://link.springer.com/journal/208",
keyword = "Mathematics and Statistics",
language = "German",
}
@Article{Lanczos:1926:VQN,
author = "Kornel Lanczos",
title = "{Variationsprinzip und Quantenbedingung in der neuen
Quantenmechanik}. ({German}) [{Variation} principle and
quantum conditions in the new quantum mechanics]",
journal = j-Z-PHYSIK,
volume = "36",
number = "6",
pages = "401--409",
month = "????",
year = "1926",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01382945",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:29:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1927:BAR,
author = "Kornel Lanczos",
title = "{Zum Bewegungsprinzip der allgemeinen
Relativit{\"a}tstheorie}. ({German}) [{On} the
Principle of Motion of the {Theory of General
Relativity}]",
journal = j-PHYSIKAL-Z,
volume = "28",
number = "??",
pages = "723--726",
month = "????",
year = "1927",
CODEN = "PHZTAO",
ISSN = "0369-982X",
bibdate = "Thu Jun 09 14:51:04 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Physikalische Zeitschrift",
journal-URL = "http://catalog.hathitrust.org/Record/000541302",
language = "German",
remark = "After this paper, Lanczos spelled his given name as
Cornel.",
}
@Article{Lanczos:1927:DAR,
author = "Kornel Lanczos",
title = "{Zur Dynamik der allgemeinen Relativit{\"a}tstheorie}.
({German}) [{On} the Dynamics of the {Theory of General
Relativity}]",
journal = j-Z-PHYSIK,
volume = "44",
number = "11--12",
pages = "773--792",
month = "????",
year = "1927",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01390854",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 14:51:04 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1929:EFD,
author = "Cornel Lanczos",
title = "{Die Erhaltungss{\"a}tze in der feldm{\"a}{\ss}igen
Darstellung der Diracschen Theorie}. ({German})
[{Conservation} laws in the field-theoretical
representation of {Dirac}'s theory]",
journal = j-Z-PHYSIK,
volume = "57",
number = "7--8",
pages = "484--493",
month = "????",
year = "1929",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01340276",
ISSN = "0044-3328",
bibdate = "Wed Jun 08 16:26:33 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1929:KFD,
author = "Cornel Lanczos",
title = "{Zur kovarianten Formulierung der Diracschen
Gleichung}. ({German}) [{On} a covariant formulation of
{Dirac}' Equation]",
journal = j-Z-PHYSIK,
volume = "57",
number = "7--8",
pages = "474--483",
month = "????",
year = "1929",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01340275",
ISSN = "0044-3328",
bibdate = "Wed Jun 08 16:27:56 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "JFM 55.0515.06",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1929:MEI,
author = "L{\'a}nczos{ }Korn{\'e}l",
title = "A megmarad{\'a}si elvek invari{\'a}ns fogalmaz{\'a}sa
az {\'a}ltal{\'a}nos relativit{\'a}si elm{\'e}letben.
({Hungarian}) [{An} Invariant formulation of the
conservation laws in the {Theory of General
Relativity}]",
journal = "A Magyar Tudom{\'a}nyos Akad{\'e}mia. III
Oszt{\'a}ly{\'a}nak K{\"o}zlem{\'e}nyei",
volume = "46",
number = "??",
pages = "554--575",
month = "????",
year = "1929",
bibdate = "Thu Jun 09 18:15:30 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
language = "Hungarian",
}
@Article{Lanczos:1929:TBD,
author = "Cornel Lanczos",
title = "{Die tensoranalytischen Beziehungen der Diracschen
Gleichung}. ({German}) [{The} tensor-analytical
relationships of {Dirac}'s Equation]",
journal = j-Z-PHYSIK,
volume = "57",
number = "7--8",
pages = "447--473",
month = "????",
year = "1929",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01340274",
ISSN = "0044-3328",
bibdate = "Wed Jun 08 16:29:27 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
remark = "Contains brief account of Lanczos's Ph.D. thesis
\cite{Lanczos:1921:FBM}.",
}
@Article{Lanczos:1930:DWT,
author = "Cornelius Lanczos",
title = "{Dirac's wellenmechanische Theorie des Elektrons und
ihre feldtheoretische Ausgestaltung}. ({German})
[{Dirac}'s wave-mechanical theory of the electron and
its field-theoretical interpretation]",
journal = j-PHYSIKAL-Z,
volume = "31",
number = "??",
pages = "120--130",
month = "????",
year = "1930",
CODEN = "PHZTAO",
ISSN = "0369-982X",
bibdate = "Wed Jun 08 16:36:37 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Physikalische Zeitschrift",
journal-URL = "http://catalog.hathitrust.org/Record/000541302",
language = "German",
}
@Article{Lanczos:1930:IFE,
author = "Cornel Lanczos",
title = "{{\"U}ber eine invariante Formulierung der
Erhaltungss{\"a}tze in der allgemeinen
Relativit{\"a}tstheorie}. ({German}) [{On} an invariant
formulation of the conservation laws in the {Theory of
General Relativity} ]",
journal = j-Z-PHYSIK,
volume = "59",
number = "7--8",
pages = "514--539",
month = "????",
year = "1930",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01336958",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:30:44 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1930:ISL,
author = "Cornel Lanczos",
title = "{Zur Intensit{\"a}tsanomalie der Starkeffekt-Linien in
sehr starken Feldern}. ({German}) [{On} the anomalous
intensity of the Stark-effect lines in very strong
fields]",
journal = j-NATURWISSENSCHAFTEN,
volume = "18",
number = "15",
pages = "329--330",
month = "????",
year = "1930",
CODEN = "NATWAY",
DOI = "https://doi.org/10.1007/BF01494973",
ISSN = "0028-1042 (print), 1432-1904 (electronic)",
ISSN-L = "0028-1042",
bibdate = "Wed Jun 08 16:35:38 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "JFM 56.0763.22",
acknowledgement = ack-nhfb,
fjournal = "Naturwissenschaften",
journal-URL = "http://link.springer.com/journal/114",
language = "German",
}
@Article{Lanczos:1930:TSH,
author = "Cornel Lanczos",
title = "{Zur Theorie des Starkeffekts in hohen Feldern}.
({German}) [{On} the theory of the {Stark} effect in
high fields]",
journal = j-Z-PHYSIK,
volume = "62",
number = "7--8",
pages = "518--544",
month = "????",
year = "1930",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01339678",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:34:54 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1930:VWH,
author = "C. Lanczos",
title = "{Zur Verschiebung der Wasserstoffterme in hohen
elektrischen Feldern}. ({German}) [{On} the shift of
the hydrogen terms in strong electrical fields]",
journal = j-Z-PHYSIK,
volume = "65",
number = "7--8",
pages = "431--455",
month = "????",
year = "1930",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01397042",
ISSN = "0044-3328",
bibdate = "Wed Jun 08 16:37:21 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "JFM 56.0749.04",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1931:EFN,
author = "Cornelius Lanczos",
title = "The electromagnetic field as a natural property of
{Riemannian} geometry",
journal = j-BULL-AMS,
volume = "37",
number = "??",
pages = "829--829",
month = "????",
year = "1931",
CODEN = "BAMOAD",
DOI = "https://doi.org/10.1063/1.1705286",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Wed Jun 08 16:42:22 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "JFM 57.1205.03",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Article{Lanczos:1931:ISH,
author = "Cornel Lanczos",
title = "{Zur Intensit{\"a}tsschw{\"a}chung der Spektrallinien
in hohen elektrischen Feldern}. ({German}) [{On}
intensity weakening of spectral lines in strong
electrical fields]",
journal = j-Z-PHYSIK,
volume = "68",
number = "3--4",
pages = "204--232",
month = "????",
year = "1931",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01390967",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:32:21 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1931:NFE,
author = "Cornel Lanczos",
title = "{Die neue Feldtheorie Einsteins}. ({German})
[{Einstein}'s new field theory]",
journal = j-ERGEB-EXAKTEN-NATURWISS,
volume = "10",
number = "??",
pages = "97--132",
month = "????",
year = "1931",
CODEN = "EENAA3",
ISSN = "0367-0325",
bibdate = "Wed Jun 08 16:43:12 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Ergebnisse der Exakten Naturwissenschaften",
language = "German",
}
@Article{Lanczos:1932:AVR,
author = "Cornel Lanczos",
title = "{Zum Auftreten des Vektorpotentials in der
Riemannschen Geometrie}. ({German}) [{on} the
appearance of the vector potential in {Riemannian}
geometry]",
journal = j-Z-PHYSIK,
volume = "75",
number = "1--2",
pages = "63--77",
month = "????",
year = "1932",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01340514",
ISSN = "0044-3328",
bibdate = "Wed Jun 08 16:34:07 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1932:EIS,
author = "Cornelius Lanczos",
title = "Ether --- Is It a Substance?",
journal = "The Purdue Engineer",
volume = "29",
number = "??",
pages = "87--102",
month = "????",
year = "1932",
bibdate = "Thu Jun 09 18:26:00 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1932:ENEa,
author = "Cornel Lanczos",
title = "{Elektromagnetismus als nat{\"u}rliche Eigenschaft der
Riemannschen Geometrie }. ({German})
[{Electromagnetism} as a natural property of {Riemann}
geometry]",
journal = j-Z-PHYSIK,
volume = "73",
number = "3--4",
pages = "147--168",
month = "????",
year = "1932",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01351210",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:41:29 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1932:ENEb,
author = "Cornelius Lanczos",
title = "Electricity as a natural element of {Riemannian}
geometry",
journal = j-PHYS-REV-2,
volume = "39",
number = "1",
pages = "188--188",
month = jan,
year = "1932",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.39.175",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
bibdate = "Wed Jun 08 16:34:45 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://prola.aps.org/abstract/PR/v39/i1/p175_1",
acknowledgement = ack-nhfb,
fjournal = "Physical Review (2)",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Lanczos:1932:ENP,
author = "Cornelius Lanczos",
title = "Electricity as a natural property of {Riemannian}
geometry",
journal = j-PHYS-REV-2,
volume = "39",
number = "4",
pages = "716--736",
month = feb,
year = "1932",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.39.716",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
bibdate = "Wed Jun 08 16:34:45 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRev.39.716",
acknowledgement = ack-nhfb,
fjournal = "Physical Review (2)",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Lanczos:1932:FRL,
author = "Cornel Lanczos",
title = "{Zur Frage der regul{\"a}ren L{\"o}sungen der
Einsteinschen Gravitationsgleichungen}. ({German})
[{On} the problem of the regular solutions of
{Einstein}'s equations of gravity]",
journal = j-ANN-PHYS-5,
volume = "13",
number = "5",
pages = "621--635",
month = "????",
year = "1932",
CODEN = "ANPYA2",
DOI = "https://doi.org/10.1002/andp.19324050506",
ISSN = "0003-3804 (print), 1521-3889 (electronic)",
bibdate = "Thu Jun 09 18:21:55 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Annalen der Physik 5 (Berlin, Germany)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-3889",
language = "German",
wiley-volume = "405",
}
@Article{Lanczos:1932:SRA,
author = "Cornel Lanczos",
title = "{Stellung der Relativit{\"a}tstheorie zu andern
physikalischen Theorien}. ({German}) [{The} position of
{Relativity Theory} to others physical theories]",
journal = j-NATURWISSENSCHAFTEN,
volume = "20",
number = "7",
pages = "113--116",
month = "????",
year = "1932",
CODEN = "NATWAY",
DOI = "https://doi.org/10.1007/BF01503458",
ISSN = "0028-1042 (print), 1432-1904 (electronic)",
ISSN-L = "0028-1042",
bibdate = "Wed Jun 08 16:32:54 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Naturwissenschaften",
journal-URL = "http://link.springer.com/journal/114",
language = "German",
}
@Article{Lanczos:1933:FCB,
author = "Cornelius Lanczos",
title = "A fundamental connection between {Hamiltonian}
dynamics and wave mechanics",
journal = j-PHYS-REV,
volume = "44",
number = "4",
pages = "318--318",
month = aug,
year = "1933",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.44.313",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
bibdate = "Mon Jun 20 14:54:37 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Abstract of talk.",
URL = "http://link.aps.org/doi/10.1103/PhysRev.44.313",
abstract = "Field equations which are deduced from a variational
principle can be considered in the function space to
represent the dynamical problem of a moving mass point.
The variational principle is the ``Hamiltonian
principle'' of this dynamics. The Lagrangian equations
of motion are equivalent to the given system of field
equations. Introducing instead of Lagrange's dynamics,
Hamilton's dynamics the canonical equations of motion
and canonical transformations are obtained: they are
equations of first order while the number of variables
is doubled. The possibility of canonical
transformations can be used for prescribing special
requirements that the Hamiltonian function shall
satisfy. We require that the canonical equations of
motion shall form a self-adjoint system of differential
equations. The 4 field equations of the vector
potential may then be written as 2 complex equations of
second order. The coordinated canonical equations of
motion in the Hamiltonian dynamics of the function
space result in a system of 4 complex equations of
first order: they are Dirac's equation of a free
electron.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Lanczos:1933:HDF,
author = "Cornel Lanczos",
title = "{Zur Hamiltonschen Dynamik des Funktionenraumes}.
({German}) [{On} the {Hamiltonian} dynamics of function
spaces]",
journal = j-Z-PHYSIK,
volume = "85",
number = "1--2",
pages = "107--127",
month = "????",
year = "1933",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01330781",
ISSN = "0044-3328",
bibdate = "Wed Jun 08 16:46:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1933:WHD,
author = "Cornel Lanczos",
title = "{Die Wellenmechanik als Hamiltonsche Dynamik des
funktionenraumes. Eine neue Ableitung der Diracschen
Gleichung}. ({German}) [{Wave} mechanics as the
{Hamiltonian} dynamics of the function space: a new
derivation of the {Dirac Equation}]",
journal = j-Z-PHYSIK,
volume = "81",
number = "11--12",
pages = "703--732",
month = "????",
year = "1933",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01342068",
ISSN = "0044-3328",
bibdate = "Wed Jun 08 16:47:13 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1934:NTL,
author = "Cornel Lanczos",
title = "{Eine neue Transformationstheorie linearer kanonischer
Gleichungen}. ({German}) [{A} new transformation theory
of linear canonical equations]",
journal = j-ANN-PHYS-5,
volume = "20",
number = "6",
pages = "653--688",
month = "????",
year = "1934",
CODEN = "ANPYA2",
DOI = "https://doi.org/10.1002/andp.19344120608",
ISSN = "0003-3804 (print), 1521-3889 (electronic)",
bibdate = "Wed Jun 08 16:49:07 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Annalen der Physik 5 (Berlin, Germany)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-3889",
language = "German",
wiley-volume = "412",
}
@Article{Lanczos:1934:NTT,
author = "Cornelius Lanczos",
title = "A new transformation theory of linear canonical
equations",
journal = j-PHYS-REV,
volume = "45",
number = "8",
pages = "560--560",
month = apr,
year = "1934",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.45.558",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
bibdate = "Thu Jun 09 18:27:14 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Abstract only.",
URL = "http://prola.aps.org/abstract/PR/v45/i8/p558_1",
acknowledgement = ack-nhfb,
fjournal = "Physical Review",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Lanczos:1935:NAM,
author = "Cornelius Lanczos",
title = "A new approximation method in solving linear
differential equations with non-oscillating
coefficients",
journal = j-BULL-AMS,
volume = "41",
number = "??",
pages = "183--185",
month = "????",
year = "1935",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Wed Jun 08 16:51:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Article{Lanczos:1935:NAW,
author = "Cornel Lanczos",
title = "{Ein neuer Aufbau der Weltgeometrie}. ({German}) [{A}
new formulation of world geometry]",
journal = j-Z-PHYSIK,
volume = "96",
number = "1--2",
pages = "76--106",
month = "????",
year = "1935",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01341506",
ISSN = "0044-3328",
bibdate = "Wed Jun 08 16:50:30 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Z. Phys.",
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Lanczos:1936:NAM,
author = "Cornelius Lanczos",
title = "A new approximation method in solving linear
differential equations with rational coefficients",
journal = j-BULL-AMS,
volume = "42",
number = "??",
pages = "30--30",
month = "????",
year = "1936",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Wed Jun 08 16:52:27 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "JFM 62.0645.14",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Article{Lanczos:1936:SRM,
author = "Cornelius Lanczos",
title = "A simple recursion method for solving a set of linear
equations",
journal = j-BULL-AMS,
volume = "42",
number = "??",
pages = "325--325",
month = "????",
year = "1936",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Wed Jun 08 16:52:27 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "JFM 62.0645.13",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Unpublished{Lanczos:1937:PAR,
author = "Cornelius Lanczos",
title = "The philosophical aspects of {Relativity}",
pages = "1--24",
year = "1937",
LCCN = "QC6 .L25 1937",
bibdate = "Thu Jun 09 18:28:42 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Two lectures delivered by invitation on March 2 and 4,
1937 in the course {\em Life Views of Great Men of
Science}, Philosophy 143b at Indiana University",
URL = "http://catalog.hathitrust.org/Record/000483261",
acknowledgement = ack-nhfb,
subject-dates = "Albert Einstein (1879--1955)",
}
@Article{Lanczos:1938:RPR,
author = "Cornelius Lanczos",
title = "A remarkable property of the {Riemann--Christoffel}
tensor in four dimensions",
journal = j-ANN-MATH-2,
volume = "39",
number = "4",
pages = "842--850",
year = "1938",
CODEN = "ANMAAH",
DOI = "https://doi.org/10.2307/1968467",
ISSN = "0003-486X (print), 1939-8980 (electronic)",
ISSN-L = "0003-486X",
MRclass = "Contributed Item",
MRnumber = "1503440",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "JFM 64.0767.03",
acknowledgement = ack-nhfb,
fjournal = "Annals of Mathematics. Second Series",
journal-URL = "http://www.jstor.org/action/showPublication?journalCode=annamath",
}
@Unpublished{Lanczos:1938:SIM,
author = "C. Lanczos",
title = "A simple interpolation method for the representation
of rugged curves",
month = nov,
year = "1938",
bibdate = "Sun Jun 19 16:04:16 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Abstract of contributed paper given at the November
Meeting of the AMS in Cleveland, OH, November 25 -26,
1938.",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1938:TIE,
author = "C. Lanczos",
title = "Trigonometric Interpolation of Empirical and
Analytical Functions",
journal = j-J-MATH-PHYS-MIT,
volume = "17",
number = "??",
pages = "123--199",
month = "????",
year = "1938",
CODEN = "JMPHA9",
ISSN = "0097-1421",
bibdate = "Wed Jun 8 17:01:15 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "Zbl 0020.01301",
acknowledgement = ack-nhfb,
fjournal = "Journal of mathematics and physics / Massachusetts
Institute of Technology",
remark = "This paper is the origin of the Lanczos {\em tau}
method (called the {\em telescoping method} by Lanczos
in later papers). According to the biography in
\cite[p. xxvii]{Brown:1994:PCL}, for some functions,
the method produced approximations a million times
better than traditional approaches. See, however,
remarks in
\cite{Coleman:1976:LTM,Hazewinkel:2002:EM}.",
}
@Article{Lanczos:1939:ATI,
author = "C. Lanczos and G. C. Danielson",
title = "Application of trigonometric interpolation to {X}-ray
analysis",
journal = j-PHYS-REV,
volume = "55",
number = "2",
pages = "242--242",
month = jan,
year = "1939",
CODEN = "PHRVAO",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
bibdate = "Thu Jun 09 18:30:33 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Abstract of talk.",
abstract = "The integral representing the intensity distribution
of x-ray [sic] diffraction in liquids can be evaluated
by the method of trigonometric interpolation instead of
approximating the integral by the sum of a large number
of terms. This reduces considerably the number of
ordinates required in the calculation without
decreasing the accuracy. As an example, the diffraction
patterns of vitreous selenium and liquid KCl and LiCI,
obtained and analyzed by K. Lark-Horovitz and E. P.
Miller, have been interpreted. For the curves so far
analyzed, 36 ordinates were found to be sufficient.
Owing to symmetry properties the Fourier coefficients
can be found with a minimum of calculation. This yields
directly the value of the distribution function in
discrete equidistant points. The value of the function
for any intermediate point may then be determined in a
simple manner by pure calculation. The resulting curves
agree very closely with those obtained by Lark-Horovitz
and Miller.",
acknowledgement = ack-nhfb,
fjournal = "Physical Review",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Lanczos:1941:DPG,
author = "C. Lanczos",
title = "The dynamics of a particle in {General Relativity}",
journal = j-PHYS-REV-2,
volume = "59",
number = "10",
pages = "813--819",
month = may,
year = "1941",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.59.813",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
MRclass = "70.1X",
MRnumber = "0004142 (2,326i)",
MRreviewer = "A. H. Taub",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
SAO/NASA Astrophysics Data System",
URL = "http://adsabs.harvard.edu/abs/1941PhRv...59..813L;
http://link.aps.org/doi/10.1103/PhysRev.59.813",
acknowledgement = ack-nhfb,
fjournal = "Physical Review (2)",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Lanczos:1941:TMP,
author = "Cornelius Lanczos",
title = "The total mass of a particle in {General Relativity}",
journal = j-PHYS-REV-2,
volume = "59",
number = "9",
pages = "708--716",
month = may,
year = "1941",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.59.708",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
bibdate = "Wed Jun 08 16:56:12 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRev.59.708",
ZMnumber = "Zbl 0025.12901",
acknowledgement = ack-nhfb,
fjournal = "Physical Review (2)",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Danielson:1942:SIPa,
author = "Gordon C. Danielson and Cornelius Lanczos",
title = "Some improvements in practical {Fourier} analysis and
their application to {X-ray} scattering from liquids",
journal = j-J-FRANKLIN-INST,
volume = "233",
number = "4",
pages = "365--380",
month = apr,
year = "1942",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/S0016-0032(42)90767-1",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "65.0X",
MRnumber = "0006233 (3,276f)",
MRreviewer = "W. Feller",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib",
acknowledgement = ack-nhfb,
author-dates = "Gordon C. Danielson (1912--1983); Cornelius Lanczos
(1893--1974)",
fjournal = "Journal of the Franklin Institute",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
keywords = "Fast Fourier Transform",
xxnumber = "??",
}
@Article{Danielson:1942:SIPb,
author = "Gordon C. Danielson and Cornelius Lanczos",
title = "Some improvements in practical {Fourier} analysis and
their application to {X-ray} scattering from liquids",
journal = j-J-FRANKLIN-INST,
volume = "233",
number = "5",
pages = "435--452",
month = may,
year = "1942",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/S0016-0032(42)90624-0",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
MRclass = "65.0X",
MRnumber = "0006233 (3,276f)",
MRreviewer = "W. Feller",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib",
acknowledgement = ack-nhfb,
author-dates = "Gordon C. Danielson (1912--1983); Cornelius Lanczos
(1893--1974)",
fjournal = "Journal of the Franklin Institute",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
keywords = "Fast Fourier Transform",
xxnumber = "??",
}
@Article{Lanczos:1942:DR,
author = "Cornelius Lanczos",
title = "{Dynamic Relativity}",
journal = "Main Currents in Modern Thought",
volume = "3",
number = "??",
pages = "4--7",
month = "????",
year = "1942",
CODEN = "????",
ISSN = "0025-0570",
LCCN = "AP2 .M252",
bibdate = "Mon Jun 20 15:00:01 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Unpublished{Lanczos:1942:HMP,
author = "Cornelius Lanczos",
title = "The History of Mathematics, Part 1, Prologue",
year = "1942",
bibdate = "Thu Jun 09 17:22:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Unpublished lecture notes, Purdue University Library,
West Lafayette, IN, 47907, USA, and D. H. Hill Library,
North Carolina State University, Raleigh, NC,
27695-8202, USA.",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1942:MWE,
author = "Cornelius Lanczos",
title = "Matter waves and electricity",
journal = j-PHYS-REV-2,
volume = "61",
number = "11--12",
pages = "713--720",
month = jun,
year = "1942",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.61.713",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
MRclass = "83.0X",
MRnumber = "0006883 (4,56e)",
MRreviewer = "A. H. Taub",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRev.61.713",
acknowledgement = ack-nhfb,
fjournal = "Physical Review (2)",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Article{Lanczos:1949:LMR,
author = "Cornelius Lanczos",
title = "{Lagrangian} multiplier and {Riemannian} spaces",
journal = j-REV-MOD-PHYS,
volume = "21",
number = "3",
pages = "497--502",
month = jul,
year = "1949",
CODEN = "RMPHAT",
DOI = "https://doi.org/10.1103/RevModPhys.21.497",
ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
ISSN-L = "0034-6861",
MRclass = "83.0X",
MRnumber = "0034136 (11,548c)",
MRreviewer = "M. Pinl",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.aps.org/doi/10.1103/RevModPhys.21.497",
acknowledgement = ack-nhfb,
fjournal = "Reviews of Modern Physics",
journal-URL = "http://rmp.aps.org/browse",
}
@Book{Lanczos:1949:VPM,
author = "Cornelius Lanczos",
title = "The Variational Principles of Mechanics",
volume = "4",
publisher = pub-U-TORONTO,
address = pub-U-TORONTO:adr,
pages = "xxv + 307",
year = "1949",
LCCN = "A805 .L25 1949",
MRclass = "71.0X",
MRnumber = "0034139 (11,549a)",
MRreviewer = "D. C. Lewis",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "Mathematical Expositions",
URL = "http://catalog.hathitrust.org/Record/000357344",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1950:IMS,
author = "Cornelius Lanczos",
title = "An iteration method for the solution of the eigenvalue
problem of linear differential and integral operators",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "45",
number = "4",
pages = "255--282",
month = oct,
year = "1950",
DOI = "https://doi.org/10.6028/jres.045.026",
ISSN = "0160-1741 (print), 2376-5259 (electronic)",
ISSN-L = "0160-1741",
MRclass = "65.0X",
MRnumber = "0042791 (13,163d)",
MRreviewer = "P. Funk",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "0067.33703",
abstract = "The present investigation designs a systematic method
for finding the latent roots and the principal axes of
a matrix, without reducing the order of the matrix. It
is characterized by a wide field of applicability and
great accuracy, since the accumulation of rounding
errors is avoided, through the process of ``minimized
iterations''. Moreover, the method leads to a well
convergent successive approximation procedure by which
the solution of integral equations of the Fredholm type
and the solution of the eigenvalue problem of linear
differential and integral operators may be
accomplished.",
acknowledgement = ack-nhfb,
ajournal = "J. Research Nat. Bur. Standards",
fjournal = "Journal of Research of the National Bureau of
Standards",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "This paper contains the Lanczos algorithm for
iterative computation of eigenvalues and eigenvectors,
sometimes called the {\em power method}; this algorithm
appears to be the most-widely cited of Lanczos's
works.",
}
@InProceedings{Lanczos:1951:IMSa,
author = "Cornelius Lanczos",
booktitle = "{Proceedings of a Second Symposium on Large-Scale
Digital Calculating Machinery, 1949}",
title = "An iteration method for the solution of the eigenvalue
problem of linear differential and integral operators",
publisher = pub-HARVARD,
address = pub-HARVARD:adr,
pages = "164--206",
year = "1951",
MRclass = "65.0X",
MRnumber = "0045470 (13,589e)",
MRreviewer = "P. Funk",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lanczos:1951:IMSb,
author = "Cornelius Lanczos",
booktitle = "{Proceedings of the Symposium on Spectral Theory and
Differential Problems (June 20--July 12, 1950)}",
title = "An iteration method for the solution of the eigenvalue
problem of linear differential and integral operators",
publisher = "Oklahoma Agricultural and Mechanical College",
address = "Stillwater, OK, USA",
pages = "301--316",
year = "1951",
MRclass = "65.0X",
MRnumber = "0044913 (13,497b)",
MRreviewer = "G. E. H. Reuter",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
xxpages = "301--323",
}
@Article{Rosser:1951:SCE,
author = "J. B. Rosser and C. Lanczos and M. R. Hestenes and W.
Karush",
title = "Separation of close eigenvalues of a real symmetric
matrix",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "47",
number = "4",
pages = "291--297",
month = oct,
year = "1951",
DOI = "https://doi.org/10.6028/jres.047.037",
ISSN = "0091-0635 (print), 2376-5305 (electronic)",
ISSN-L = "0091-0635",
MRclass = "65.0X",
MRnumber = "0048914 (14,92d)",
MRreviewer = "G. E. Forsythe",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Research Paper 2256.",
abstract = "In order to test two methods, one proposed by C.
Lanczos and the other by M. R. Hestenes and W. Karush,
for the numerical calculation of eigenvalues of
symmetric matrices, an 8 by 8 matrix is constructed
that has several sets of eigenvalues close together.
The application of the two methods to this test matrix
is described, and in addition, a third method for
dealing with such problems is proposed.",
acknowledgement = ack-nhfb,
author-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
}
@TechReport{Lanczos:1952:APC,
author = "Cornelius Lanczos",
title = "Analytical and practical curve fitting of equidistant
data",
type = "Report",
number = "1591",
institution = pub-NBS,
address = pub-NBS:adr,
pages = "1--102",
year = "1952",
bibdate = "Thu Jun 09 18:37:14 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Lanczos:1952:F,
author = "Cornelius Lanczos",
title = "Introduction",
crossref = "Anonymous:1952:TCP",
pages = "v--xxvi",
year = "1952",
bibdate = "Wed Jun 08 19:00:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Lanczos:1952:SND,
author = "Cornelius Lanczos",
title = "Smoothing of noisy data by trigonometric truncation",
type = "Report",
number = "1582",
institution = pub-NBS,
address = pub-NBS:adr,
pages = "16",
day = "9",
month = apr,
year = "1952",
bibdate = "Thu Jun 09 18:34:37 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1952:SSL,
author = "Cornelius Lanczos",
title = "Solution of systems of linear equations by
minimized-iterations",
journal = j-J-RES-NATL-BUR-STAND-1934,
volume = "49",
pages = "33--53",
year = "1952",
ISSN = "0091-0635",
MRclass = "65.0X",
MRnumber = "0051583 (14,501g)",
MRreviewer = "P. Funk",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "https://nvlpubs.nist.gov/nistpubs/jres/049/jresv49n1p33_A1b.pdf",
acknowledgement = ack-nhfb,
ajournal = "J. Research Nat. Bur. Standards",
fjournal = "Journal of Research of the National Bureau of
Standards (1934)",
journal-URL = "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
remark = "Submitted 28-Sep-1951, Los Angeles, CA, USA.",
}
@InProceedings{Lanczos:1953:CPS,
author = "Cornelius Lanczos",
booktitle = "{Proceedings of the Association for Computing
Machinery, Toronto, 1952}",
title = "{Chebyshev} polynomials in the solution of large-scale
linear systems",
publisher = "Sauls Lithograph Co. (for the Association for
Computing Machinery)",
address = "Washington, DC, USA",
pages = "124--133",
year = "1953",
MRclass = "65.0X",
MRnumber = "0067580 (16,751e)",
MRreviewer = "G. E. Forsythe",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1955:AET,
author = "C. Lanczos",
title = "{Albert Einstein} and the {Theory of Relativity}",
journal = j-NUOVO-CIMENTO-10,
volume = "2",
number = "Supplement 5",
pages = "1193--1220",
year = "1955",
CODEN = "NUCIAD",
DOI = "https://doi.org/10.1007/BF02748283",
ISSN = "0029-6341 (print), 1827-6121 (electronic)",
ISSN-L = "0029-6341",
MRclass = "01.0X",
MRnumber = "0076684 (17,931t)",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Il Nuovo Cimento (10)",
journal-URL = "http://link.springer.com/journal/11583",
}
@InProceedings{Lanczos:1955:IMS,
author = "C. Lanczos",
title = "An iteration method for the solution of the eigenvalue
problem of linear differential and integral operators",
crossref = "Anonymous:1955:PSS",
pages = "301--316",
year = "1955",
bibdate = "Wed Jun 8 17:00:44 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "0067.33703",
acknowledgement = ack-nhfb,
keywords = "{integral equations, integral transforms}",
}
@Article{Lanczos:1955:SEA,
author = "C. Lanczos",
title = "Spectroscopic eigenvalue analysis",
journal = j-J-WASH-ACAD-SCI,
volume = "45",
number = "10",
pages = "315--323",
month = oct,
year = "1955",
CODEN = "JWASA3",
ISSN = "0043-0439",
MRclass = "65.0X",
MRnumber = "0074934 (17,669b)",
MRreviewer = "E. Stiefel",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/24533653",
acknowledgement = ack-nhfb,
ajournal = "J. Washington Acad. Sci.",
fjournal = "Journal of the Washington Academy of Sciences",
journal-URL = "http://www.jstor.org/journal/jwashacadscie",
}
@Article{Lanczos:1955:SS,
author = "Cornelius Lanczos",
title = "Science and Society",
journal = "Icarus (Trinity College, Dublin)",
volume = "5",
number = "16",
pages = "31--37",
month = "????",
year = "1955",
bibdate = "Thu Jun 09 18:38:15 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1956:AA,
author = "Cornelius Lanczos",
title = "Applied Analysis",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xx + 539",
year = "1956",
ISBN = "0-486-65656-X",
ISBN-13 = "978-0-486-65656-4",
LCCN = "QA401 .L3 1988",
MRclass = "65.0X",
MRnumber = "0084175 (18,823c)",
MRreviewer = "F. B. Hildebrand",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Dedicated to the memory of the six million who died
for Kiddush Hashem. Reprinted by Dover, New York,
1988.",
URL = "http://catalog.hathitrust.org/Record/000617776;
http://hdl.handle.net/2027/mdp.39015016057468",
acknowledgement = ack-nhfb,
remark = "Chapter 3 discusses the Lanczos algorithms for solving
eigenvalue problems \cite{Lanczos:1950:IMS} and
linear-equation systems \cite{Lanczos:1952:SSL}. Pages
464--507 treat the Lanczos tau method for function
approximation.",
}
@Article{Lanczos:1957:EGR,
author = "Cornelius Lanczos",
title = "Electricity and {General Relativity}",
journal = j-REV-MOD-PHYS,
volume = "29",
number = "3",
pages = "337--350",
month = jul,
year = "1957",
CODEN = "RMPHAT",
DOI = "https://doi.org/10.1103/RevModPhys.29.337",
ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
ISSN-L = "0034-6861",
MRclass = "83.0X",
MRnumber = "0091193 (19,926e)",
MRreviewer = "J. L. Synge",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.aps.org/doi/10.1103/RevModPhys.29.337",
acknowledgement = ack-nhfb,
fjournal = "Reviews of Modern Physics",
journal-URL = "http://rmp.aps.org/browse",
}
@Article{Lanczos:1958:ERG,
author = "Cornelius Lanczos",
title = "Electricit{\'e} de relativit{\'e} g{\'e}n{\'e}rale.
({French}) [{Electricity} and {General Relativity}]",
journal = j-CAH-PHYS,
volume = "95",
number = "??",
pages = "247--255",
month = jul,
year = "1958",
CODEN = "CAPHAI",
ISSN = "0366-5291",
bibdate = "Thu Jun 09 18:42:40 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Cahiers de Physique",
language = "French",
}
@Article{Lanczos:1958:ISL,
author = "C. Lanczos",
title = "Iterative Solution of Large-Scale Linear Systems",
journal = j-J-SIAM,
volume = "6",
number = "1",
pages = "91--109",
month = mar,
year = "1958",
CODEN = "JSIMAV",
DOI = "https://doi.org/10.1137/0106006",
ISSN = "0368-4245 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
MRclass = "65.00",
MRnumber = "0093902 (20 \#422)",
MRreviewer = "M. Hestenes",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2098863",
ZMnumber = "Zbl 0085.3320",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
journal-URL = "http://epubs.siam.org/loi/smjmap.1",
}
@Article{Lanczos:1958:LSS,
author = "C. Lanczos",
title = "Linear Systems in Self-Adjoint Form",
journal = j-AMER-MATH-MONTHLY,
volume = "65",
number = "9",
pages = "665--679",
month = nov,
year = "1958",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "15.00",
MRnumber = "0103196 (21 \#1978)",
MRreviewer = "H. F. Weinberger",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2308707",
ZMnumber = "Zbl 0083.00604",
acknowledgement = ack-nhfb,
fjournal = "The American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@TechReport{Lanczos:1958:RCC,
author = "Cornelius Lanczos",
title = "Remarks concerning the canonical formulation of field
equations",
type = "Report",
institution = "Facult{\'e} des Sciences de Paris, S{\'e}minaire
Janet. M{\'e}canique analytique et m{\'e}canique
c{\'e}leste, tome 1, Ann{\'e}e 1957--1958",
address = "Paris, France",
pages = "1--14",
day = "17",
month = may,
year = "1958",
bibdate = "Thu Jun 09 18:40:58 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://archive.numdam.org/ARCHIVE/SJ/SJ_1957-1958__1_/SJ_1957-1958__1__A8_0/SJ_1957-1958__1__A8_0.pdf",
acknowledgement = ack-nhfb,
}
@InCollection{Lanczos:1958:TC,
author = "Cornelius Lanczos",
editor = "E. U. Condon",
booktitle = "Handbook of Physics",
title = "Tensor Calculus",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "I-140--I-151",
year = "1958",
LCCN = "????",
bibdate = "Thu Jun 09 18:44:19 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Part I, Chapter 10.",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1959:AER,
author = "Cornelius Lanczos",
title = "{Albert Einstein} and the role of theory in
contemporary physics",
journal = j-AM-SCI,
volume = "47",
number = "??",
pages = "41--59",
month = mar,
year = "1959",
CODEN = "AMSCAC",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Thu Jun 09 18:45:56 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "American Scientist",
journal-URL = "http://www.americanscientist.org/issues/past.aspx",
}
@InCollection{Lanczos:1960:EBV,
author = "C. Lanczos",
booktitle = "Proceedings of the International Congress of
Mathematicians, Edinburgh (14--21 August, 1958)",
title = "Extended boundary value problems",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "154--181",
year = "1960",
MRclass = "35.00",
MRnumber = "0118944 (22 \#9713)",
MRreviewer = "L. E. Payne",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "Zbl 0119.33501",
acknowledgement = ack-nhfb,
}
@InCollection{Lanczos:1960:SOD,
author = "C. Lanczos",
booktitle = "Symposium on the numerical treatment of ordinary
differential equations, integral and
integro-differential equations ({Rome}, 1960)",
title = "Solution of ordinary differential equations by
trigonometric interpolation",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "22--32",
year = "1960",
MRclass = "65.61",
MRnumber = "0145667 (26 \#3196)",
MRreviewer = "P. Henrici",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "Zbl 0107.33403",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1961:AA,
author = "Cornelius Lanczos",
title = "Applied Analysis",
publisher = pub-PH,
address = pub-PH:adr,
pages = "xx + 539",
year = "1961",
LCCN = "????",
bibdate = "Wed Jun 08 17:08:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Dedicated to the memory of the six million who died
for Kiddush Hashem.",
URL = "http://babel.hathitrust.org/cgi/pt?id=mdp.39015016057468",
ZMnumber = "Zbl 0111.12403",
acknowledgement = ack-nhfb,
remark = "Chapter 3 discusses the Lanczos algorithms for solving
eigenvalue problems \cite{Lanczos:1950:IMS} and
linear-equation systems \cite{Lanczos:1952:SSL}. Pages
464--507 treat the Lanczos tau method for function
approximation.",
}
@Book{Lanczos:1961:LDO,
author = "Cornelius Lanczos",
title = "Linear differential operators",
publisher = "D. Van Nostrand Co. Ltd.",
address = "London, UK / Toronto, ON, Canada / New York, NY, USA /
Princeton, NJ, USA",
pages = "xvi + 564",
year = "1961",
MRclass = "34.00 (47.60)",
MRnumber = "0129153 (23 \#B2190)",
MRreviewer = "P. Roman",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://catalog.hathitrust.org/Record/000621357",
ZMnumber = "Zbl 0111.08305",
acknowledgement = ack-nhfb,
}
@InCollection{Lanczos:1961:MLG,
author = "C. Lanczos",
booktitle = "Colloques sur l'analyse num{\'e}rique ({Mons}, 1961)",
title = "{M}{\'e}thodes locales et globales pour
l'int{\'e}gration des probl{\`e}mes de trajectories",
publisher = "Librairie Universitaire",
address = "Louvain, Belgium",
pages = "37--49",
year = "1961",
MRclass = "65.61",
MRnumber = "0152127 (27 \#2107)",
MRreviewer = "E. Leimanis",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Centre Belge de Recherches Math{\'e}matiques",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1961:PMP,
author = "Cornelius Lanczos",
title = "Prakti{\c{c}}eskije metody prikladnogo analiza:
Spravo{\v{c}}noje rukovodstvo. ({Russian}) [{Practical}
Methods in Applied Analysis]",
publisher = "Fizmatgiz",
address = "Moscow, USSR",
pages = "524",
year = "1961",
LCCN = "????",
bibdate = "Wed Jun 08 18:39:30 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Translated from the English by M. Z. Kajnera, and
edited by A. M. Lop{\v{s}}ica.",
acknowledgement = ack-nhfb,
language = "Russian",
}
@InCollection{Lanczos:1962:IAC,
author = "C. Lanczos",
title = "An integral approach to the calculus of variations",
crossref = "Szego:1962:SMA",
pages = "191--198",
year = "1962",
MRclass = "49.00",
MRnumber = "0147933 (26 \#5445)",
MRreviewer = "M. R. Hestenes",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "Zbl 0112.06301",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1962:IGF,
author = "Cornelius Lanczos",
title = "Int{\'e}gration globale. ({French}) [{Global}
integration]",
journal = "Annales de la Facult{\'e} des sciences de
l'universit{\'e} de {Clermont}, Actes Coll. Math.
Tricent. mort {B. Pascal}",
volume = "2",
number = "??",
pages = "97--107",
month = "????",
year = "1962",
bibdate = "Fri Jun 10 06:25:28 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://archive.numdam.org/ARCHIVE/ASCFM/ASCFM_1962__8_2/ASCFM_1962__8_2_97_0/ASCFM_1962__8_2_97_0.pdf",
acknowledgement = ack-nhfb,
ajournal = "Ann. Fac. Sci. Univ. {Clermont}, Actes Coll. Math.
Tricent. mort {B. Pascal}",
language = "French",
}
@InCollection{Lanczos:1962:SPR,
author = "C. Lanczos",
title = "Some properties of the {Riemann--Christoffel}
curvature tensor",
crossref = "Anonymous:1962:RDG",
pages = "313--321",
year = "1962",
MRclass = "83.53 (53.70)",
MRnumber = "0164703 (29 \#1999)",
MRreviewer = "F. A. E. Pirani",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
SAO/NASA Astrophysics Data System",
URL = "http://adsabs.harvard.edu/abs/1962rdgr.book..313L",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1962:SRT,
author = "C. Lanczos",
title = "The splitting of the {Riemann} tensor",
journal = j-REV-MOD-PHYS,
volume = "34",
number = "3",
pages = "379--389",
month = jul,
year = "1962",
CODEN = "RMPHAT",
DOI = "https://doi.org/10.1103/RevModPhys.34.379",
ISSN = "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
ISSN-L = "0034-6861",
MRclass = "53.35 (53.70)",
MRnumber = "0140360 (25 \#3782)",
MRreviewer = "H. A. Buchdahl",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://adsabs.harvard.edu/abs/1962RvMP...34..379L;
http://link.aps.org/doi/10.1103/RevModPhys.34.379",
ZMnumber = "Zbl 0106.41701",
acknowledgement = ack-nhfb,
fjournal = "Reviews of Modern Physics",
journal-URL = "http://rmp.aps.org/browse",
}
@Article{Lanczos:1962:TRQ,
author = "C. Lanczos",
title = "Le tenseur de {Riemann} {\`a} quatre dimensions.
({With} discussion)",
journal = "Annales de la Facult{\'e} des Sciences de
l'Universit{\'e} de Clermont-Ferrand",
volume = "8",
number = "2",
pages = "167--170",
month = "????",
year = "1962",
MRclass = "53.35 (83.00)",
MRnumber = "0283711 (44 \#941)",
MRreviewer = "W. B. Bonnor",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.numdam.org/item?id=ASCFM_1962__8_2_167_0",
acknowledgement = ack-nhfb,
ajournal = "Ann. Fac. Sci. Univ. Clermont-Ferrand No.",
}
@Book{Lanczos:1962:VPM,
author = "Cornelius Lanczos",
title = "The variational principles of mechanics",
volume = "4",
publisher = pub-U-TORONTO,
address = pub-U-TORONTO:adr,
edition = "Second",
pages = "xxv + 367",
year = "1962",
LCCN = "QA805 .L25 1962",
MRclass = "70.00",
MRnumber = "0166957 (29 \#4230)",
MRreviewer = "H. Saunders",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "Mathematical Expositions",
URL = "http://catalog.hathitrust.org/Record/000357368",
ZMnumber = "Zbl 0138.19705",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1963:MPP,
author = "Cornelius Lanczos",
title = "Modern physics in perspective",
journal = "Studies: An {Irish} Quarterly Review ({Dublin})",
volume = "52",
number = "207",
pages = "283--293",
month = "Fall",
year = "1963",
ISSN = "0039-3495",
bibdate = "Fri Jun 10 06:31:17 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/30088788",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1963:URS,
author = "C. Lanczos",
title = "Undulatory {Riemannian} spaces",
journal = j-J-MATH-PHYS,
volume = "4",
number = "7",
pages = "951--959",
month = jul,
year = "1963",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1704021",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "53.78 (83.00)",
MRnumber = "0152350 (27 \#2330)",
MRreviewer = "A. H. Taub",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "Zbl 0118.23104",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Lanczos:1964:END,
author = "C. Lanczos",
title = "Evaluation of Noisy Data",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "1",
number = "??",
pages = "76--85",
month = "????",
year = "1964",
DOI = "https://doi.org/10.1137/0701007",
ISSN = "0887-459X (print), 1095-7170 (electronic)",
ISSN-L = "0887-459X",
MRclass = "65.90",
MRnumber = "0179909 (31 \#4146)",
MRreviewer = "W. J. Kotz{\'e}",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2949766",
ZMnumber = "Zbl 0142.12504",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics: Series B, Numerical Analysis",
journal-URL = "http://epubs.siam.org/loi/sjnaam.1",
}
@Article{Lanczos:1964:I,
author = "Cornelius Lanczos",
title = "Introduction",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "1",
number = "??",
pages = "1--1",
month = "????",
year = "1964",
DOI = "https://doi.org/10.1137/0701intro1",
ISSN = "0887-459X (print), 1095-7170 (electronic)",
ISSN-L = "0887-459X",
bibdate = "Wed Jun 08 18:21:14 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/2949759",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics: Series B, Numerical Analysis",
journal-URL = "http://epubs.siam.org/loi/sjnaam.1",
remark = "The article begins ``With this issue, SIAM initiates a
new series of its Journal devoted to the field of
Numerical Analysis in its broader connotations.",
}
@Article{Lanczos:1964:IGH,
author = "Cornelius Lanczos",
title = "The Inspired Guess in the History of Physics",
journal = "Studies: An {Irish} Quarterly Review ({Dublin})",
volume = "53",
number = "212",
pages = "398--412",
month = "Winter",
year = "1964",
ISSN = "0039-3495",
bibdate = "Thu Jun 09 17:50:45 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/30087796",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1964:LDO,
author = "Cornelius Lanczos",
title = "Linear Differential Operators",
publisher = "Van Nostrand",
address = "London, UK",
pages = "564",
year = "1964",
LCCN = "????",
bibdate = "Wed Jun 08 18:38:25 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1964:MPP,
author = "Cornelius Lanczos",
title = "Modern Physics in Perspective",
journal = "Studies: An {Irish} Quarterly Review ({Dublin})",
volume = "52",
number = "207",
pages = "283--293",
month = "Autumn",
year = "1964",
ISSN = "0039-3495",
bibdate = "Thu Jun 09 17:50:45 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/30088788",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1964:PAG,
author = "Cornelius Lanczos",
title = "A Precision Approximation of the Gamma Function",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "1",
number = "1",
pages = "86--96",
month = "????",
year = "1964",
DOI = "https://doi.org/10.1137/0701008",
ISSN = "0887-459X (print), 1095-7170 (electronic)",
ISSN-L = "0887-459X",
MRclass = "33.15",
MRnumber = "0176115 (31 \#390)",
MRreviewer = "S. C. van Veen",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2949767",
ZMnumber = "Zbl 0136.05201",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics: Series B, Numerical Analysis",
journal-URL = "http://epubs.siam.org/loi/sjnaam.1",
}
@Article{Lanczos:1964:SPP,
author = "Cornelius Lanczos",
title = "Signal propagation in a positive definite {Riemannian}
space",
journal = j-PHYS-REV-2,
volume = "134B",
number = "2",
pages = "476--480",
month = apr,
year = "1964",
CODEN = "PHRVAO",
DOI = "https://doi.org/10.1103/PhysRev.134.B476",
ISSN = "0031-899X (print), 1536-6065 (electronic)",
ISSN-L = "0031-899X",
MRclass = "83.53",
MRnumber = "0162611 (28 \#5809)",
MRreviewer = "H. Rund",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRev.134.B476",
ZMnumber = "Zbl 0116.44302",
acknowledgement = ack-nhfb,
fjournal = "Physical Review (2)",
journal-URL = "http://prola.aps.org/browse/PR",
}
@Book{Lanczos:1964:VPM,
author = "Cornelius Lanczos",
title = "The variational principles of mechanics",
volume = "4",
publisher = pub-U-TORONTO,
address = pub-U-TORONTO:adr,
edition = "Second",
pages = "xxv + 367",
year = "1964",
LCCN = "QA805 .L25 1964",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "Mathematical Expositions",
URL = "http://catalog.hathitrust.org/Record/000357368",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1965:AEC,
author = "Cornelius Lanczos",
title = "{Albert Einstein} and the cosmic world order: six
lectures delivered at the {University of Michigan} in
the {Spring} of 1962",
publisher = pub-INTERSCIENCE,
address = pub-INTERSCIENCE:adr,
pages = "vi + 139",
year = "1965",
LCCN = "QC 16 .E35 L252 1965",
MRclass = "00.50 (83.00)",
MRnumber = "0171673 (30 \#1902)",
MRreviewer = "N. L. Balazs",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib",
URL = "http://catalog.hathitrust.org/Record/001477802",
acknowledgement = ack-nhfb,
subject-dates = "1879--1955",
}
@Book{Lanczos:1965:VPM,
author = "Cornelius Lanczos",
title = "Variacionnyje principy mechaniki. ({Russian}) [{The}
variational principles of mechanics]",
publisher = pub-MIR,
address = pub-MIR:adr,
pages = "408",
year = "1965",
LCCN = "????",
bibdate = "Wed Jun 08 18:42:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Lanczos:1966:BVP,
author = "C. Lanczos",
title = "Boundary Value Problems and Orthogonal Expansions",
journal = j-SIAM-J-APPL-MATH,
volume = "14",
number = "4",
pages = "831--863",
month = jul,
year = "1966",
CODEN = "SMJMAP",
DOI = "https://doi.org/10.1137/0114070",
ISSN = "0036-1399 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
MRclass = "31.20",
MRnumber = "0208008 (34 \#7819)",
MRreviewer = "R. P. Srivastav",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2946140",
ZMnumber = "Zbl 0147.09702",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Applied Mathematics",
journal-URL = "http://epubs.siam.org/siap",
remark = "The article begins with a large photograph of Richard
Courant.",
}
@Book{Lanczos:1966:DFSa,
author = "Cornelius Lanczos",
title = "Discourse on {Fourier} series",
publisher = "Oliver \& Boyd",
address = "Edinburgh, UK / London, UK",
pages = "viii + 255",
year = "1966",
MRclass = "42.00",
MRnumber = "0199629 (33 \#7772)",
MRreviewer = "F. C. Hsiang",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "University mathematical monographs",
URL = "http://catalog.hathitrust.org/Record/000620782",
ZMnumber = "Zbl 0163.07601",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1966:DFSb,
author = "Cornelius Lanczos",
title = "Discourse on {Fourier} series",
publisher = "Hafner Publishing Co.",
address = "New York, NY, USA",
pages = "viii + 255",
year = "1966",
MRclass = "42.00",
MRnumber = "0199629 (33 \#7772)",
MRreviewer = "F. C. Hsiang",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "Zbl 0163.07601",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1966:MLP,
author = "C. Lanczos",
title = "Metrical lattice and the problem of electricity",
journal = j-J-MATH-PHYS,
volume = "7",
number = "2",
pages = "316--324",
month = feb,
year = "1966",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1704935",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "83.53",
MRnumber = "0191597 (32 \#9002)",
MRreviewer = "P. G. Bergmann",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "J. Mathematical Phys.",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@InProceedings{Lanczos:1966:TFD,
author = "Cornelius Lanczos",
title = "{Tetraden-Formalismus und definite
Raum--Zeit-Struktur}. ({German}) [{Tetrad} formalism
and definite space--time structure]",
crossref = "Treder:1966:ESE",
pages = "38--56",
year = "1966",
bibdate = "Fri Jun 10 06:36:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
language = "German",
xxbooktitle = "{Entstehung, Entwicklung und Perspektiven der
Einsteinschen Gravitationstheorie, Deutsche Akademie
der Wissenschaften, November 2--5, 1965} [{Emergence},
development and perspectives of the {Einstein Theory of
Gravitation}]",
}
@Book{Lanczos:1966:VPM,
author = "Cornelius Lanczos",
title = "The variational principles of mechanics",
publisher = pub-U-TORONTO,
address = pub-U-TORONTO:adr,
edition = "Third",
pages = "xxv + 375",
year = "1966",
LCCN = "QA805 .L278 1966",
MRclass = "69.00",
MRnumber = "0431821 (55 \#4815)",
bibdate = "Sat Jun 11 15:46:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "Mathematical Expositions, No. 4",
URL = "http://catalog.hathitrust.org/Record/004452275",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1967:AEP,
author = "Cornelius Lanczos",
title = "{Albert Einstein} i porz{\k{a}}dek wszech{\'s}wiata",
volume = "92",
publisher = "Pa{\'n}stwowe Wydawnictwo Naukowe",
address = "Warszawa, Poland",
pages = "146 + 4",
year = "1967",
LCCN = "????",
bibdate = "Wed Jun 08 18:46:11 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Translated from English to Polish by Barbara
Stanosz.",
series = "Omega: wsp{\'o}{\l}czesna biblioteka naukowa",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1967:AES,
author = "Cornelius Lanczos",
title = "{Albert Einshtein} i stroenie kosmosa: Shest lektsii,
Prochitannykh vesnoi 1962 {G}. v {Michiganskom}
universitete. ({Russian}) [{Albert Einstein} and the
cosmic world order: six lectures delivered at the
{University of Michigan} in the {Spring} of 1962]",
publisher = pub-NAUKA,
address = pub-NAUKA:adr,
pages = "156",
year = "1967",
LCCN = "????",
bibdate = "Wed Jun 08 19:01:37 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Translated from English to Russian by V. A. Ugarova.",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Lanczos:1967:BRM,
author = "Cornelius Lanczos",
title = "Book Review: {{\em The Mathematical Papers of Sir
William Rowna Hamilton: Volume III, Algebra}, edited by
H. Halberstam and R. E. Ingram, London: Cambridge
University Press 1967. pp 672}",
journal = "Studies: An {Irish} Quarterly Review ({Dublin})",
volume = "56",
number = "224",
pages = "423--425",
month = "Winter",
year = "1967",
ISSN = "0039-3495",
bibdate = "Sun Jun 19 16:17:27 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/30087259",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1967:CCV,
author = "Cornelius Lanczos",
title = "Che cosa ha veramente detto {Einstein}?. ({Italian})
[{What} did {Einstein} really say?]",
publisher = "Ubaldini",
address = "Rome, Italy",
pages = "154",
year = "1967",
LCCN = "????",
bibdate = "Wed Jun 08 19:06:15 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
language = "Italian",
}
@Article{Lanczos:1967:EEE,
author = "Cornelius Lanczos",
title = "{Einstein} equations and electromagnetism",
journal = j-J-MATH-PHYS,
volume = "8",
number = "4",
pages = "829--836",
month = apr,
year = "1967",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1705286",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Jun 10 06:51:48 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@InProceedings{Lanczos:1967:RPW,
author = "Cornelius Lanczos",
title = "Rationalism and the physical world",
crossref = "Cohen:1967:PBC",
pages = "181--198",
year = "1967",
bibdate = "Fri Jun 10 06:44:04 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1967:WM,
author = "Cornelius Lanczos",
title = "Why Mathematics?",
journal = "{Irish Mathematical Teachers Association} Newsletter",
volume = "9",
number = "??",
pages = "3--??",
month = "????",
year = "1967",
bibdate = "Thu Jun 09 14:07:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
xxpages = "1--5",
}
@Article{Lanczos:1967:WRHa,
author = "Cornelius Lanczos",
title = "{William Rowan Hamilton}, an appreciation",
journal = j-AM-SCI,
volume = "55",
number = "??",
pages = "129--143",
month = "????",
year = "1967",
CODEN = "AMSCAC",
ISSN = "0003-0996 (print), 1545-2786 (electronic)",
ISSN-L = "0003-0996",
bibdate = "Fri Jun 10 06:50:30 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "American Scientist",
journal-URL = "http://www.americanscientist.org/issues/past.aspx",
}
@Article{Lanczos:1967:WRHb,
author = "Cornelius Lanczos",
title = "{William Rowan Hamilton}, an appreciation",
journal = "University Review",
volume = "4",
number = "2",
pages = "151--166",
month = "Summer",
year = "1967",
CODEN = "????",
ISSN = "0566-2478",
bibdate = "Sun Jun 19 15:57:50 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/25504779",
acknowledgement = ack-nhfb,
}
@InCollection{Lanczos:1968:BVP,
author = "C. Lanczos",
booktitle = "Programmation en Math{\'e}matiques Num{\'e}riques
(Actes Colloq. Internat. C.N.R.S. No. 165,
Besan{\c{c}}on, 1966)",
title = "Boundary value problems and the algebraic method",
publisher = "{\'E}ditions Centre Nat. Recherche Sci., Paris",
pages = "205--215",
year = "1968",
MRclass = "65.65",
MRnumber = "0231547 (37 \#7100)",
MRreviewer = "R. Nicolovius",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "Zbl 0212.17902",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1968:NE,
author = "Cornelius Lanczos",
title = "Numbers without end",
volume = "22",
publisher = "Oliver and Boyd",
address = "Edinburgh, Scotland",
pages = "x + 164",
year = "1968",
LCCN = "QA9 L35; 1875",
bibdate = "Wed Jun 8 18:31:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
library.ox.ac.uk:210/ADVANCE",
series = "Contemporary science paperbacks",
URL = "http://catalog.hathitrust.org/Record/009325177",
acknowledgement = ack-nhfb,
author-dates = "1893--1974",
subject = "Number concept; Numerals",
}
@InProceedings{Lanczos:1968:QRI,
author = "Cornelius Lanczos",
booktitle = "{Coll. Inter. Centre Nat. Rech. Sci., No. 165:
Programmation en math{\'e}matique num{\'e}rique,
Besan{\c{c}}on (7--14 septembre, 1966)}",
title = "Quelques remarques en introduction. ({French}) [{Some}
Introductory Remarks]",
publisher = "{\'E}ditions du Centre National de la Recherche",
address = "Paris, France",
pages = "21--23",
year = "1968",
LCCN = "????",
bibdate = "Fri Jun 10 06:53:43 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
language = "French",
remark = "Find remaining publications in Lanczos bibliography in
\cite{Brown:1994:PCL}.",
}
@Article{Lanczos:1969:QAP,
author = "C. Lanczos",
title = "Quadratic action principle of relativity",
journal = j-J-MATH-PHYS,
volume = "10",
number = "6",
pages = "1057--1064",
month = jun,
year = "1969",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1664934",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Jan 2 14:59:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
classification = "A0420 (General relativity)",
corpsource = "Dublin Inst. for Advanced Studies, Ireland",
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
keywords = "General Relativity",
}
@InProceedings{Lanczos:1969:VP,
author = "Cornelius Lanczos",
title = "Variational principles",
crossref = "Clark:1969:MMS",
pages = "1--45",
year = "1969",
bibdate = "Mon Jun 20 15:10:31 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1970:JS,
author = "Cornelius Lanczos",
title = "{Judaism} and science",
volume = "11",
publisher = "Leeds University Press",
address = "Leeds, UK",
pages = "ii + 23",
year = "1970",
ISBN = "0-85316-021-X",
ISBN-13 = "978-0-85316-021-2",
LCCN = "BM 538 .S3 L25",
bibdate = "Wed Jun 08 18:44:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "Selig Brodetsky memorial lecture",
URL = "http://catalog.hathitrust.org/Record/001402814",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1970:STA,
author = "Cornelius Lanczos",
title = "Space through the ages: the evolution of geometrical
ideas from {Pythagoras} to {Hilbert} and {Einstein}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "x + 320",
year = "1970",
MRclass = "01.01 (50.00)",
MRnumber = "0270861 (42 \#5747)",
MRreviewer = "Kenneth May",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://catalog.hathitrust.org/Record/000164850",
ZMnumber = "Zbl 0196.23601",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1970:TO,
author = "Cornelius Lanczos",
title = "Tal i o{\"a}ndlighet",
publisher = "Gleerups",
address = "Lund, Sweden",
pages = "192",
year = "1970",
LCCN = "????",
bibdate = "Wed Jun 08 19:08:25 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Translation of {\em Numbers without end} to Swedish by
Einar Fredriksson.",
acknowledgement = ack-nhfb,
language = "Swedish",
}
@Book{Lanczos:1970:VPM,
author = "Cornelius Lanczos",
title = "The variational principles of mechanics",
publisher = pub-U-TORONTO,
address = pub-U-TORONTO:adr,
edition = "Fourth",
pages = "xxix + 418",
year = "1970",
LCCN = "QA805 .L25 1970",
MRclass = "69.00",
MRnumber = "0431821 (55 \#4815)",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "Mathematical Expositions, No. 4",
URL = "http://catalog.hathitrust.org/Record/000001426",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1971:LND,
author = "Cornelius Lanczos",
title = "{L}'univers des nombres: {\`a} la d{\'e}couverte des
math{\'e}matiques. ({French}) [{The} universe of
numbers: the discovery of mathematics]",
volume = "43",
publisher = pub-DUNOD,
address = pub-DUNOD:adr,
pages = "xii + 188",
year = "1971",
LCCN = "????",
bibdate = "Wed Jun 08 19:04:12 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Translation of {\em Numbers without end} to French by
Ren{\'e} Marchand.",
series = "Science-poche",
acknowledgement = ack-nhfb,
language = "French",
}
@InCollection{Lanczos:1972:EPS,
author = "C. Lanczos",
title = "{Einstein}'s path from {Special} to {General
Relativity}",
crossref = "Synge:1972:GRP",
pages = "5--19",
year = "1972",
MRclass = "83.00 (01A60)",
MRnumber = "0503381 (58 \#20148)",
MRreviewer = "Vadim Komkov",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
SAO/NASA Astrophysics Data System",
URL = "http://adsabs.harvard.edu/abs/1972grec.conf....5L",
acknowledgement = ack-nhfb,
}
@InCollection{Lanczos:1972:PB,
author = "Cornelius Lanczos",
title = "The {Poisson} bracket",
crossref = "Salam:1972:AQT",
pages = "169--178",
year = "1972",
bibdate = "Tue Jun 14 15:14:26 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Book{Lanczos:1972:SMH,
author = "L{\'a}nczos{ }Korn{\'e}l",
title = "Sz{\'a}mok minden{\"u}tt. ({Hungarian}) [{Numbers}
without end]",
publisher = "Gondolat",
address = "Budapest, Hungary",
pages = "202",
year = "1972",
LCCN = "????",
bibdate = "Tue Jun 14 15:20:05 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
language = "Hungarian",
}
@Article{Lanczos:1972:VPQ,
author = "C. Lanczos",
title = "Vector potential and quadratic action",
journal = j-FOUND-PHYS,
volume = "2",
number = "4",
pages = "271--285",
month = "????",
year = "1972",
CODEN = "FNDPA4",
DOI = "https://doi.org/10.1007/BF00708412",
ISSN = "0015-9018 (print), 1572-9516 (electronic)",
ISSN-L = "0015-9018",
MRclass = "83.53",
MRnumber = "0339770 (49 \#4527)",
MRreviewer = "A. Wyler",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Foundations of Physics. An International Journal
Devoted to the Conceptual Bases and Fundamental
Theories of Modern Physics, Biophysics, and Cosmology",
journal-URL = "http://link.springer.com/journal/10701",
}
@InProceedings{Lanczos:1973:CTA,
author = "C. Lanczos",
title = "Computing through the ages",
crossref = "Miller:1973:TNA",
pages = "1--12",
year = "1973",
MRclass = "65-03 (01A05)",
MRnumber = "0339437 (49 \#4196)",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1973:ENC,
author = "C. Lanczos",
title = "{Emmy Noether} and the calculus of variations",
journal = j-BULL-INST-MATH-APPL,
volume = "9",
number = "8",
pages = "253--258",
year = "1973",
CODEN = "IMTABW",
ISSN = "0950-5628",
MRclass = "01A60",
MRnumber = "0504981 (58 \#21260)",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
}
@InCollection{Lanczos:1973:LVC,
author = "C. Lanczos",
title = "{Legendre} versus {Chebyshev} polynomials",
crossref = "Miller:1973:TNA",
pages = "191--201",
year = "1973",
MRclass = "65L10",
MRnumber = "0341880 (49 \#6626)",
MRreviewer = "Clarence M. Ablow",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "Zbl 0297.65008",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1973:TMM,
author = "L{\'a}nczos{ }Korn{\'e}l",
title = "A tudom{\'a}ny mint a m{\"u}v{\'e}szet egyik
form{\'a}ja. ({Hungarian}) [{Science} as a kind of
art]",
journal = j-FIZ-SZ,
volume = "23",
number = "8",
pages = "225--231",
month = aug,
year = "1973",
CODEN = "FISZA6",
ISSN = "0015-3257 (print), 1588-0540 (electronic)",
ISSN-L = "0015-3257",
bibdate = "Thu Jun 09 17:56:39 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Fizikai Szemle (Budapest)",
journal-URL = "http://www.kfki.hu/fszemle/archivum",
language = "Hungarian",
xxpages = "231--??",
}
@Book{Lanczos:1974:EDa,
author = "Cornelius Lanczos",
title = "The {Einstein} decade (1905--1915)",
publisher = "Elek Science",
address = "London, UK",
pages = "xiv + 230",
year = "1974",
ISBN = "0-236-17632-3",
ISBN-13 = "978-0-236-17632-8",
LCCN = "QC16.E5 L33 1974b",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
z3950.loc.gov:7090/Voyager",
series = "Histories of science series",
URL = "http://catalog.hathitrust.org/api/volumes/oclc/1113008.html;
http://catalog.hathitrust.org/Record/000033210",
acknowledgement = ack-nhfb,
author-dates = "1893--1974",
subject = "Einstein, Albert",
subject-dates = "1879--1955",
tableofcontents = "Part One: Einstein --- an Analysis \\
1. Biographical sketch / 3 \\
2. Albert Einstein / 11 \\
3. Conceptions and Misconceptions / 21 \\
4. Einstein's Cosmic Philosophy / 36 \\
5. Einstein, Master of Statistical Reasoning / 51 \\
6. The Space--Time Revolution of 1905--15 / 68 \\
7. $E = m c^2$ / 96 \\
8. Einstein's Genius / 106 \\
9. An Interview with Einstein in 1908 / ??? \\
Part Two: Synopsis of Einstein's scientific
publications between 1905 and 1915 \\
1905 / 127 \\
1906 / 140 \\
1907 / 145 \\
1908 / 155 \\
1909 / 160 \\
1910 / 165 \\
1911 / 173 \\
1912 / 182 \\
1913 / 192 \\
1914 / 200 \\
1915 / 208",
}
@Book{Lanczos:1974:EDb,
author = "Cornelius Lanczos",
title = "The {Einstein} decade, 1905--1915",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiv + 230",
year = "1974",
ISBN = "0-12-435840-3",
ISBN-13 = "978-0-12-435840-9",
LCCN = "QC16.E5 L33 1974",
MRclass = "01A75 (01A70)",
MRnumber = "0389517 (52 \#10348)",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://catalog.hathitrust.org/api/volumes/oclc/1113008.html;
http://catalog.hathitrust.org/Record/000033210",
acknowledgement = ack-nhfb,
author-dates = "1893--1974",
subject = "Einstein, Albert",
subject-dates = "1879--1955",
}
@Article{Lanczos:1974:EJE,
author = "L{\'a}nczos{ }Korn{\'e}l",
title = "{Einstein} {\'e}s a {J}{\"o}v{\'o} [{Einstein} and the
Future]",
journal = j-FIZ-SZ,
volume = "24",
number = "6",
pages = "161--167",
month = "????",
year = "1974",
CODEN = "FISZA6",
ISSN = "0015-3257 (print), 1588-0540 (electronic)",
ISSN-L = "0015-3257",
bibdate = "Mon Jun 20 15:20:26 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Lecture was given by Lanczos in Hungarian on the
occasion when he was elected as an honorary member of
the Roland E{\"o}tv{\"o}s Physical Society in Budapest,
1973.",
acknowledgement = ack-nhfb,
fjournal = "Fizikai Szemle (Budapest)",
journal-URL = "http://www.kfki.hu/fszemle/archivum",
language = "Hungarian",
}
@Article{Lanczos:1974:EJH,
author = "L{\'a}nczos{ }Korn{\'e}l",
title = "{Einstein} {\'e}s a J{\"o}v{\'o}. ({Hungarian})
[{Einstein} and the future]",
journal = j-FIZ-SZ,
volume = "24",
number = "6",
pages = "166--??",
month = jun,
year = "1974",
CODEN = "FISZA6",
ISSN = "0015-3257 (print), 1588-0540 (electronic)",
ISSN-L = "0015-3257",
bibdate = "Thu Jun 09 17:52:29 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Fizikai Szemle (Budapest)",
journal-URL = "http://www.kfki.hu/fszemle/archivum",
language = "Hungarian",
}
@InProceedings{Lanczos:1974:SPG,
author = "Cornelius Lanczos",
title = "Symmetry and the principles of geometry",
crossref = "Glockner:1974:SSG",
pages = "3--21",
year = "1974",
bibdate = "Mon Jun 20 15:25:29 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Lanczos:1974:VPR,
author = "C. Lanczos",
title = "Vector potential and {Riemannian} space",
journal = j-FOUND-PHYS,
volume = "4",
number = "1",
pages = "137--147",
month = "????",
year = "1974",
CODEN = "FNDPA4",
DOI = "https://doi.org/10.1007/BF00708564",
ISSN = "0015-9018 (print), 1572-9516 (electronic)",
ISSN-L = "0015-9018",
MRclass = "83.53",
MRnumber = "0408718 (53 \#12481)",
MRreviewer = "C. W. Kilmister",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "This paper uncovers the basic reason for the
mysterious change of sign from plus to minus in the
fourth coordinate of nature's Pythagorean law, usually
accepted on empirical grounds, although it destroys the
rational basis of a Riemannian geometry. Here we assume
a genuine, positive-definite Riemannian space and an
action principle which is quadratic in the curvature
quantities (and thus scale invariant). The constant $
\sigma $ between the two basic invariants is equated to
1/2. Then the matter tensor has the trace zero. In
consequence of the constancy of the scalar curvature
and the divergence identity of the matter tensor, the
perturbation metric has to satisfy a scalar and a
vector condition, with a negative sign in the fourth
coordinate. These conditions lead to the Lorentz
condition and the wave equation for the vector
potential. Thus the entire Maxwell--Lorentz type of
electrodynamics becomes logically derivable, making no
concession to any irrationality.",
acknowledgement = ack-nhfb,
fjournal = "Foundations of Physics. An International Journal
Devoted to the Conceptual Bases and Fundamental
Theories of Modern Physics, Biophysics, and Cosmology",
journal-URL = "http://link.springer.com/journal/10701",
}
@Article{Lanczos:1975:FAR,
author = "Cornelius Lanczos and Barbara Gellai",
title = "{Fourier} analysis of random sequences",
journal = j-COMPUT-MATH-APPL,
volume = "1",
number = "3--4",
pages = "269--276",
month = "????",
year = "1975",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(75)90025-5",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
MRclass = "65C10",
MRnumber = "0448801 (56 \#7106)",
MRreviewer = "George Marsaglia",
bibdate = "Wed Jun 8 13:51:09 2011",
bibdate = "Wed Mar 1 18:51:12 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122175900255",
ZMnumber = "Zbl 0366.65005",
abstract = "Computer-generated random sequences were submitted to
a Fourier analysis. The distribution of the phase angle
was not uniform over the circle, but some ``bald
patches'' remained. The Fourier analysis itself allows
the construction of ideal random sequences. For an
``ideal white noise'' the amplitudes were chosen as
one, whereas the phase angles were uniformly
distributed. For an ``ideal random noise'' both phase
angles and amplitudes were uniformly distributed. Thus,
ideal noise patterns were obtained which were analysed
statistically.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From the publisher: Professor Lanczos dealt with the
topic mentioned in the title of this article during the
last months of his life, however, he did not prepare
any manuscript. The co-author's aim has been to collect
and arrange the ideas obtained from him by oral
communication or by letter into this single article
which should by no means be regarded as a complete
work. Had he not died, Lanczos would most certainly
have provided theoretical and practical complementation
of the topic. Nevertheless, publication is felt to be
appropriate since the considerations presented here may
well be of interest.",
}
@Article{Lanczos:1975:GRS,
author = "C. Lanczos",
title = "Gravitation and {Riemannian} space",
journal = j-FOUND-PHYS,
volume = "5",
number = "1",
pages = "9--18",
month = "????",
year = "1975",
CODEN = "FNDPA4",
DOI = "https://doi.org/10.1007/BF01100310",
ISSN = "0015-9018 (print), 1572-9516 (electronic)",
ISSN-L = "0015-9018",
MRclass = "83.33",
MRnumber = "0484223 (58 \#4150)",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "The field equations of the quadratic action principle
of relativity are solved, assuming a weak perturbation
of the basic structure, which is a highly agitated
Riemannian lattice field of a very small lattice
constant. A field emerges which can be interpreted as
the weak gravitational field of an apparently
Minkowskian space. This field does not coincide with
Einstein's theory of weak gravitational fields. Whereas
the redshift remains unchanged, the light deflection
becomes reduced by 11.1\% of the value predicted by
Einstein.",
acknowledgement = ack-nhfb,
fjournal = "Foundations of Physics. An International Journal
Devoted to the Conceptual Bases and Fundamental
Theories of Modern Physics, Biophysics, and Cosmology",
journal-URL = "http://link.springer.com/journal/10701",
}
@Book{Lanczos:1976:GTF,
author = "L{\'a}nczos{ }Korn{\'e}l",
title = "A Geometriai {T}{\'e}rfogalom Fejl{\H{o}}d{\'e}se: {A}
geometriai fogalmak fejl d{\'e}se
{P}{\"u}thagoraszt{\'o}l Hilbertig {\'e}s Einsteinig
[{The} geometric concept of space development: The
development of geometric concepts from {Pythagoras} to
{Hilbert} and {Einstein}]",
publisher = "Gondolat",
address = "Budapest, Hungary",
pages = "323",
year = "1976",
ISBN = "963-280-206-3",
ISBN-13 = "978-963-280-206-0",
LCCN = "MC 71.363",
bibdate = "Mon Jun 20 15:26:29 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Translation to Hungarian by J{\'o}zsef Merza of {\em
Space Through the Ages}, Academic Press (1970).",
acknowledgement = ack-nhfb,
language = "Hungarian",
}
@Book{Lanczos:1977:VPM,
author = "Cornelius Lanczos",
title = "The variational principles of mechanics",
volume = "4",
publisher = pub-U-TORONTO,
address = pub-U-TORONTO:adr,
edition = "Fourth",
pages = "xxix + 418",
year = "1977",
ISBN = "0-8020-1743-6",
ISBN-13 = "978-0-8020-1743-7",
LCCN = "QA805 .L278 1970",
bibdate = "Wed Jun 8 14:22:37 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
library.anu.edu.au:210/INNOPAC",
series = "Mathematical expositions",
acknowledgement = ack-nhfb,
subject = "Mechanics, Analytic",
}
@Book{Lanczos:1978:EEH,
author = "L{\'a}nczos{ }Korn{\'e}l",
title = "{Einstein} {\'e}vtizede (1905--1915). ({Hungarian})
[{The} {Einstein} decade (1905--1915)]",
publisher = "Magvet{\H{o}}",
address = "Budapest, Hungary",
pages = "233",
year = "1978",
ISBN = "963-270-754-0",
ISBN-13 = "978-963-270-754-9",
LCCN = "????",
bibdate = "Tue Jun 14 15:46:48 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Translated from English to Hungarian by Stephen Terts.
Preface by Anthony Muller. Commentary by Imre Kondor.",
acknowledgement = ack-nhfb,
language = "Hungarian",
}
@InCollection{Lanczos:1978:LSS,
author = "Cornelius Lanczos",
title = "Linear systems in self-adjoint form",
crossref = "Abbott:1978:CPC",
pages = "??--??",
year = "1978",
bibdate = "Wed Jun 08 17:32:43 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
remark = "Chauvenet Prize paper.",
}
@Book{Lanczos:1986:VPM,
author = "Cornelius Lanczos",
title = "The variational principles of mechanics",
publisher = pub-DOVER,
address = pub-DOVER:adr,
edition = "Fourth",
pages = "xxix + 418",
year = "1986",
ISBN = "0-486-65067-7 (paperback)",
ISBN-13 = "978-0-486-65067-8 (paperback)",
LCCN = "QA805 .L278 1986",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$10.00",
series = "Dover books on physics and chemistry",
URL = "http://www.loc.gov/catdir/description/dover032/85029168.html;
http://www.loc.gov/catdir/toc/dover031/85029168.html",
acknowledgement = ack-nhfb,
author-dates = "1893--1974",
remark = "Reprint. Originally published: Toronto: University of
Toronto Press, c1970. (Mathematical expositions; no.
4).",
subject = "Mechanics, Analytic; Variational principles",
}
@Book{Lanczos:1988:AA,
author = "Cornelius Lanczos",
title = "Applied analysis",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xx + 539",
year = "1988",
ISBN = "0-486-65656-X",
ISBN-13 = "978-0-486-65656-4",
MRclass = "65-01",
MRnumber = "1020056 (90k:65004)",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
note = "Reprint of the 1956 original",
series = "Dover Books on Advanced Mathematics",
URL = "http://www.loc.gov/catdir/description/dover032/88003961.html",
acknowledgement = ack-nhfb,
remark = "Chapter 3 discusses the Lanczos algorithms for solving
eigenvalue problems \cite{Lanczos:1950:IMS} and
linear-equation systems \cite{Lanczos:1952:SSL}. Pages
464--507 treat the Lanczos tau method for function
approximation.",
subject = "Mathematical analysis; Mathematical physics",
}
@Book{Marx:1993:LK,
author = "{Marx Gy{\"o}rgy}",
title = "{L{\'a}nczos Korn{\'e}l: 1893\slash 1993}",
volume = "15",
publisher = "Fej{\'e}r Megyei Lev{\'e}lt{\'a}r",
address = "Sz{\'e}kesfeh{\'e}rv{\'a}r, Hungary",
pages = "122",
year = "1993",
ISBN = "963-7233-17-2",
ISBN-13 = "978-963-7233-17-3",
LCCN = "QA29 .L36 1995",
bibdate = "Wed Jun 08 19:10:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "Fej{\'e}r Megyei Lev{\'e}lt{\'a}r
k{\"o}zlem{\'e}nyei",
acknowledgement = ack-nhfb,
language = "Hungarian",
xxnote = "Check publisher and address??",
}
@Book{Lanczos:1996:LDO,
author = "Cornelius Lanczos",
title = "Linear differential operators",
volume = "18",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xviii + 564",
year = "1996",
ISBN = "0-89871-370-6 (paperback), 1-61197-118-7 (e-book)",
ISBN-13 = "978-0-89871-370-1 (paperback), 978-1-61197-118-7
(e-book)",
LCCN = "QA432 .L3 1996",
MRclass = "00A05 (01A75 34-00 35-00 65-00)",
MRnumber = "1393942 (97c:00002)",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Corrected reprint of the 1961 original",
series = "Classics in Applied Mathematics",
abstract = "Originally published in 1961, this Classics edition
continues to be appealing because it describes a large
number of techniques still useful today. Although the
primary focus is on the analytical theory, concrete
cases are cited to forge the link between theory and
practice. Considerable manipulative skill in the
practice of differential equations is to be developed
by solving the 350 problems in the text. The problems
are intended as stimulating corollaries linking theory
with application and providing the reader with the
foundation for tackling more difficult problems.
Lanczos begins with three introductory chapters that
explore some of the technical tools needed later in the
book, and then goes on to discuss interpolation,
harmonic analysis, matrix calculus, the concept of the
function space, boundary value problems, and the
numerical solution of trajectory problems, among other
things. The emphasis is constantly on one question:
``What are the basic and characteristic properties of
linear differential operators?'' In the author's words,
this book is written for those ``to whom a problem in
ordinary or partial differential equations is not a
problem of logical acrobatism, but a problem in the
exploration of the physical universe. To get an
explicit solution of a given boundary value problem is
in this age of large electronic computers no longer a
basic question. But of what value is the numerical
answer if the scientist does not understand the
peculiar analytical properties and idiosyncrasies of
the given operator? The author hopes that this book
will help in this task by telling something about the
manifold aspects of a fascinating field.''.",
acknowledgement = ack-nhfb,
subject = "Calculus, Operational; Differential equations,
Linear",
tableofcontents = "Preface \\
Bibliography \\
Chapter 1. Interpolation \\
Chapter 2. Harmonic analysis \\
Chapter 3. Matrix calculus \\
Chapter 4. The function space \\
Chapter 5. The Green's function \\
Chapter 6. Communication problems \\
Chapter 7. Sturm-Liouville problems \\
Chapter 8. Boundary value problems \\
Chapter 9. Numerical solution of trajectory problems
\\
Appendix \\
Index",
}
@Book{Lanczos:1997:LDO,
author = "Cornelius Lanczos",
title = "Linear differential operators",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xvi + 564",
year = "1997",
ISBN = "0-486-68035-5",
ISBN-13 = "978-0-486-68035-4",
LCCN = "QA432 .L3 1997",
MRclass = "34-01 (65-01)",
MRnumber = "1613431 (98m:34001)",
bibdate = "Wed Jun 8 13:51:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Reprint of the 1961 original",
URL = "http://www.loc.gov/catdir/description/dover031/97026069.html",
acknowledgement = ack-nhfb,
subject = "Calculus, Operational; Differential equations,
Linear",
}
@Article{Lanczos:1997:SCS,
author = "Cornelius Lanczos",
title = "On a Stationary Cosmology in the Sense of {Einstein}'s
{Theory of Gravitation}",
journal = j-GEN-RELATIVITY-GRAV,
volume = "29",
number = "3",
pages = "363--399",
month = "????",
year = "1997",
CODEN = "GRGVA8",
DOI = "https://doi.org/10.1023/A:1010277120072",
ISSN = "0001-7701 (print), 1572-9532 (electronic)",
ISSN-L = "0001-7701",
bibdate = "Thu Jun 09 16:51:27 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
SAO/NASA Astrophysics Data System",
note = "Translation by C. Hoenselaers of original German
version \cite{Lanczos:1924:SKI}.",
URL = "http://adsabs.harvard.edu/abs/1997GReGr..29..361L",
abstract = "A world is to be considered stationary in the sense of
general relativity if the coefficients of its metric
are independent of time in a coordinate system in which
the masses are at rest on average. The remark on the
system of coordinates is important because time itself
is no invariant notion but is taken only in the sense
of proper time. Our definition is unique, in the form
given above. On the other hand it is also possible to
have points where no matter is present. At such points
we may place a test body of infinitesimally small mass
and analyse whether it remains at rest in our
coordinate system. A necessary and sufficient condition
for this is that the time lines of our coordinate
system are geodesics. Therefore the static solution
given by de Sitter is not an example of a stationary
world. The Schwarzschild line element which, from a
cosmological point of view, is a world with a single
central body can also not be considered a stationary
solution. Indeed, there are no stationary solutions
which are also spherically symmetric for the original
field equations. The only such solution for the
cosmological equations is Einstein's cylinder world. It
is, to my knowledge, the only stationary world known so
far. In that case the average matter density and the
total mass of the world has to have a well defined
value given by the cosmological constant which
doubtless would be purely coincidental and is thus not
a satisfactory assumption. In the following we shall
discuss a new solution which is in accord with the
original field equations without the need of an a
priori relation between mass and cosmological constant.
However, we shall find that its mass cannot be less
than the mass of the cylinder world.",
acknowledgement = ack-nhfb,
fjournal = "General Relativity and Gravitation",
journal-URL = "http://link.springer.com/journal/10714",
xxpages = "361--399",
}
@Article{Lanczos:2004:RHM,
author = "C. Lanczos",
title = "The relations of the homogeneous {Maxwell}'s equations
to the theory of functions",
journal = "ArXiv Physics e-prints",
month = aug,
year = "2004",
CODEN = "APRHCB",
bibdate = "Fri Jun 10 15:01:33 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
SAO/NASA Astrophysics Data System",
URL = "http://adsabs.harvard.edu/abs/2004physics...8079L",
acknowledgement = ack-nhfb,
eprint = "arXiv:physics/0408079",
keywords = "Physics - History of Physics, Physics - Classical
Physics",
}
@Article{Lanczos:2005:CFD,
author = "C. Lanczos",
title = "On the covariant formulation of {Dirac}'s equation",
journal = "ArXiv Physics e-prints",
month = aug,
year = "2005",
CODEN = "APRHCB",
bibdate = "Fri Jun 10 15:02:03 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
SAO/NASA Astrophysics Data System",
URL = "http://adsabs.harvard.edu/abs/2005physics...8012L",
acknowledgement = ack-nhfb,
eprint = "arXiv:physics/0508012",
keywords = "Physics - History of Physics",
}
@Article{Lanczos:2005:CLF,
author = "C. Lanczos",
title = "The conservation laws in the field theoretical
representation of {Dirac}'s theory",
journal = "ArXiv Physics e-prints",
month = aug,
year = "2005",
CODEN = "APRHCB",
bibdate = "Fri Jun 10 15:02:03 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
SAO/NASA Astrophysics Data System",
URL = "http://adsabs.harvard.edu/abs/2005physics...8013L",
acknowledgement = ack-nhfb,
eprint = "arXiv:physics/0508013",
keywords = "Physics - History of Physics",
}
@Article{Lanczos:2005:DWM,
author = "C. Lanczos",
title = "{Dirac}'s wave mechanical theory of the electron and
its field theoretical interpretation",
journal = "ArXiv Physics e-prints",
month = aug,
year = "2005",
CODEN = "APRHCB",
bibdate = "Fri Jun 10 15:02:03 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
SAO/NASA Astrophysics Data System",
URL = "http://adsabs.harvard.edu/abs/2005physics...8009L",
acknowledgement = ack-nhfb,
eprint = "arXiv:physics/0508009",
keywords = "Physics - History of Physics",
}
@Article{Lanczos:2005:TAR,
author = "C. Lanczos",
title = "The tensor analytical relationships of {Dirac}'s
equation",
journal = "ArXiv Physics e-prints",
month = aug,
year = "2005",
CODEN = "APRHCB",
bibdate = "Fri Jun 10 15:02:03 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
SAO/NASA Astrophysics Data System",
URL = "http://adsabs.harvard.edu/abs/2005physics...8002L",
acknowledgement = ack-nhfb,
eprint = "arXiv:physics/0508002",
keywords = "Physics - History of Physics",
}
%%% ====================================================================
%%% Part 2 (of 2): publications about Lanczos and his works
%%%
%%% NB: There are MANY published mathematical and scientific papers with
%%% Lanczos in their titles, but we include only a subset of them here
%%% to give an idea of the impact of Lanczos' work.
@Article{Reichenbacher:1923:BAK,
author = "Ernst Reichenb{\"a}cher",
title = "{Bemerkung zu der Arbeit von Kornel Lanczos: Zum
Rotationsproblem der allgemeinen
Relativit{\"a}tstheorie}. ({German}) [{Remark} on the
work of {Kornel Lanczos}: {{\em On the Rotation Problem
in the Theory of General Relativity}}]",
journal = j-Z-PHYSIK,
volume = "15",
number = "1",
pages = "273--275",
month = "????",
year = "1923",
CODEN = "ZEPYAA",
DOI = "https://doi.org/10.1007/BF01330477",
ISSN = "0044-3328",
bibdate = "Thu Jun 09 15:19:38 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "{Zeitschrift f{\"u}r Physik}",
journal-URL = "http://link.springer.com/journal/218",
language = "German",
}
@Article{Eckart:1926:SPS,
author = "Carl Eckart",
title = "The Solution of the Problem of the Simple Oscillator
by a Combination of the {Schroedinger} and the
{Lanczos} Theories",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "12",
number = "6",
pages = "473--476",
month = "????",
year = "1926",
CODEN = "PNASA6",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Fri Jun 10 15:16:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
}
@Book{Kryloff:1931:MSA,
author = "N. Kryloff",
title = "Les m{\'e}thodes de solution approch{\'e}e des
probl{\`e}mes de la physique math{\'e}matique",
publisher = "Gauthier-Villars",
address = "Paris, France",
pages = "????",
year = "1931",
LCCN = "????",
bibdate = "Sat Jun 11 15:13:04 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Krylov:1931:NSE,
author = "A. N. Krylov",
title = "On the numerical solution of the equation by which, in
technical matters, frequencies of small oscillations of
material systems are determined",
journal = "Izvestija Akademia Nauk SSSR. Otdel. mat. i estest.
nauk",
volume = "7",
number = "4",
pages = "491--539",
month = "????",
year = "1931",
bibdate = "Sat Jun 11 12:23:04 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://alexei-krylov.co.tv/;
http://ta.twi.tudelft.nl/users/viuk/burgers/krylov.html;
http://www.encyclopedia.com/doc/1G2-2830902397.html",
acknowledgement = ack-nhfb,
keywords = "iteration solution of large eigenvalue problems",
language = "Russian",
remark = "This is the paper in which the Krylov subspace method
for eigensolutions is introduced.",
xxtitle = "On the numerical solution of equations whose solution
determine the frequency of small vibrations of material
systems",
}
@Article{Luzin:1931:MMK,
author = "N. Luzin",
title = "Sur la m{\'e}thode de {Mr. A. Krylov} de composition
de l'{\'e}quation s{\'e}culaire. ({French}) [{On} the
method of {Mr. A. Krylov} for the composition of the
secular equation]",
journal = "Bull. Acad. Sci. URSS",
volume = "1931",
number = "7",
pages = "903--958",
year = "1931",
bibdate = "Fri Nov 10 16:19:00 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "0004.04902",
acknowledgement = ack-nhfb,
fjournal = "Bulletin de l'Acad{\'e}mie des Sciences de l'URSS.
VII. S{\'e}rie",
language = "Russian",
ZBmath = "3004266",
}
@PhdThesis{Danielson:1940:IPF,
author = "Gordon Charles Danielson",
title = "Improvement in practical {Fourier} analysis and their
application to {X}-ray scattering from liquids",
type = "{Ph.D.} Thesis",
school = "Purdue University",
address = "West Lafayette, IN, USA",
pages = "95",
year = "1940",
bibdate = "Sat Jun 11 16:38:19 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
author-dates = "1912--1983",
remark = "Nowack \cite[p. 396]{Nowack:1994:DFA} says ``Mrs.
Dorothy Danielson recently commented that her husband
came to know Lanczos as a graduate student in one of
his mathematics classes, and that Lanczos suggested
that they work together on an idea for rapid evaluation
in Fourier analysis (personal communication, 1993).
This became part of Danielson's Ph.D. thesis. as well
as publications with Lanczos
\cite{Danielson:1942:SIPa,Danielson:1942:SIPa}.''",
}
@Article{Cooper:1948:SNF,
author = "J. L. B. Cooper",
title = "The Solution of Natural Frequency Equations by
Relaxation Methods",
journal = j-QUART-APPL-MATH,
volume = "6",
number = "??",
pages = "179--183",
month = "????",
year = "1948",
CODEN = "QAMAAY",
ISSN = "0033-569x (print), 1552-4485 (electronic)",
ISSN-L = "0033-569X",
bibdate = "Sat Jun 11 12:48:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.ams.org/publications/journals/journalsframework/qam",
acknowledgement = ack-nhfb,
fjournal = "Quarterly of Applied Mathematics",
journal-URL = "http://dl.acm.org/citation.cfm?id=J641;
http://www.ams.org/journals/qam",
keywords = "iteration solution of large eigenvalue problems",
remark = "Back issues of this journal, but only to 2005, are
available at links from the URL.",
}
@Article{Arnoldi:1951:PMI,
author = "W. E. Arnoldi",
title = "The principle of minimized iteration in the solution
of the matrix eigenvalue problem",
journal = j-QUART-APPL-MATH,
volume = "9",
number = "??",
pages = "17--29",
month = "????",
year = "1951",
CODEN = "QAMAAY",
ISSN = "0033-569x (print), 1552-4485 (electronic)",
ISSN-L = "0033-569X",
bibdate = "Sat Jun 11 12:21:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.ams.org/publications/journals/journalsframework/qam",
acknowledgement = ack-nhfb,
ajournal = "Quart. Appl. Math.",
fjournal = "Quarterly of Applied Mathematics",
journal-URL = "http://dl.acm.org/citation.cfm?id=J641;
http://www.ams.org/journals/qam",
keywords = "iteration solution of large eigenvalue problems",
remark = "This is the paper in which the Arnoldi method for
eigensolutions is introduced.",
remark-2 = "Back issues of this journal, but only to 2005, are
available at links from the URL.",
}
@Article{Karush:1951:IMF,
author = "W. Karush",
title = "An iterative method for finding characteristic vectors
of a symmetric matrix",
journal = j-PAC-J-MATH,
volume = "1",
number = "2",
pages = "233--248",
month = "????",
year = "1951",
CODEN = "PJMAAI",
DOI = "https://doi.org/10.2140/pjm.1951.1.233",
ISSN = "0030-8730 (print), 1945-5844 (electronic)",
ISSN-L = "0030-8730",
bibdate = "Fri Nov 10 07:22:10 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "https://msp.org/pjm/1951/1-2/p07.xhtml",
acknowledgement = ack-nhfb,
fjournal = "Pacific Journal of Mathematics",
journal-URL = "http://msp.org/pjm",
}
@Article{Lewis:1951:BRC,
author = "D. C. Lewis",
title = "Book Review: {Cornelius Lanczos, {\em The variational
principles of mechanics}, (Mathematical Expositions,
no. 4.) Toronto, University of Toronto Press, 1949. xxv
+ 307 pp}",
journal = j-BULL-AMS,
volume = "57",
number = "1 (part 1)",
pages = "88--91",
month = "????",
year = "1951",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Sat Jun 11 00:10:37 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://projecteuclid.org/euclid.bams/1183515808",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Article{Rutishauser:1953:BKB,
author = "H. Rutishauser",
title = "{Beitrage zur Kentniss des
Biorthogonalisierungs-Algorithmus von Lanczos}.
({German}) [{Contributions} to the understanding of the
{Lanczos} biorthogonalization algorithm]",
journal = j-Z-ANGE-MATH-PHYS,
volume = "4",
number = "??",
pages = "35--56",
month = "????",
year = "1953",
CODEN = "ZAMPDB",
ISSN = "0044-2275 (print), 1420-9039 (electronic)",
ISSN-L = "0044-2275",
MRnumber = "MR55307",
bibdate = "Sat Jun 11 00:06:52 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "0050.01008",
acknowledgement = ack-nhfb,
ajournal = "Z. Angew. Math. Physik",
fjournal = "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik
= Journal of Applied Mathematics and Physics}",
journal-URL = "http://link.springer.com/journal/33",
language = "German",
}
@Article{Anonymous:1956:CLM,
author = "Anonymous",
title = "Computation by {Lanczos}'s method",
journal = j-J-INST-ELECTR-ENG,
volume = "2",
number = "22",
pages = "607--607",
month = "????",
year = "1956",
CODEN = "JISEAL",
DOI = "https://doi.org/10.1049/jiee-3.1956.0275",
ISSN = "0368-2692",
bibdate = "Sat Jun 11 00:37:44 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institution of Electrical Engineers",
journal-URL = "http://ieeexplore.ieee.org/servlet/opac?punumber=5308791",
}
@Article{Brooker:1956:MLC,
author = "R. A. Brooker and F. H. Sumner",
title = "The method of {Lanczos} for calculating the
characteristic roots and vectors of a real symmetric
matrix",
journal = "Proceedings of the IEE --- Part B: Radio and
Electronic Engineering",
volume = "103",
number = "1",
pages = "114--119",
month = apr,
year = "1956",
DOI = "https://doi.org/10.1049/pi-b-1.1956.0024",
bibdate = "Sat Jun 11 00:29:22 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "The paper draws attention to a method suggested by
Lanczos for arriving at the reduced characteristic
function of a matrix, and shows how it may be used with
an electronic computer to evaluate automatically the
characteristic roots and vectors of a real symmetric
matrix, no matter how degenerate.",
acknowledgement = ack-nhfb,
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5242809",
}
@TechReport{Minhinnick:1956:TDN,
author = "I. T. Minhinnick",
title = "The Theoretical Determination of Normal Modes and
Frequencies of Vibration",
type = "A.R.C. Technical Reports and Memoranda",
number = "3039",
institution = "Aeronautical Research Council, Ministry of Supply",
address = "Bedford, UK",
pages = "i + 31",
year = "1956",
bibdate = "Sat Jun 11 15:01:27 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://aerade.cranfield.ac.uk/ara/arc/rm/3039.pdf",
acknowledgement = ack-nhfb,
remark = "Refers to \cite{Kryloff:1931:MSA}, but not to Arnoldi
or Lanczos.",
}
@Article{Bellman:1957:RPA,
author = "Richard Bellman",
title = "Recent Publications: {{\em Applied Analysis}, by C.
Lanczos. Prentice-Hall, Englewood Cliffs, NJ, 1957, xx
+ 539pp. \$9.00}",
journal = j-AMER-MATH-MONTHLY,
volume = "64",
number = "6",
pages = "447--448",
month = jun # "\slash " # jul,
year = "1957",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:40 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2310192",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Teichmann:1957:BRA,
author = "T. Teichmann",
title = "Book Review: {{\em Applied Analysis} by Cornelius
Lanczos, 539 pp. Prentice-Hall, Inc., Englewood Cliffs,
NJ, 1956}",
journal = j-PHYS-TODAY,
volume = "10",
number = "6",
pages = "44--44",
month = jun,
year = "1957",
CODEN = "PHTOAD",
DOI = "https://doi.org/10.1063/1.3060400",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
ISSN-L = "0031-9228",
bibdate = "Fri Jun 10 13:03:41 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Physics Today",
journal-URL = "http://www.physicstoday.org/",
}
@InProceedings{Wilkinson:1957:CEC,
author = "J. H. Wilkinson",
title = "The Calculation of the Eigenvectors of Codiagonal
Matrices Produced by the {Givens} and {Lanczos}
Processes",
crossref = "Griffith:1957:DPA",
pages = "112:1--112:15",
year = "1957",
bibdate = "Fri Jun 10 12:38:24 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@Article{Gregory:1958:RUL,
author = "Robert T. Gregory",
title = "Results Using {Lanczos}' Method for Finding
Eigenvalues of Arbitrary Matrices",
journal = j-J-SIAM,
volume = "6",
number = "2",
pages = "182--188",
month = jun,
year = "1958",
CODEN = "JSIMAV",
ISSN = "0368-4245 (print), 1095-712X (electronic)",
ISSN-L = "0036-1399",
bibdate = "Thu Oct 15 18:16:06 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
journal-URL = "http://epubs.siam.org/loi/smjmap.1",
}
@Article{Todd:1958:BRC,
author = "John Todd",
title = "Book Review: {Cornelius Lanczos, {\em Applied
analysis}}",
journal = j-BULL-AMS,
volume = "64",
number = "4",
pages = "210--211",
month = "????",
year = "1958",
CODEN = "BAMOAD",
ISSN = "0002-9904 (print), 1936-881X (electronic)",
ISSN-L = "0002-9904",
bibdate = "Sat Jun 11 00:08:53 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://projecteuclid.org/euclid.bams/1183522571",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the American Mathematical Society",
journal-URL = "http://www.ams.org/journals/bull/all_issues.html",
}
@Article{Wilkinson:1958:CEM,
author = "J. H. Wilkinson",
title = "The Calculation of Eigenvectors by the Method of
{Lanczos}",
journal = j-COMP-J,
volume = "1",
number = "3",
pages = "148--152",
month = oct,
year = "1958",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.00",
MRnumber = "MR0102915 (21 \#1700)",
MRreviewer = "H. Rutishauser",
bibdate = "Fri Sep 29 08:55:05 MDT 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/010148.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/148.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/149.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/150.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/151.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/152.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Schwerdtfeger:1960:DPL,
author = "H. Schwerdtfeger",
title = "Direct Proof of {Lanczos}' Decomposition Theorem",
journal = j-AMER-MATH-MONTHLY,
volume = "67",
number = "9",
pages = "855--860",
month = nov,
year = "1960",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:36:05 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Causey:1961:LAT,
author = "R. L. Causey and R. T. Gregory",
title = "On {Lanczos}' Algorithm for Tridiagonalizing
Matrices",
journal = j-SIAM-REVIEW,
volume = "3",
number = "4",
pages = "322--328",
month = "????",
year = "1961",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1003063",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:04:46 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/3/4;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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 1961",
}
@Article{Gillis:1962:BRL,
author = "J. Gillis",
title = "Book Review: {{\em Linear Differential Operators}, by
Cornelius Lanczosc}",
journal = j-PHYS-TODAY,
volume = "15",
number = "7",
pages = "51--51",
month = jul,
year = "1962",
CODEN = "PHTOAD",
DOI = "https://doi.org/10.1063/1.3058271",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
ISSN-L = "0031-9228",
bibdate = "Fri Jun 10 13:07:29 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Physics Today",
journal-URL = "http://www.physicstoday.org/",
}
@Article{Barton:1963:BRBf,
author = "D. E. Barton",
title = "Book Review: {{\booktitle{Linear Differential
Operators}}, by C. Lanczos. London; New York; Princeton
and Toronto: D. Van Nostrand Co. 1961, 564 pp}",
journal = j-BIOMETRIKA,
volume = "50",
number = "3/4",
pages = "555--555",
month = dec,
year = "1963",
CODEN = "BIOKAX",
DOI = "https://doi.org/10.2307/2333943",
ISSN = "0006-3444 (print), 1464-3510 (electronic)",
ISSN-L = "0006-3444",
bibdate = "Sat Jun 21 14:33:13 MDT 2014",
bibsource = "http://www.jstor.org/journals/00063444.html;
http://www.jstor.org/stable/i315448;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/biometrika1960.bib",
URL = "http://www.jstor.org/stable/2333943",
acknowledgement = ack-nhfb,
fjournal = "Biometrika",
journal-URL = "http://www.jstor.org/journals/00063444.html",
}
@Article{Smithies:1963:BRL,
author = "F. Smithies",
title = "Book Review: {{\em Linear Differential Operators}, by
C. Lanczos. 580 pp. 1961 (Van Nostrand, London)}",
journal = j-MATH-GAZ,
volume = "47",
number = "361",
pages = "265--266",
month = oct,
year = "1963",
CODEN = "MAGAAS",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
bibdate = "Wed Jun 08 18:24:06 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/3613434",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@InCollection{Householder:1964:PVV,
author = "Alston Scott Householder",
title = "Proper values and vectors: normalization and reduction
of the matrix (methods of {Krylov, Webber-Voetter,
Danilevskii, Hessenberg, Lanczos, Samuelson and Bryan,
Leverrier}, etc.)",
crossref = "Householder:1964:TMN",
chapter = "6",
pages = "??--??",
year = "1964",
bibdate = "Tue Jun 19 06:30:20 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Houston:1965:BRA,
author = "William V. Houston",
title = "Book Review: {{\em Albert Einstein and the cosmic
world order}, by Cornelius Lanczos, Interscience
Publishers, vi + 139 pp}",
journal = j-PHYS-TEACHER,
volume = "3",
number = "5",
pages = "231--231",
month = "????",
year = "1965",
CODEN = "PHTEAH",
DOI = "https://doi.org/10.1119/1.2349117",
ISSN = "0031-921X (print), 1943-4928 (electronic)",
ISSN-L = "0031-921X",
bibdate = "Fri Jun 10 13:12:45 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "The Physics Teacher",
journal-URL = "http://scitation.aip.org/content/aapt/journal/tpt",
}
@Article{Malamud:1965:BRA,
author = "Herbert Malamud",
title = "Book Review: {{\em Albert Einstein and the cosmic
world order}, by Cornelius Lanczos, Interscience
Publishers, vi + 139 pp}",
journal = j-PHYS-TODAY,
volume = "18",
number = "6",
pages = "54--54",
month = jun,
year = "1965",
CODEN = "PHTOAD",
DOI = "https://doi.org/10.1063/1.3047488",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
ISSN-L = "0031-9228",
bibdate = "Fri Jun 10 13:12:45 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Physics Today",
journal-URL = "http://www.physicstoday.org/",
}
@Article{Nesbet:1965:ADL,
author = "R. K. Nesbet",
title = "Algorithm for Diagonalization of Large Matrices",
journal = j-J-CHEM-PHYS,
volume = "43",
number = "1",
pages = "311--312",
month = "????",
year = "1965",
CODEN = "JCPSA6",
DOI = "https://doi.org/10.1063/1.1696477",
ISSN = "0021-9606 (print), 1089-7690 (electronic)",
ISSN-L = "0021-9606",
bibdate = "Fri Jun 10 21:51:24 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "See modification \cite{Shavitt:1970:MNA}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Chemical Physics",
journal-URL = "http://scitation.aip.org/content/aip/journal/jcp/browse",
keywords = "iteration solution of large eigenvalue problems",
}
@Article{Seeger:1965:BRA,
author = "Raymond J. Seeger",
title = "Book Review: {{\em Albert Einstein and the cosmic
world order}, by Cornelius Lanczos, Interscience
Publishers, vi + 139 pp}",
journal = j-AMER-J-PHYSICS,
volume = "33",
number = "11",
pages = "972--972",
month = nov,
year = "1965",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.1971103",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Fri Jun 10 13:17:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
}
@Article{Brill:1966:RPP,
author = "Dieter Brill",
title = "Recent Publications and Presentations: {{\em Albert
Einstein and the Cosmic World Order}, by Cornelius
Lanczos}",
journal = j-AMER-MATH-MONTHLY,
volume = "73",
number = "10",
pages = "1145--1145",
month = dec,
year = "1966",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:27 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Broadbent:1966:BRA,
author = "T. A. A. Broadbent",
title = "Book Review: {{\em Albert Einstein and the Cosmic
World Order}, by Cornelius Lanczos. vi + 139 pp. 1956
(Wiley)}",
journal = j-MATH-GAZ,
volume = "50",
number = "371",
pages = "60--60",
month = feb,
year = "1966",
CODEN = "MAGAAS",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
bibdate = "Wed Jun 08 18:28:59 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/3614838",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@Article{Kizner:1966:ECL,
author = "W. Kizner",
title = "Error curves for {Lanczos}' `selected points' method",
journal = j-COMP-J,
volume = "8",
number = "4",
pages = "372--382",
month = jan,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:10 MDT 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/",
note = "See comment \cite{Wright:1966:CEC}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/080372.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/372.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/373.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/374.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/375.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/376.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/377.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/378.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/379.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/380.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/381.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/382.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wragg:1966:ULM,
author = "A. Wragg",
title = "The use of {Lanczos} $ \tau $-methods in the numerical
solution of a {Stefan} problem",
journal = j-COMP-J,
volume = "9",
number = "1",
pages = "106--109",
month = may,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:12 MDT 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_01/090106.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_01/tiff/106.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_01/tiff/107.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_01/tiff/108.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_01/tiff/109.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wrede:1966:BRA,
author = "R. C. Wrede",
title = "Book Review: {{\em Albert Einstein and the Cosmic
World Order}, by Cornelius Lanczos. vi + 139 pp. 1956
(Wiley)}",
journal = j-MATH-MAG,
volume = "39",
number = "1",
pages = "65--65",
month = jan,
year = "1966",
CODEN = "MAMGA8",
ISSN = "0025-570X",
bibdate = "Wed Jun 08 18:31:26 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/2688999",
acknowledgement = ack-nhfb,
fjournal = "Mathematics Magazine",
journal-URL = "http://www.maa.org/pubs/mathmag.html",
}
@Article{Wright:1966:CEC,
author = "K. Wright",
title = "Correspondence: On {``Error curves for Lanczos
`selected points' method''}",
journal = j-COMP-J,
volume = "9",
number = "1",
pages = "115--115",
month = may,
year = "1966",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:56:12 MDT 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_01/",
note = "See \cite{Kizner:1966:ECL}.",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_01/tiff/115.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Dickinson:1967:RDF,
author = "David Dickinson",
title = "Reviews: {{\em Discourse on Fourier Series}}, by
{Cornelius Lanczos}",
journal = j-AMER-MATH-MONTHLY,
volume = "74",
number = "6",
pages = "750--750",
month = jun # "\slash " # jul,
year = "1967",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:38:41 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Yamamoto:1968:LAT,
author = "Tetsuro Yamamoto",
title = "On {Lanczos}' algorithm for tri-diagonalization",
journal = "J. Sci. Hiroshima Univ. Ser. A-I Math.",
volume = "32",
number = "2",
pages = "259--284",
month = "????",
year = "1968",
MRnumber = "MR0245193",
bibdate = "Sat Jun 11 00:04:38 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://projecteuclid.org/euclid.hmj/1206138652",
ZMnumber = "0181.17202",
acknowledgement = ack-nhfb,
}
@Article{Ortiz:1969:TM,
author = "Eduardo L. Ortiz",
title = "The Tau Method",
journal = j-SIAM-J-NUMER-ANAL,
volume = "6",
number = "3",
pages = "480--492",
month = sep,
year = "1969",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0706044",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@TechReport{Paige:1969:EAS,
author = "C. C. Paige",
title = "Error analysis of the symmetric {Lanczos} process for
the eigenproblem",
type = "Technical. Note",
number = "207",
institution = "Institute of Computer Science, The University of
London",
address = "London, UK",
pages = "????",
year = "1969",
bibdate = "Fri Nov 10 07:26:59 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Bender:1970:IPC,
author = "C. F. Bender and I. Shavitt",
title = "An Iterative Procedure for the Calculation of the
Lowest Real Eigenvalue and Eigenvector of a
Non-Symmetric Matrix",
journal = j-J-COMPUT-PHYS,
volume = "6",
number = "1",
pages = "146--149",
month = aug,
year = "1970",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(70)90014-8",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:01 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999170900148",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
keywords = "iteration solution of large eigenvalue problems",
}
@Article{Filippov:1970:BRN,
author = "Yu. A. Filippov",
title = "Book Review: {{\em Numbers without end}, by C.
Lanczos. Oliver and Boyd, Edinburgh, x + 164 pp.,
1968}",
journal = j-USSR-COMP-MATH-MATH-PHYS,
volume = "10",
number = "5",
pages = "335--336",
month = "????",
year = "1970",
CODEN = "CMMPA9",
DOI = "https://doi.org/10.1016/0041-5553(70)90062-5",
ISSN = "0041-5553, 0502-9902",
ISSN-L = "0041-5553",
bibdate = "Fri Jun 10 17:45:51 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "U.S.S.R. Computational Mathematics and Mathematical
Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00415553",
}
@Article{Goodstein:1970:BRN,
author = "R. L. Goodstein",
title = "Book Review: {{\em Numbers without end}, by C.
Lanczos, 164 p. 1968, Oliver \& Boyd, Edinburgh}",
journal = j-MATH-GAZ,
volume = "54",
number = "388",
pages = "174--175",
month = may,
year = "1970",
CODEN = "MAGAAS",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
bibdate = "Wed Jun 08 18:16:59 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/3612127",
abstract = "This little book is based on a series of lectures at
Purdue University during World War II on mathematics as
a cultural subject and its vital role in the evolution
of human thought.",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@Article{Jammer:1970:BRS,
author = "Max Jammer",
title = "Book Review: {Space through the Ages. The Evolution of
Geometrical Ideas from Pythagoras to Hilbert and
Einstein. Cornelius Lanczos. Academic Press, New York,
1970. x + 322 pp., illus. \$11.50}",
journal = j-SCIENCE,
volume = "170",
number = "3963",
pages = "1183--1183",
day = "11",
month = dec,
year = "1970",
CODEN = "SCIEAS",
DOI = "https://doi.org/10.1126/science.170.3963.1183",
ISSN = "0036-8075 (print), 1095-9203 (electronic)",
ISSN-L = "0036-8075",
bibdate = "Wed Jun 08 17:57:25 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Science",
journal-URL = "http://www.sciencemag.org/archive/",
}
@Article{Paige:1970:PUS,
author = "C. C. Paige",
title = "Practical Use of the Symmetric {Lanczos} Process with
Re-Orthogonalization",
journal = j-BIT,
volume = "10",
number = "2",
pages = "183--195",
month = jun,
year = "1970",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01936866",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:11 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=10&issue=2;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=10&issue=2&spage=183",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Shavitt:1970:MNA,
author = "Isaiah Shavitt",
title = "Modification of {Nesbet}'s algorithm for the iterative
evaluation of eigenvalues and eigenvectors of large
matrices",
journal = j-J-COMPUT-PHYS,
volume = "6",
number = "1",
pages = "124--130",
month = aug,
year = "1970",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(70)90010-0",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:01 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
note = "See \cite{Nesbet:1965:ADL}.",
URL = "http://www.sciencedirect.com/science/article/pii/0021999170900100",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
keywords = "iteration solution of large eigenvalue problems",
}
@Article{Wright:1970:SRB,
author = "K. Wright",
title = "Some Relationships between Implicit {Runge--Kutta},
Collocation and {Lanczos} $ \tau $ Methods, and their
Stability Properties",
journal = j-BIT,
volume = "10",
number = "2",
pages = "217--227",
month = jun,
year = "1970",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01936868",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:11 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=10&issue=2;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=10&issue=2&spage=217",
acknowledgement = ack-nhfb,
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Bireline:1971:BRS,
author = "J. Bireline",
title = "Book Review: {{\booktitle{Space through the ages: the
evolution of geometrical ideas from Pythagoras to
Hilbert and Einstein}}, by Cornelius Lanczos. 320
pages. London, New York, Academic Press, 1970}",
journal = j-J-FRANKLIN-INST,
volume = "291",
number = "5",
pages = "403",
month = may,
year = "1971",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(71)90075-5",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
bibdate = "Fri Jun 10 17:47:45 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of {The Franklin Institute}",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
}
@Article{Coulson:1971:BRS,
author = "C. A. Coulson",
title = "Book Review: {{\em Space through the Ages}, by
Cornelius Lanczos, x + 320 pp., \pounds 4.00, 1970
(Academic Press, London and New York)}",
journal = j-MATH-GAZ,
volume = "55",
number = "393",
pages = "334--344",
month = jun,
year = "1971",
CODEN = "MAGAAS",
ISSN = "0025-5572 (print), 2056-6328 (electronic)",
bibdate = "Wed Jun 08 18:27:06 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/3615043",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Gazette",
journal-URL = "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}
@Article{Grattan-Guinness:1971:BRD,
author = "I. Grattan-Guinness",
title = "Book Review: {{\em Discourse on Fourier series}, by C.
Lanczos. 255 pages. Edinburgh and London, Oliver and
Boyd. 1966}",
journal = j-J-FRANKLIN-INST,
volume = "292",
number = "4",
pages = "308--308",
month = oct,
year = "1971",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(71)90105-0",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
bibdate = "Fri Jun 10 17:44:04 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of {The Franklin Institute}",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
}
@Article{Moon:1971:BRN,
author = "Parry Moon",
title = "Book Review: {{\em Numbers without end}, by Cornelius
Lanczos. 164 pages. Edinburgh, Oliver \& Boyd, 1968}",
journal = j-J-FRANKLIN-INST,
volume = "292",
number = "5",
pages = "387--388",
month = nov,
year = "1971",
CODEN = "JFINAB",
DOI = "https://doi.org/10.1016/0016-0032(71)90065-2",
ISSN = "0016-0032 (print), 1879-2693 (electronic)",
ISSN-L = "0016-0032",
bibdate = "Fri Jun 10 17:42:28 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of {The Franklin Institute}",
journal-URL = "http://www.sciencedirect.com/science/journal/00160032",
}
@PhdThesis{Paige:1971:CEE,
author = "Christopher Conway Paige",
title = "The computation of eigenvalues and eigenvectors of
very large sparse matrices",
type = "{Ph.D.} dissertation",
school = "The University of London",
address = "London, UK",
pages = "????",
year = "1971",
bibdate = "Fri Nov 10 07:30:40 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "https://www.proquest.com/pqdtglobal/docview/1794120404",
abstract = "Several methods are avai1able for computing
eigenvalues and eigenvectors of large sparse matrices,
but as yet no outstandingly good algorithm is generally
known. For the symmetric matrix case one of the most
elegant algorithms theoretically is the method of
m1rini1zed iterations developed by Lanczos in 1950 This
method reduces the original matrix to the diagonal form
from which the eigensystem can easily be found. The
method can be used iteratively, and here the
convergence properties and different possible
eigenvalue intervals are first considered assuming
infinite precision computation. Next rounding error
analyses are given for the method both with and without
re-orthogonalization. It is shown that the method has
been unjustly neglected, in fact a particular
computational algorithm for the method without
re-orthogonalization is shown to have remarkably good
error properties. As well as this the algorithm is very
fast and can be programmed to require very little store
compared with other comparable methods, and this
suggests that this variant of the Lanczos process is
likely to become an extremely useful algorithm for
finding several extreme eigenvalues, and their
eigenvectors if needed, of very large sparse symmetric
matrices.",
acknowledgement = ack-nhfb,
remark = "Thesis not available online, so no pagecount data are
available.",
}
@TechReport{Golub:1972:LAS,
author = "G. H. Golub and R. Underwood and J. H. Wilkinson",
title = "The {Lanczos} Algorithm for the Symmetric {$ A x =
\lambda {Bx} $} Problem",
type = "Technical Report",
number = "STAN-CS-72-270",
institution = "Computer Science, Stanford University",
address = "Stanford, CA",
pages = "24",
month = "??",
year = "1972",
bibdate = "Fri Jun 10 12:38:26 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
keywords = "nla, geig, Lanczos algorithm",
}
@Article{Haydock:1972:ESB,
author = "R. Haydock and Volker Heine and M. J. Kelley",
title = "Electronic Structure Based on the Local Atomic
Environment for Tight-Binding Bands",
journal = j-J-PHYS-C,
volume = "5",
number = "20",
pages = "2845--2858",
month = "????",
year = "1972",
CODEN = "JPSOAW",
DOI = "https://doi.org/10.1088/0022-3719/5/20/004",
ISSN = "0022-3719 (print), 1747-3802 (electronic)",
ISSN-L = "0022-3719",
bibdate = "Fri Nov 10 06:38:33 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "See also paper 2 \cite{Haydock:1975:ESB}.",
URL = "https://iopscience.iop.org/article/10.1088/0022-3719/5/20/004",
acknowledgement = ack-nhfb,
fjournal = "Journal of Physics C: Solid state physics",
journal-URL = "http://iopscience.iop.org/0022-3719",
received = "23 June 1972",
remark = "This paper, from researchers at the Cavendish
Laboratory, Cambridge, UD, independently rediscovers
the Lanczos algorithm \cite{Lanczos:1950:IMS} for
symmetric matrices, and calls it the ``recursion
method''.",
}
@Article{Paige:1972:CVL,
author = "C. C. Paige",
title = "Computational variants of the {Lanczos} method for the
eigenproblem",
journal = j-J-INST-MATH-APPL,
volume = "10",
number = "3",
pages = "373--381",
month = dec,
year = "1972",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/10.3.373",
ISSN = "0020-2932",
ISSN-L = "0020-2932",
MRclass = "65F15",
MRnumber = "48 #12799",
MRreviewer = "B. Levinger",
bibdate = "Sat Apr 6 16:27:10 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
ZMnumber = "0253.65020",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Book{Synge:1972:GRP,
editor = "J. L. (John Lighton) Synge and L. (Lochlainn)
{O'Raifeartaigh, ed}",
title = "General relativity; papers in honour of {J. L.
Synge}",
publisher = pub-CLARENDON,
address = pub-CLARENDON:adr,
pages = "ix + 277",
year = "1972",
ISBN = "0-19-851126-4",
ISBN-13 = "978-0-19-851126-7",
LCCN = "QC6 .G358",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
z3950.loc.gov:7090/Voyager",
note = "Edited for the Royal Irish Academy by L.
O'Raifeartaigh.",
acknowledgement = ack-nhfb,
subject = "Relativity (Physics); Synge, J. L. (John Lighton)",
subject-dates = "1897--",
tableofcontents = "Lanczos, C. / Einstein's path from special to
general relativity \\
Balazs, N. L. / The acceptability of physical theories:
Poincar\'e versus Einstein \\
Ellis, G. F. R. / Global and non-global problems in
cosmology, by G. F. R. Ellis and D. W. Sciama \\
Ehlers, J. The geometry of free fall and light
propagation, by J. Ehlers, F. A. E. Pirani and A.
Schild / \\
Trautman, A. / Invariance of Lagrangian systems \\
Penrose, R. / The geometry of impulsive gravitational
waves \\
Exact solutions of the Einstein--Maxwell equations for
an accelerated charge \\
Taub, A. H. / Plane-symmetric similarity solutions for
self-gravitating fluids \\
Robinson, I. / Equations of motion in the linear
approximation, by I. Robinson and J. R. Robinson \\
Florides, P. W. / Rotating bodies in General Relativity
\\
Chandrasekhar, S. / A limiting case of relativistic
equilibrium \\
Israel, W. / The relativistic Boltzmann equation \\
Thompson, W. B. / The self-consistent test-particle
approach to relativistic kinetic theory",
}
@InCollection{Golub:1973:SUL,
author = "G. H. Golub",
title = "Some uses of the {Lanczos} algorithm in numerical
algebra",
crossref = "Miller:1973:TNA",
pages = "173--184",
year = "1973",
MRclass = "65F15",
MRnumber = "50 \#11743",
MRreviewer = "F. Szidarovszky",
bibdate = "Fri Dec 20 17:46:23 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-sf,
}
@Article{Shavitt:1973:ICS,
author = "I. Shavitt and C. F. Bender and A. Pipano and R. P.
Hosteny",
title = "The iterative calculation of several of the lowest or
highest eigenvalues and corresponding eigenvectors of
very large symmetric matrices",
journal = j-J-COMPUT-PHYS,
volume = "11",
number = "1",
pages = "90--108",
month = jan,
year = "1973",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(73)90149-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:08 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999173901496",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
keywords = "iteration solution of large eigenvalue problems",
}
@TechReport{Cullum:1974:BGS,
author = "Jane Cullum and W. E. Donath",
title = "A Block Generalization of the Symmetric {$S$}-Step
{Lanczos} Algorithm",
type = "Report",
number = "RC 4845",
institution = "IBM T. J. Watson Research Center",
address = "Yorktown Heights, NY, USA",
month = may,
year = "1974",
bibdate = "Fri Nov 10 06:51:19 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cullum:1974:BLA,
author = "Jane Cullum and W. E. Donath",
editor = "{IEEE}",
booktitle = "Proceedings of 1974 {IEEE} Conference on Decision and
Control",
title = "A Block {Lanczos} Algorithm for Computing the $q$
Algebraically Largest Eigenvalues and a Corresponding
Eigenspace for Large, Sparse Symmetric Matrices",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "505--509",
year = "1974",
bibdate = "Fri Nov 10 06:54:03 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Evans:1974:ISM,
author = "D. J. Evans",
editor = "D. J. Evans",
booktitle = "Software for Numerical Mathematics: proceedings of the
{Loughborough University of Technology Conference of
the Institute of Mathematics and Its Applications held
in April 1973}",
title = "Iterative Sparse Matrix Algorithms",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
bookpages = "xi + 451",
pages = "49--53",
year = "1974",
ISBN = "0-12-243750-0",
ISBN-13 = "978-0-12-243750-2",
LCCN = "QA297 .S59",
bibdate = "Fri Nov 10 06:57:20 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
remark = "Points out the utility of the Lanczos algorithm for
finding eigenvalues.",
}
@Article{Feler:1974:CEL,
author = "M. Guy Feler",
title = "Calculation of Eigenvectors of Large Matrices",
journal = j-J-COMPUT-PHYS,
volume = "14",
number = "4",
pages = "341--349",
month = mar,
year = "1974",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(74)90017-5",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:13 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999174900175",
abstract = "A method of calculating eigenvectors by variance
minimization is presented. The procedure of adjusting
sequentially each component of a trial vector is
discussed and it is shown that variance minimization
and the MOR method both generate an approximate
subspace of the true eigenspace. Procedure to deal with
this subspace are given which both improve the MOR
method and make the method of variance minimization
suitable for obtaining non-extremal eigenvalues and
eigenvectors of matrices with nearly degenerate
eigenvalues.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@TechReport{Kahan:1974:ALA,
author = "W. Kahan and B. N. Parlett",
title = "An Analysis of {Lanczos} Algorithms for Symmetric
Matrices",
number = "ERL-M467",
institution = "University of California, Berkeley",
address = "Berkeley, CA, USA",
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/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
}
@InBook{Kardos:1974:LK,
author = "I. Kardos",
booktitle = "Sokszemk{\"o}zt Tud{\'o}sokkal. ({Hungarian}) [{TV}
interviews with scientists]",
title = "{L}{\'a}nczos{ }Korn{\'e}l",
publisher = "MRT-Minerva",
address = "Budapest, Hungary",
pages = "452ff",
year = "1974",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Thu Jun 09 17:48:25 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
language = "Hungarian",
}
@Article{Lyness:1974:CTB,
author = "J. N. Lyness",
title = "Computational techniques based on the {Lanczos}
representation",
journal = j-MATH-COMPUT,
volume = "28",
number = "125",
pages = "81--123",
month = jan,
year = "1974",
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/l/lanczos-cornelius.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
corpsource = "Argonne Nat. Lab., IL, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "computational techniques; convergence; divergence;
Euler/Maclaurin series; Fourier analysis; Fourier
coefficients; function approximation; Lanczos
representation; polynomial; polynomials",
treatment = "T Theoretical or Mathematical",
}
@Book{Rivlin:1974:CPC,
author = "Theodore J. Rivlin",
title = "The {Chebyshev} Polynomials",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "vi + 186",
year = "1974",
ISBN = "0-471-72470-X",
ISBN-13 = "978-0-471-72470-4",
LCCN = "QA404.5 .R58 1974",
bibdate = "Fri Apr 17 10:09:05 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
series = "Pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "The Lanczos Tau Method is discussed on pp. 98--101.",
subject = "Chebyshev polynomials",
}
@Misc{Torkoly:1974:LK,
author = "Anna T{\"o}rk{\"o}ly",
title = "{L}{\'a}nczos{ }Korn{\'e}l",
howpublished = "MTV Televideo Publishers, Budapest, Hungary",
year = "1974",
bibdate = "Tue Jun 14 15:51:14 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Video film about Cornelius Lanczos. Possibly reissued
in 1993.",
acknowledgement = ack-nhfb,
}
@Article{Balazs:1975:BRE,
author = "Nandor L. Balazs",
title = "Book Review: {{\em The Einstein Decade (1905--1915)},
by Cornelius Lanczos}",
journal = j-PHYS-TODAY,
volume = "28",
number = "8",
pages = "70--70",
month = aug,
year = "1975",
CODEN = "PHTOAD",
DOI = "https://doi.org/10.1063/1.3069137",
ISSN = "0031-9228 (print), 1945-0699 (electronic)",
ISSN-L = "0031-9228",
bibdate = "Fri Jun 10 13:18:47 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Physics Today",
journal-URL = "http://www.physicstoday.org/",
}
@Article{Butler:1975:LL,
author = "R. Butler",
title = "The {Lanczos} Legend",
journal = j-COMPUT-MATH-APPL,
volume = "1",
number = "??",
pages = "258--??",
month = "????",
year = "1975",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Jun 09 17:35:00 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Davidson:1975:NIC,
author = "Ernest R. Davidson",
title = "Note: The iterative calculation of a few of the lowest
eigenvalues and corresponding eigenvectors of large
real-symmetric matrices",
journal = j-J-COMPUT-PHYS,
volume = "17",
number = "1",
pages = "87--94",
month = jan,
year = "1975",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(75)90065-0",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:16 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
note = "This paper generalizes the work of Lanczos
\cite{Lanczos:1950:IMS} by a modification that improves
the convergence. See also later generalizations
\cite{Morgan:1986:GDM,Rettrup:1982:IMC,Sadkane:1989:ANM}.",
URL = "http://comptop.stanford.edu/u/references/da.pdf;
http://www.sciencedirect.com/science/article/pii/0021999175900650",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
keywords = "iteration solution of large eigenvalue problems",
remark = "This paper refers to
\cite{Cooper:1948:SNF,Lanczos:1950:IMS,Nesbet:1965:ADL,Shavitt:1970:MNA,Shavitt:1973:ICS}
for prior work on eigensolutions, but has no mention of
the work of Arnoldi \cite{Arnoldi:1951:PMI} or Krylov
\cite{Krylov:1931:NSE}.",
}
@Article{Davis:1975:ESL,
author = "W. R. Davis and L. H. Green and L. K. Norris",
title = "Elucidation of some of {Lanczos}' thoughts concerning
spacetime curvature and the local and non-local parts
of the {Riemann} tensor",
journal = j-COMPUT-MATH-APPL,
volume = "1",
number = "3--4",
pages = "361--364",
month = "????",
year = "1975",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(75)90036-X",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:12 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812217590036X",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Haydock:1975:ESB,
author = "R. Haydock and Volker Heine and M. J. Kelley",
title = "Electronic structure based on the local atomic
environment for tight-binding bands. {II}",
journal = j-J-PHYS-C,
volume = "8",
number = "16",
pages = "2591--2605",
month = aug,
year = "1975",
CODEN = "JPSOAW",
DOI = "https://doi.org/10.1088/0022-3719/8/16/011",
ISSN = "0022-3719 (print), 1747-3802 (electronic)",
ISSN-L = "0022-3719",
bibdate = "Fri Nov 10 16:09:31 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "See also paper 1 \cite{Haydock:1972:ESB}.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Physics C: Solid State Physics",
journal-URL = "http://iopscience.iop.org/0022-3719",
}
@InCollection{Householder:1975:PVV,
author = "Alston Scott Householder",
title = "Proper values and vectors: normalization and reduction
of the matrix (methods of {Krylov, Webber-Voetter,
Danilevskii, Hessenberg, Lanczos, Samuelson and Bryan,
Leverrier}, etc.)",
crossref = "Householder:1975:TMN",
chapter = "6",
pages = "??--??",
year = "1975",
bibdate = "Tue Jun 19 06:30:20 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{McConnell:1975:CLD,
author = "J. R. McConnell",
title = "{Cornelius Lanczos} in {Dublin} (1953--1974)",
journal = j-COMPUT-MATH-APPL,
volume = "1",
number = "??",
pages = "263--264",
month = "????",
year = "1975",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Jun 09 17:35:00 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
xxnote = "Check: is this part of \cite{Rodin:1975:MCL}??",
}
@Article{Ortiz:1975:LIA,
author = "Eduardo L. Ortiz",
title = "{Lanczos} and the {Institute for Advanced Studies} in
the Early Sixties",
journal = j-COMPUT-MATH-APPL,
volume = "1",
number = "??",
pages = "266--??",
month = "????",
year = "1975",
CODEN = "CMAPDK",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Thu Jun 09 17:35:00 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Ortiz:1975:SST,
author = "E. L. Ortiz",
title = "Step by step {Tau} method. {Part I}. {Piecewise}
polynomial approximations",
journal = j-COMPUT-MATH-APPL,
volume = "1",
number = "3--4",
pages = "381--392",
month = "????",
year = "1975",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(75)90040-1",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:12 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122175900401",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Rodin:1975:MCL,
author = "Ervin Y. Rodin and R. Butler and A. Erd{\'e}lyi and B.
Gellai and J. R. McConnell and Eduardo L. Ortiz and I.
Rhodes",
title = "In memory of {Cornelius L{\'a}nczos}",
journal = j-COMPUT-MATH-APPL,
volume = "1",
number = "3--4",
pages = "257--268",
month = "????",
year = "1975",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(75)90024-3",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:12 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122175900243",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "The title uses an acute accent in the last word, even
though Lanczos himself only used that accent in
Hungarian.",
}
@Article{Taub:1975:LSR,
author = "A. H. Taub",
title = "{Lanczos}' splitting of the {Riemann} tensor",
journal = j-COMPUT-MATH-APPL,
volume = "1",
number = "3--4",
pages = "377--380",
month = "????",
year = "1975",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(75)90039-5",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:12 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122175900395",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@PhdThesis{Underwood:1975:IBL,
author = "Richard Ray Underwood",
title = "An Iterative Block {Lanczos} Method for the Solution
of Large Sparse Symmetric Eigenproblems",
type = "{Ph.D.} thesis",
school = "Department of Computer Science, Stanford University",
address = "Stanford, CA, USA",
pages = "v + 133",
month = may,
year = "1975",
bibdate = "Fri Nov 10 07:03:07 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Also issued as report STAN-CS-75-496",
URL = "https://www.proquest.com/pqdtglobal/docview/302727419/",
acknowledgement = ack-nhfb,
advisor = "Gene H. Golub",
}
@Article{Yourgrau:1975:CL,
author = "Wolfgang Yourgrau",
title = "{Cornelius Lanczos (1893--1974)}",
journal = j-FOUND-PHYS,
volume = "5",
number = "1",
pages = "19--20",
month = "????",
year = "1975",
CODEN = "FNDPA4",
ISSN = "0015-9018 (print), 1572-9516 (electronic)",
ISSN-L = "0015-9018",
bibdate = "Thu Jun 09 17:54:46 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Foundations of Physics",
journal-URL = "http://link.springer.com/journal/10701",
xxpages = "20--??",
}
@Article{Blackmore:1976:BRE,
author = "John T. Blackmore",
title = "Book Review: {{\booktitle{The Einstein decade}}: By
Cornelius Lanczos. New York and London (Academic
Press), 1974. \$12.50}",
journal = j-HIST-MATH,
volume = "3",
number = "2",
pages = "236--236",
month = may,
year = "1976",
CODEN = "HIMADS",
DOI = "https://doi.org/10.1016/0315-0860(76)90059-8",
ISSN = "0315-0860 (print), 1090-249X (electronic)",
ISSN-L = "0315-0860",
bibdate = "Wed Jun 26 06:16:38 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
https://www.math.utah.edu/pub/tex/bib/histmath.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0315086076900598",
acknowledgement = ack-nhfb,
fjournal = "Historia Mathematica",
journal-URL = "http://www.sciencedirect.com/science/journal/03150860/",
}
@InProceedings{Cline:1976:CNM,
author = "A. K. Cline and G. H. Golub and G. W. Platzman",
title = "Calculation of Normal Modes of Oceans Using a
{Lanczos} Method",
crossref = "Bunch:1976:SMC",
pages = "409--426",
year = "1976",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, eig, Lanczos algorithm",
}
@Article{Coleman:1976:LTM,
author = "J. P. Coleman",
title = "The {Lanczos} tau-method",
journal = j-J-INST-MATH-APPL,
volume = "17",
number = "1",
pages = "85--97",
year = "1976",
CODEN = "JMTAA8",
DOI = "https://doi.org/10.1093/imamat/17.1.85",
ISSN = "0020-2932",
MRclass = "41A20",
MRnumber = "53 #6160",
MRreviewer = "Jack Williams",
bibdate = "Sat Apr 6 16:27:10 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://imamat.oxfordjournals.org/content/17/1/85.abstract",
abstract = "A number of variants of the $ \tau $-method, giving
polynomial and rational approximations, are examined by
applying them to the initial-value problem $ y^\prime -
y = 0 $, $ y(0) = 1 $ on the interval $ [0, 1] $. Error
estimates are derived for the rational approximations.
A rational approximation, obtained by using a multiple
of the shifted Legendre polynomial as the perturbing
term, proves to be the most accurate of the
approximations studied.",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
remark = "From pp. 96--97, ``Rivlin \cite{Rivlin:1974:CPC} shows
that, [the Chebyshev form of the integrated tau-method
approximation] is arbitrarily close to the minimax
approximation of degree $n$ for $n$ sufficiently
large.'' See also the related remark in
\cite{Hazewinkel:2002:EM}.",
}
@InCollection{Kahan:1976:HFSa,
author = "W. Kahan and B. N. Parlett",
editor = "J. Bunch and D. Rose",
booktitle = "Sparse matrix computations (Proc. Sympos., Argonne
Nat. Lab., Lemont, Ill., 1975)",
title = "How far should you go with the {Lanczos} process?",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "131--144",
year = "1976",
MRclass = "65F15",
MRnumber = "MR0458836 (56 \#17036)",
MRreviewer = "Michael S. Martin",
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/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Paige:1976:EAL,
author = "C. C. Paige",
title = "Error Analysis of the {Lanczos} Algorithm for
Tridiagonalizing a Symmetric Matrix",
journal = j-J-INST-MATH-APPL,
volume = "18",
number = "??",
pages = "341--349",
month = "????",
year = "1976",
CODEN = "JMTAA8",
ISSN = "0020-2932",
bibdate = "Fri Jun 10 12:14:06 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
kwds = "lanczos",
}
@Book{Rodin:1976:CMA,
editor = "Ervin Y. Rodin",
title = "Computers and mathematics with applications: in memory
of {Cornelius Lanczos}",
publisher = pub-PERGAMON,
address = pub-PERGAMON:adr,
pages = "ix + 257--428",
year = "1976",
ISBN = "0-08-020521-6",
ISBN-13 = "978-0-08-020521-2",
LCCN = "QA76 .C576",
bibdate = "Wed Jun 8 18:51:05 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "Published as a special issue of the journal Computers
and mathematics with applications, volume I, number
3/4.",
subject = "Lanczos, Cornelius; Electronic data processing;
Mathematics; Data processing",
subject-dates = "1893--1974",
}
@Article{Horvay:1977:CLM,
author = "Gabriel Horvay",
title = "{Cornelius Lanczos}, in memoriam",
journal = j-COMPUT-MATH-APPL,
volume = "3",
number = "4",
pages = "251--252",
month = "????",
year = "1977",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(77)90082-7",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 18:51:15 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122177900827",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Book{Jennings:1977:MCE,
author = "Alan Jennings",
title = "Matrix Computation for Engineers and Scientists",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "xv + 330",
year = "1977",
ISBN = "0-471-99421-9 (hardcover), 0-471-27832-7 (paperback)",
ISBN-13 = "978-0-471-99421-3 (hardcover), 978-0-471-27832-0
(paperback)",
LCCN = "TA347 .D4J461",
bibdate = "Wed Dec 15 10:35:36 1993",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1: Basic algebraic and numerical concepts \\
What is a matrix \\
The matrix equation \\
Matrix multiplication \\
Some special matrix forms \\
The matrix transpose and symmetry \\
The determinant of a matrix \\
The solution of simultaneous equations \\
Gaussian elimination and pivotal condensation \\
Equations with multiple right-hand sides \\
Transforming matrix equations \\
The rank of a matrix \\
The matrix inverse \\
Significance of the inverse \\
The transpose and inverse in matrix expressions \\
Partitioning of matrices \\
The eigenvalues of a matrix \\
Some eigenvalue properties \\
Eigenvectors \\
Norms and normalization \\
Orthogonality conditions for eigenvectors of symmetric
matrices \\
Quadric forms and positive definite matrices \\
Gerschgorin discs \\
2: Some matrix problems \\
An electrical resistance network \\
Alternative forms of the network equations \\
Properties of electrical resistance network equations
\\
Other network problems \\
Least squares for overdetermined equations \\
Error adjustments in surveying \\
Curve fitting by least squares \\
A heat transfer field problem \\
The finite difference method \\
The finite element method \\
A source and sink method \\
A non-linear cable analysis by the Newton--Raphson
method \\
3: Computer implementation \\
Storage of numbers \\
Rounding errors \\
Array storage for matrices \\
Matrix multiplication using two dimensional arrays \\
On program efficiency \\
One-dimensional storage for matrix operations \\
One the use of backing store \\
Computer packages \\
Sparse storage \\
Random packing \\
The use of address links \\
Systematic packing \\
Some notes on sparse packing schemes \\
Operations involving systematically packed matrices \\
Series storage of sparse matrices \\
regular pattern storage schemes \\
variable bandwidth storage \\
Submatrix storage schemes \\
4: Elimination methods for linear equations \\
Triangular decomposition \\
Equivalence of Gaussian elimination of triangular
decomposition \\
When pivot selection is unnecessary \\
Pivot selection \\
Row and column scaling \\
On loss of accuracy in elimination \\
On pivot selection \\
Ill-conditioning \\
\ldots{} in practice \\
Residuals and iterative improvement \\
Twin pivoting for symmetric matrices \\
Equations with prescribed variables \\
5: Sparse matrix elimination \\
Changes in sparsity pattern during elimination \\
Graphical interpretation of sparse elimination \\
Diagonal band elimination \\
A variable bandwidth elimination algorithm \\
The Cuthill--McKee algorithm and its reverse \\
Some other renumbering schemes \\
Elimination in a packed store \\
Elimination using submatrices \\
Substructure methods \\
Nested dissection \\
On the use of backing store \\
Unsymmetric band elimination \\
Unsymmetric elimination in a packed store \\
Computing elements of a sparse inverse \\
6: Some matrix eigenvalue problems \\
Column buckling \\
Structural vibration \\
Linearized eigenvalue problems \\
Damped vibration \\
Dynamic stability \\
reduction of the quadratic eigenvalue problem to
standard form \\
Principal component analysis \\
A geometrical interpretation of principal component
analysis \\
Markov chains \\
Markov chains for assessing computer performance \\
Some eigenvalue properties of stochastic matrices \\
7: Transformation methods for eigenvalue problems \\
Orthogonal transformation of a matrix \\
Jacobi diagonalization \\
Computer implementation of Jacobi diagonalization \\
Givens tridiagonalization \\
Householder's transformation \\
Implementation of Householder's tridiagonalization \\
Transformation of band symmetric matrices \\
Eigenvalue properties of unsymmetric matrices \\
Similarity transformations \\
Reduction to upper Hessenberg form \\
The LR transformation \\
Convergence of the LR method \\
The QR and QL transformations \\
Origin shift with the QR method \\
Discussion of the QR method \\
The application of the transformation methods \\
8: Sturm sequence methods \\
The characteristic equation \\
The Sturm sequence property \\
Bisection for tridiagonal matrices \\
Discussion of bisection for tridiagonal matrices \\
Bisection for general symmetric matrices \\
Bisection for band matrices \\
Non-linear symmetric eigenvalue problems \\
9: Vector iterative methods for partial eigensolution
\\
The power method \\
Convergence characteristics of the power method \\
Eigenvalue shift and inverse iteration \\
A simultaneous iteration method \\
The convergence rate and efficiency of simultaneous
iteration \\
Simultaneous iteration for symmetric matrices \\
\ldots{} unsymmetric \\
Simultaneous and subspace iteration for vibration
frequency analysis \\
The symmetric Lanczos method \\
Theoretical basis for the Lanczos \\
Convergence characteristics of Lanczos' method \\
Extensions of Lanczos' method \\
Shift strategies with advanced vector \\
10: Orthogonalization and re-solution techniques for
linear equations \\
Decompositions of a rectangular matrix \\
Efficiency and accuracy in least squares problems \\
Sparse least squares problems \\
Singular value decomposition \\
Use of singular value composition \\
The solution of modified equations \\
The use of supplementary variables \\
Updating factorization \\
Discussion of equation modification \\
11: Iterative methods for linear equations \\
Jacobi and Gauss--Seidel iteration \\
Successive over-relaxation \\
General characterization of iterative methods \\
The iteration matrix \\
SOR convergence with a symmetric positive definite
matrix \\
Matrices with property A \\
On the acceleration of stationary methods \\
The method of steepest decent \\
The method of conjugate gradients (CG) \\
Convergence of the CG method \\
Generalized CG formulations \\
Block relaxation \\
Preconditioning \\
ICCG methods \\
12: Non-linear equations \\
The Newton--Raphson method \\
Globally convergent algorithms \\
Dealing with ill-conditioning \\
Avoiding the need to compute derivatives \\
Overdetermined sets of equations \\
Practical considerations \\
13: Parallel and vector computing \\
Mutual independence in matrix operations \\
High-speed computer architecture \\
Matrix--vector multiplication on non-sequential
machines \\
Solving dense sets of linear equations on
non-sequential machines \\
Solution of banded equations \\
General sparse equations \\
Parallelizing a sequential code",
}
@Book{Abbott:1978:CPC,
editor = "James Crawford Abbott",
title = "The {Chauvenet} papers: a collection of prize-winning
expository papers in mathematics",
publisher = pub-MATH-ASSOC-AMER,
address = pub-MATH-ASSOC-AMER:adr,
pages = "xviii + 312 (vol. 1), vii + 313--595 (vol. 2)",
year = "1978",
ISBN = "0-88385-425-2 (vol. 1), 0-08-835427-9 (vol. 2)",
ISBN-13 = "978-0-88385-425-9 (vol. 1), 978-0-08-835427-1 (vol.
2)",
LCCN = "QA7 .C43 1978",
bibdate = "Wed Jun 8 17:26:38 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
note = "Two volumes.",
acknowledgement = ack-nhfb,
remark = "Volume 1 \\
Algebraic functions and their divisors / Gilbert Ames
Bliss \\
The Borel theorem and its generalizations / Theophil
Henry Hildebrandt \\
An introduction to the theory of numbers / Godfrey
Harold Hardy \\
Series of orthogonal polynomials, Orthogonal
trigonometric sums, The convergence of Fourier series /
Dunham Jackson \\
On the structure of continua / Gordon Thomas Whyburn
\\
Some recent advances in algebra, Modular fields /
Saunders MacLane \\
Some introductory exercises in the manipulation of
Fourier, Transforms / Robert H. Cameron \\
The foundations of probability / Paul Richard Halmos
\\
Random walk and the theory of Brownian motion / Mark
Kac \\
Partial orderings and Moore--Smith limits / Edward
James McShane \\
Recent advances in the foundations of Euclidean plane
geometry / Richard Hubert Bruck and others \\
Volume 2. \\
Linear systems in self-adjoint form / Cornelius Lanczos
\\
Leonhard Euler's integral: a historical profile of the
gamma function / Philip J. Davis \\
Are logic and mathematics identical? / Leon A. Henkin
\\
Differential equations: linearity vs. non-linearity /
Jack K. Hale and Joseph P. LaSalle \\
Harmonic analysis / Guido L. Weiss \\
Can one hear the shape of a drum? / Mark Kac \\
Curves and surfaces in Euclidean space / Shiing--Shen
Chern \\
A motivated account of an elementary proof of the prime
number theorem / Norman Levinson \\
On local solvability of linear partial differential
equations / Jean Fran{\c{c}}ois Tr{\`e}ves \\
The simple continued fraction expansion of e / Carl
Douglas Olds \\
The formation and decay of shock waves / Peter D. Lax
\\
Hilbert's tenth problem / Martin D. Davis and Reuben
Hersh \\
Real proofs of complex theorems (and vice versa) /
Lawrence Zalcman",
subject = "mathematics",
xxauthor = "G. H. Hardy and P. Halmos and L. Henkin and M. Davis
and R. Hersh and R. Cameron and Fran{\c{c}}ois
Tr{\`e}ves and P. Lax and Hale--La Salle and S. Chern
and M. Kac and L. Zalcman and Gordon T. Whyburn and R.
Bruck and N. Levinson and T. Hildebrandt and E. McShane
and D. Jackson and S. MacLane and Ph. Davis and G.
Bliss and C. Lanczos and C. Olds and Halle La Salle and
G. Weiss",
}
@Article{Ray:1978:VDB,
author = "John R. Ray",
title = "A variational derivation of the {Bach--Lanczos}
identity",
journal = j-J-MATH-PHYS,
volume = "19",
number = "1",
pages = "100--102",
month = jan,
year = "1978",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.523525",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Jun 10 07:50:26 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Edwards:1979:ULM,
author = "J. T. Edwards and D. C. Licciardello and D. J.
Thouless",
title = "Use of the {Lanczos} method for finding complete sets
of eigenvalues of large sparse symmetric matrices",
journal = j-J-INST-MATH-APPL,
volume = "23",
number = "3",
pages = "277--283",
year = "1979",
CODEN = "JMTAA8",
ISSN = "0020-2932",
MRclass = "65F15",
MRnumber = "80c:65086",
bibdate = "Fri Apr 5 05:48:27 MST 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Article{Parlett:1979:LAS,
author = "Beresford N. Parlett and David S. Scott",
title = "The {Lanczos} Algorithm with Selective
Orthogonalization",
journal = j-MATH-COMPUT,
volume = "33",
number = "145",
pages = "217--238",
month = jan,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "80c:65090",
MRreviewer = "Colette Lebaud",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database; Theory/Matrix.bib",
acknowledgement = ack-nhfb,
classcodes = "C4140 (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; extreme; independence; Lanczos algorithm;
large symmetric matrix; linear; selective
orthogonalization",
kwds = "nla, eig, Lanczos Algorithm, orthogonalization",
treatment = "T Theoretical or Mathematical",
}
@Article{Scott:1979:HML,
author = "D. S. Scott",
title = "How to Make the {Lanczos} Algorithm Converge Slowly",
journal = j-MATH-COMPUT,
volume = "33",
number = "145",
pages = "239--247",
month = jan,
year = "1979",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "80c:65091",
MRreviewer = "Colette Lebaud",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database; Theory/Matrix.bib",
acknowledgement = ack-nhfb,
classcodes = "C4140 (Linear algebra)",
corpsource = "Math. and Statistics Res. Dept., Union Carbide Corp.,
Oak Ridge, TN, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "convergence; convergence of numerical methods;
eigenfunctions; eigenvalues; eigenvalues and; iterative
method; Lanczos Algorithm; large; perverse starting
vector; sparse symmetric matrices",
kwds = "nla, eig, Lanczos algorithm",
treatment = "T Theoretical or Mathematical",
}
@Article{Cullum:1980:LPI,
author = "Jane Cullum and Ralph A. Willoughby",
title = "The {Lanczos} phenomenon---an interpretation based
upon conjugate gradient optimization",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "29",
number = "??",
pages = "63--90",
month = feb,
year = "1980",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(80)90231-1",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (65F25)",
MRnumber = "81d:65017",
MRreviewer = "Norihiko Adachi",
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/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "The equivalence in exact arithmetic of the Lanczos
tridiagonalization procedure and the conjugate gradient
optimization procedure for solving $ A x = b $, where
$A$ is a real symmetric, positive definite matrix, is
well known. We demonstrate that a relaxed equivalence
is valid in the presence of errors. Specifically we
demonstrate that local var epsilon-orthonormality of
the Lanczos vectors guarantees local $ \varepsilon
$-$A$-conjugacy of the direction vectors in the
associated conjugate gradient procedure. Moreover we
demonstrate that all the conjugate gradient
relationships are satisfied approximately. Therefore,
any statements valid for the conjugate gradient
optimization procedure, which we show converges under
very weak conditions, apply directly to the Lanczos
procedure. We then use this equivalence to obtain an
explanation of the Lanczos phenomenon: the empirically
observed ``convergence'' of Lanczos eigenvalue
procedures despite total loss of the global
orthogonality of the Lanczos vectors.",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "nla, eig, Lanczos algorithm, conjugate gradients",
}
@Article{Paige:1980:AEL,
author = "C. C. Paige",
title = "Accuracy and Effectiveness of the {Lanczos} Algorithm
for the Symmetric Eigenproblem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "34",
pages = "235--258",
year = "1980",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18 15A57 65N99)",
MRnumber = "82b:65025",
MRreviewer = "L. Fox",
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/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "nla, eig, Lanczos algorithm, rounding error",
}
@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",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F10",
MRnumber = "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/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "nla, Lanczos algorithm, symmetric matrix, linear
system",
}
@TechReport{Saad:1980:LBA,
author = "Y. Saad",
title = "The {Lanczos} biorthogonalization algorithm and other
oblique projection methods for solving large
unsymmetric systems",
type = "Report",
number = "1036",
institution = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "44",
year = "1980",
bibdate = "Thu Jun 09 11:00:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Saad:1980:RCL,
author = "Y. Saad",
key = "Saadb",
title = "On the rates of convergence of the {Lanczos} and the
block {Lanczos} methods",
journal = j-SIAM-J-NUMER-ANAL,
volume = "17",
number = "5",
pages = "687--706",
month = oct,
year = "1980",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0717059",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15",
MRnumber = "588755 (82g:65022)",
MRreviewer = "W. C. Rheinboldt",
bibdate = "Sun Sep 5 09:21:22 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
JSTOR database; MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Chen:1981:SBV,
author = "Peter Y. P. Chen",
title = "Solutions of boundary-value problems by the
{Lanczos--Chebyshev} reduction method",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "17",
number = "2",
pages = "291--299",
month = feb,
year = "1981",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620170212",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "20 Jun 2005",
}
@Article{Cullum:1981:CEV,
author = "Jane Cullum and Ralph A. Willoughby",
title = "Computing eigenvalues of very large symmetric
matrices---An implementation of a {Lanczos} algorithm
with no reorthogonalization",
journal = j-J-COMPUT-PHYS,
volume = "44",
number = "2",
pages = "329--358",
month = dec,
year = "1981",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(81)90056-5",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:09 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999181900565",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Golub:1981:BLM,
author = "Gene H. Golub and Franklin T. Luk and Michael L.
Overton",
title = "A Block {Lanczos} Method for Computing the Singular
Values and Corresponding Singular Vectors of a Matrix",
journal = j-TOMS,
volume = "7",
number = "2",
pages = "149--169",
month = jun,
year = "1981",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/355945.355946",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
MRclass = "65F50 (65F15)",
MRnumber = "84h:65045",
bibdate = "Sun Jan 14 09:28:55 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "Cited in {{\AA}ke Bj{\"o}rck's} bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "block Lanczos method; Lanczos algorithm; large sparse
matrix; NLA; singular values; singular vectors;
singular-value decomposition; SVD; upper-triangular
band matrix",
}
@TechReport{Grcar:1981:ALA,
author = "Joseph F. Grcar",
title = "Analyses of the {Lanczos} algorithm and of the
approximation problem in {Richardson}'s method",
volume = "UIUCDCS-R-81-1074",
number = "1074",
institution = "Dept. of Computer Science, University of Illinois at
Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "iv + 192",
year = "1981",
LCCN = "QA76 .I4 no. 1074",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "December 1981. Originally presented as the author's
thesis (Ph.D., University of Illinois at
Urbana-Champaign, 1981).",
subject = "Sparse matrices; Data processing; Approximation
theory",
}
@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/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@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",
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/l/lanczos-cornelius.bib;
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{Schwarz:1981:SIG,
author = "H. R. Schwarz",
title = "{Simultane Iterationsverfahren f{\"u}r gro{\ss}e
allgemeine Eigenwertprobleme}. ({German})
[{Simultaneous} iteration methods for large ordinary
eigenvalue problems]",
journal = j-ARCH-APPL-MECH,
volume = "50",
number = "5",
pages = "329--338",
month = "????",
year = "1981",
CODEN = "AAMEEA",
DOI = "https://doi.org/10.1007/BF00778428",
ISSN = "0939-1533 (print), 1432-0681 (electronic)",
ISSN-L = "0939-1533",
bibdate = "Sat Jun 11 13:10:25 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Archive of Applied Mechanics = Ingenieur-Archiv",
journal-URL = "http://link.springer.com/journal/419",
keywords = "iteration solution of large eigenvalue problems",
language = "German",
}
@TechReport{Ericsson:1982:SSP,
author = "Thomas Ericsson and Axel Ruhe",
title = "{STLM} --- a software package for the Spectral
Transformation {Lanczos} algorithm",
institution = "UMINF-101",
pages = "1--32",
year = "1982",
bibdate = "Fri Jun 10 12:38:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib",
acknowledgement = ack-nhfb,
}
@Article{Parlett:1982:ELE,
author = "B. N. Parlett and H. Simon and L. M. Stringer",
title = "On Estimating the Largest Eigenvalue with the
{Lanczos} Algorithm",
journal = j-MATH-COMPUT,
volume = "38",
number = "157",
pages = "153--165",
month = jan,
year = "1982",
CODEN = "MCMPAF",
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/l/lanczos-cornelius.bib;
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",
}
@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/l/lanczos-cornelius.bib;
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{Radhakrishnan:1982:CBL,
author = "C. Radhakrishnan and S. C. K. Nair",
title = "A comparison between {Lanczos} and moment methods",
journal = j-PHYS-LET-A,
volume = "91",
number = "2",
pages = "64--66",
month = aug,
year = "1982",
CODEN = "PYLAAG",
DOI = "https://doi.org/10.1016/0375-9601(82)90266-3",
ISSN = "0375-9601 (print), 1873-2429 (electronic)",
ISSN-L = "0375-9601",
bibdate = "Fri Jun 10 17:14:11 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Physics Letters A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759601",
}
@Article{Rettrup:1982:IMC,
author = "Sten Rettrup",
title = "An iterative method for calculating several of the
extreme eigensolutions of large real non-symmetric
matrices",
journal = j-J-COMPUT-PHYS,
volume = "45",
number = "1",
pages = "100--107",
month = jan,
year = "1982",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(82)90104-8",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:10 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
note = "See \cite{Davidson:1975:NIC}.",
URL = "http://www.sciencedirect.com/science/article/pii/0021999182901048",
abstract = "A new method is described for calculating several of
the extreme eigensolutions of large real non-symmetric
matrices. The matrices considered are assumed to have
real eigenvectors and eigenvalues. An algorithm is
presented for both single and multiple vector
optimization. The efficiency of the two versions are
compared using some test calculations. The method is a
generalization of the Davidson-approach.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
keywords = "iteration solution of large eigenvalue problems",
}
@Article{Saad:1982:LBA,
author = "Y. Saad",
key = "Saade",
title = "The {Lanczos} biorthogonalization algorithm and other
oblique projection methods for solving large
unsymmetric systems",
journal = j-SIAM-J-NUMER-ANAL,
volume = "19",
number = "3",
pages = "485--506",
month = jun,
year = "1982",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0719031",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F10 (65F25)",
MRnumber = "656464 (84g:65045)",
MRreviewer = "O. O. Romanovs{\cprime}ki{\u\i}",
bibdate = "Sun Sep 5 09:21:22 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
JSTOR database; MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@InCollection{Schwarz:1982:SRQ,
author = "H. R. Schwarz",
booktitle = "Numerical Integration of Differential Equations and
Large Linear Systems",
title = "Simultaneous {Rayleigh}-quotient iteration methods for
large sparse generalized eigenvalue problems",
volume = "968",
publisher = pub-SV,
address = pub-SV:adr,
pages = "384--398",
year = "1982",
DOI = "https://doi.org/10.1007/BFb0064904",
bibdate = "Sat Jun 11 13:08:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "Lecture Notes in Mathematics",
acknowledgement = ack-nhfb,
keywords = "iteration solution of large eigenvalue problems",
}
@Article{vanderVorst:1982:GLS,
author = "H. A. van der Vorst",
title = "A generalized {Lanczos} scheme",
journal = j-MATH-COMPUT,
volume = "39",
number = "160",
pages = "559--561",
month = oct,
year = "1982",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "MR669648 (84h:65039)",
bibdate = "Sat Dec 31 06:28:14 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
JSTOR database; MathSciNet database;
Theory/Matrix.bib",
acknowledgement = ack-nhfb,
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Acad. Computer Centrum, Utrecht, Netherlands",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "eigenvalue problems; eigenvalues and eigenfunctions;
generalized; Lanczos scheme; matrix algebra;
skew-symmetric matrices",
kwds = "nla, Lanczos algorithm",
treatment = "T Theoretical or Mathematical",
}
@Article{Cullum:1983:LAC,
author = "Jane Cullum and Ralph A. Willoughby and Mark Lake",
title = "A {Lanczos} algorithm for computing singular values
and vectors of large matrices",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "4",
number = "2",
pages = "197--215",
month = jun,
year = "1983",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "65F15",
MRnumber = "84h:65035",
MRreviewer = "Robert Todd Gregory",
bibdate = "Tue Apr 29 19:18:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "IBM Thomas J. Watson Res. Center, Yorktown Heights,
NY, USA",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "eigenvalues and eigenfunctions; eigenvalues and
eigenvectors; Lanczos algorithms; large matrices;
matrix algebra; real matrix; sparse real matrices;
symmetric matrices",
treatment = "T Theoretical or Mathematical",
}
@Book{Golub:1983:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
publisher = pub-JOHNS-HOPKINS # " and " # pub-NORTH-OXFORD,
address = pub-JOHNS-HOPKINS:adr # " and " # pub-NORTH-OXFORD:adr,
pages = "xvi + 476",
year = "1983",
ISBN = "0-8018-3010-9 (hardcover), 0-8018-3011-7 (paperback),
0-946536-00-7, 0-946536-05-8 (paperback)",
ISBN-13 = "978-0-8018-3010-5 (hardcover), 978-0-8018-3011-2
(paperback), 978-0-946536-00-9, 978-0-946536-05-4
(paperback)",
LCCN = "QA188 .G65 1983",
MRclass = "65Fxx (65-02)",
MRnumber = "85h:65063",
MRreviewer = "C. Ilioi",
bibdate = "Sun Jan 14 09:27:53 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "Johns Hopkins Series in the Mathematical Sciences",
URL = "http://www.jstor.org/stable/2008107;
http://www.jstor.org/stable/2030489;
http://www.jstor.org/stable/3616959",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "algebra --- matrices --- computation by digital
computer systems; matrices --- data processing",
remark = "See review by James W. Demmel in SIAM Review, Vol. 28,
No. 2 (Jul., 1986), pp. 252-255, review by David F.
Mayers, Mathematics of Computation, Vol. 47, No. 175
(Jul., 1986), pp. 376-377, and review by T. J. Randall,
The Mathematical Gazette, Vol. 69, No. 448 (Jun.,
1985), p. 152.",
tableofcontents = "Preface to the Third Edition \\
Software \\
Selected References \\
Matrix Multiplication Problems / 1 \\
Matrix Analysis / 48 \\
General Linear Systems / 87 \\
Special Linear Systems / 133 \\
Orthogonalization and Least Squares / 206 \\
Parallel Matrix Computations / 275 \\
The Unsymmetric Eigenvalue Problem / 308 \\
The Symmetric Eigenvalue Problem / 391 \\
Lanczos Methods / 470 \\
Iterative Methods for Linear Systems / 508 \\
Functions of Matrices / 555 \\
Special Topics / 579 \\
Bibliography / 637 \\
Index / 687",
}
@Article{Hermann:1983:LPL,
author = "M. R. Hermann and P. W. Langhoff",
title = "{L{\"o}wdin} partitioning in a {Lanczos} basis:
{Applications} to scattering states",
journal = j-IJQC,
volume = "23",
number = "1",
pages = "135--146",
month = jan,
year = "1983",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/qua.560230115",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
onlinedate = "19 Oct 2004",
}
@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",
month = jun,
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 Jun 10 10:27:45 MDT 2011",
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",
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",
onlinedate = "21 Jun 2005",
}
@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 = "??",
pages = "241--252",
year = "1983",
CODEN = "CMSTCJ",
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/l/lanczos-cornelius.bib;
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",
}
@Article{Smith:1983:ULA,
author = "I. M. Smith and E. E. Heshmati",
title = "Use of a {Lanczos} algorithm in dynamic analysis of
structures",
journal = j-EARTHQUAKE-ENG-STRUCT-DYN,
volume = "11",
number = "4",
pages = "585--588",
month = jul,
year = "1983",
CODEN = "IJEEBG",
DOI = "https://doi.org/10.1002/eqe.4290110410",
ISSN = "0098-8847 (print), 1096-9845 (electronic)",
ISSN-L = "0098-8847",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Earthquake engineering \& structural dynamics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1096-9845",
onlinedate = "18 Dec 2006",
}
@Article{Bloom:1984:GTS,
author = "S. D. Bloom",
title = "{Gamow--Teller} strength functions with the {Lanczos}
algorithm",
journal = j-PROG-PART-NUCL-PHYS,
volume = "11",
number = "??",
pages = "505--528",
month = "????",
year = "1984",
CODEN = "PPNPDB",
DOI = "https://doi.org/10.1016/0146-6410(84)90025-5",
ISSN = "0146-6410 (print), 1873-2224 (electronic)",
ISSN-L = "0146-6410",
bibdate = "Fri Jun 10 17:26:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Prog. Part. Nucl. Phys.",
fjournal = "Progress in Particle and Nuclear Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/09205632",
}
@Article{Boley:1984:LAA,
author = "D. L. Boley and G. H. Golub",
title = "The {Lanczos--Arnoldi} Algorithm and controllability",
journal = j-SYST-CONTROL-LETT,
volume = "4",
number = "6",
pages = "317--324",
month = sep,
year = "1984",
CODEN = "SCLEDC",
DOI = "https://doi.org/10.1016/S0167-6911(84)80072-9",
ISSN = "0167-6911 (print), 1872-7956 (electronic)",
ISSN-L = "0167-6911",
MRclass = "93B40 (93B05)",
MRnumber = "86a:93044",
bibdate = "Fri Dec 20 17:12:57 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Systems and Control Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01676911",
keywords = "nla, controllability, Lanczos algorithm, Arnoldi's
method, algorithms",
subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
Miscellaneous",
}
@InProceedings{Cullum:1984:LPM,
author = "Jane Cullum and Ralph A. Willoughby",
editor = "{IEEE}",
booktitle = "{The 23rd IEEE Conference on Decision and Control,
December 12--14, 1984, Las Vegas, Nevada}",
title = "A {Lanczos} procedure for the modal analysis of very
large nonsymmetric matrices",
volume = "23",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "1758--1761",
month = dec,
year = "1984",
DOI = "https://doi.org/10.1109/CDC.1984.272436",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Sat Jun 11 00:31:57 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "IEEE Catalog Number 79-640961.",
acknowledgement = ack-nhfb,
}
@InProceedings{Evans:1984:ICG,
author = "D. Evans and J. Shanehchi and R. Barlow",
title = "Implementation of the Conjugate Gradient and {Lanczos}
Algorithms for Large Sparse Banded Matrices on the
{ICL} {DAP}",
crossref = "Feilmeier:1984:PCP",
pages = "143--151",
year = "1984",
bibdate = "Fri Jun 10 12:38:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Haydock:1984:CAR,
author = "Roger Haydock and D. Weaire",
title = "Computational advantages of the recursion and
{Lanczos} methods",
journal = j-COMP-PHYS-COMM,
volume = "31",
number = "4",
pages = "431--432",
month = mar,
year = "1984",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(84)90027-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Jun 10 16:58:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Kalamboukis:1984:LTA,
author = "T. Z. Kalamboukis",
title = "A {Lanczos}-type algorithm for the generalized
eigenvalue problem {$ A x = \lambda B x $}",
journal = j-J-COMPUT-PHYS,
volume = "53",
number = "1",
pages = "82--89",
month = jan,
year = "1984",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(84)90053-6",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:18 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999184900536",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Loh:1984:CFL,
author = "Chee Hoong Loh",
title = "{Chebyshev} filtering {Lanczos}' process in the
subspace iteration method",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "20",
number = "1",
pages = "182--186",
month = jan,
year = "1984",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620200114",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "21 Jun 2005",
}
@Article{Nash:1984:NTM,
author = "Stephen G. Nash",
title = "{Newton}-type minimization via the {Lanczos} method",
journal = j-SIAM-J-NUMER-ANAL,
volume = "21",
number = "4",
pages = "770--788",
month = aug,
year = "1984",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65K10 (90C30)",
MRnumber = "86h:65092",
MRreviewer = "G. R. Wood",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Nour-Omid:1984:DAS,
author = "Bahram Nour-Omid and Ray W. Clough",
title = "Dynamic analysis of structures using {Lanczos}
co-ordinates",
journal = j-EARTHQUAKE-ENG-STRUCT-DYN,
volume = "12",
number = "4",
pages = "565--577",
month = "????",
year = "1984",
CODEN = "IJEEBG",
DOI = "https://doi.org/10.1002/eqe.4290120410",
ISSN = "0098-8847 (print), 1096-9845 (electronic)",
ISSN-L = "0098-8847",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Earthquake engineering \& structural dynamics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1096-9845",
onlinedate = "28 Dec 2006",
}
@InProceedings{Parlett:1984:LAL,
author = "B. N. Parlett and D. R. Taylor and Z. S. Liu",
title = "The look ahead {Lanczos} 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/l/lanczos-cornelius.bib;
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",
ISSN = "0196-5204",
MRclass = "65F15 (65F50)",
MRnumber = "85i:65048",
MRreviewer = "David R. Kincaid",
bibdate = "Tue Apr 29 19:18:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra); C7310 (Mathematics
computing)",
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 = "eigenvalues; eigenvalues and eigenfunctions; EISPACK;
FORTRAN subroutines; Lanczos algorithm; matrix algebra;
software; software packages; sparse matrices; subspace
iteration",
sponsororg = "Army Res. Office; Office of Naval Res.; Oak Ridge Nat.
Lab",
treatment = "P Practical",
}
@Article{Simon:1984:ASL,
author = "Horst D. Simon",
title = "Analysis of the Symmetric {Lanczos} Algorithm with
Reorthogonalization Methods",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "61",
pages = "101--131",
year = "1984",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (65F10)",
MRnumber = "85k:65033",
MRreviewer = "Colette Lebaud",
bibdate = "Thu Jan 23 11:18:08 MST 1997",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "nla, eig, Lanczos algorithm, orthogonalization",
}
@Article{Simon:1984:LAP,
author = "Horst D. Simon",
title = "The {Lanczos} algorithm with partial
reorthogonalization",
journal = j-MATH-COMPUT,
volume = "42",
number = "165",
pages = "115--142",
month = jan,
year = "1984",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10 (65F25)",
MRnumber = "85h:65075",
MRreviewer = "O. O. Romanovs{\'k}i\u\i",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290P (Differential equations); C4170 (Differential
equations)",
corpsource = "Boeing Computer Services Co., Tukwila, WA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "eigenvalues; eigenvalues and eigenfunctions;
equations; full reorthogonalization; Lanczos algorithm;
linear differential; linear equations; orthogonality;
orthogonalization; partial; reorthogonalization;
roundoff errors; selective",
treatment = "T Theoretical or Mathematical",
}
@Book{Cullum:1985:LALa,
author = "Jane K. Cullum and Ralph A. Willoughby",
title = "{Lanczos} Algorithms for Large Symmetric Eigenvalue
Computations, Volume 1. Theory",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
pages = "xiv + 273",
year = "1985",
ISBN = "0-8176-3292-1 (Boston: set), 0-8176-3058-9 (Boston:
vol. 1), 0-8176-3294-8 (Boston: vol. 2), 3-7643-3292-6
(Basel: set), 3-7643-3058-9 (Basel: vol. 1),
3-7643-3294-8 (Basel: vol. 2)",
ISBN-13 = "978-0-8176-3292-2 (Boston: set), 978-0-8176-3058-4
(Boston: vol. 1), 978-0-8176-3294-6 (Boston: vol. 2),
978-3-7643-3292-1 (Basel: set), 978-3-7643-3058-3
(Basel: vol. 1), 978-3-7643-3294-5 (Basel: vol. 2)",
LCCN = "QA193 .C84 1985",
bibdate = "Mon Mar 6 15:34:09 GMT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.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",
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 (?) give any of their own.",
remark = "Volume 1. Theory",
subject = "Symmetric matrices; Data processing; Eigenvalues",
}
@Book{Cullum:1985:LALb,
author = "J. Cullum and R. A. Willoughby",
title = "{Lanczos} Algorithms for Large Symmetric Eigenvalue
Computations, Volume 2: Programs",
publisher = pub-BIRKHAUSER,
address = pub-BIRKHAUSER:adr,
year = "1985",
bibdate = "Fri Jun 10 12:38:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Cullum:1985:SLP,
author = "Jane Cullum and Ralph A. Willoughby",
title = "A survey of {Lanczos} procedures for very large real
`symmetric' eigenvalue problems",
journal = j-J-COMPUT-APPL-MATH,
volume = "12--13",
number = "??",
pages = "37--60",
month = may,
year = "1985",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(85)90006-8",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Fri Jun 10 16:10:44 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Madore:1985:KKT,
author = "J. Madore",
title = "{Kaluza--Klein} theory with the {Lanczos Lagrangian}",
journal = j-PHYS-LET-A,
volume = "110",
number = "6",
pages = "289--292",
day = "5",
month = aug,
year = "1985",
CODEN = "PYLAAG",
DOI = "https://doi.org/10.1016/0375-9601(85)90773-X",
ISSN = "0375-9601 (print), 1873-2429 (electronic)",
ISSN-L = "0375-9601",
bibdate = "Fri Jun 10 18:36:50 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Physics Letters A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759601",
}
@Article{Nour-Omid:1985:SCB,
author = "Bahram Nour-Omid and Ray W. Clough",
title = "Short communication: Block {Lanczos} method for
dynamic analysis of structures",
journal = j-EARTHQUAKE-ENG-STRUCT-DYN,
volume = "13",
number = "2",
pages = "271--275",
month = mar,
year = "1985",
CODEN = "IJEEBG",
DOI = "https://doi.org/10.1002/eqe.4290130210",
ISSN = "0098-8847 (print), 1096-9845 (electronic)",
ISSN-L = "0098-8847",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Earthquake engineering \& structural dynamics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1096-9845",
onlinedate = "28 Dec 2006",
}
@Article{Ojalvo:1985:PUL,
author = "I. U. Ojalvo",
title = "Proper use of {Lanczos} vectors for large eigenvalue
problems",
journal = j-COMP-STRUCTURES,
volume = "20",
number = "1--3",
pages = "115--120",
month = "????",
year = "1985",
CODEN = "CMSTCJ",
DOI = "https://doi.org/10.1016/0045-7949(85)90060-4",
ISSN = "0045-7949 (print), 1879-2243 (electronic)",
ISSN-L = "0045-7949",
bibdate = "Fri Jun 10 17:06:56 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
ajournal = "Comput. Struct.",
fjournal = "Computers and Structures",
journal-URL = "http://www.sciencedirect.com/science/journal/00457949",
}
@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/l/lanczos-cornelius.bib;
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 {Lanczos} algorithm for unsymmetric
matrices",
journal = j-MATH-COMPUT,
volume = "44",
number = "169",
pages = "105--124",
month = jan,
year = "1985",
CODEN = "MCMPAF",
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/l/lanczos-cornelius.bib;
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{Bauchau:1986:SEU,
author = "O. A. Bauchau",
title = "A solution of the eigenproblem for undamped gyroscopic
systems with the {Lanczos} algorithm",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "23",
number = "9",
pages = "1705--1713",
month = sep,
year = "1986",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620230910",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "22 Jun 2005",
}
@Article{Crisci:1986:TMP,
author = "M. R. Crisci",
title = "The tau method with perturbation term depending on the
differential operator",
journal = j-J-COMPUT-APPL-MATH,
volume = "15",
number = "1",
pages = "123--136",
month = may,
year = "1986",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(86)90245-1",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Mon Jun 13 14:53:57 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042786902451",
abstract = "The tau method approximates the solution of a
differential equation with a polynomial, which is the
exact solution of a differential equation obtained by
adding to the right hand side of the given equation a
perturbation term, consisting of a suitably chosen
linear combination of polynomials.\par
Until now the Chebyshev and Legendre polynomials have
been used to this purpose, but the determination of the
best perturbation term is, still, an open
problem.\par
In this paper a perturbation term depending on the
differential equation is chosen. For this formulation
of the tau method, the existence of an infinite
sequence of tau approximants and the convergence of the
error to zero is proved. An estimate of the local
truncation error is also given, and the stability
properties are discussed.\par
Numerical results are also reported.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Gupta:1986:SLS,
author = "Viney K. Gupta and Scott D. Zillmer and Robert E.
Allison",
title = "Solving Large-scale Dynamic Systems Using Band
{Lanczos} Method in {Rockwell NASTRAN} on {Cray X-MP}",
journal = j-NASA-CONF-PUBL,
pages = "236--246",
year = "1986",
CODEN = "NACPDX",
ISSN = "0191-7811",
bibdate = "Mon Aug 26 10:51:12 MDT 1996",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "The improved cost-effectiveness using better models,
more accurate and faster algorithms, and large-scale
computing offers more representative dynamic analyses.
The band Lanczos eigensolution method has been
implemented in Rockwell's version of 1984
COSMIC-released NASTRAN finite-element structural
analysis computer program to effectively solve for
structural vibration modes including those of large
complex systems exceeding 10,000 degrees of freedom.
The band Lanczos method is more reliable and accurate
and converges faster than the single vector Lanczos
Method. The band Lanczos method is comparable to the
subspace iteration method which is a block version of
the inverse power method. However, the subspace matrix
tends to be fully populated in the case of subspace
iteration and not as sparse as a band matrix.",
acknowledgement = ack-nhfb,
affiliation = "Rockwell Int, Los Angeles, CA, USA",
affiliationaddress = "Rockwell Int, Los Angeles, CA, USA",
classification = "408; 722; 723; 921; 931",
conference = "Fourteenth NASTRAN Users' Colloquium.",
fjournal = "NASA conference publication",
journalabr = "NASA Conf Publ",
keywords = "BAND LANCZOS METHOD; Computer Applications; COMPUTER
PROGRAMS; COMPUTER SYSTEMS, DIGITAL --- Fast Response
Capability; LARGE-SCALE DYNAMIC SYSTEMS; MATHEMATICAL
TECHNIQUES --- Eigenvalues and Eigenfunctions; ROCKWELL
NASTRAN; STRUCTURAL ANALYSIS; VIBRATIONS --- Analysis",
meetingaddress = "San Diego, CA, USA",
sponsor = "NASA, Washington, DC, USA",
}
@Article{Imiya:1986:SSS,
author = "Atsushi Imiya and Toshio Sasaki and Hidemitsu Ogawa",
title = "Signal smoothing by summation---generalized {Fejer}
method and generalized {Lanczos} method",
journal = j-ELECTRON-COMMUN-JPN-PART-1-COMMUN,
volume = "69",
number = "12",
pages = "21--28",
month = "????",
year = "1986",
DOI = "https://doi.org/10.1002/ecja.4410691203",
ISSN = "1520-6424 (print), 8756-6621 (electronic)",
ISSN-L = "1520-6424",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Electronics and Communications in Japan (Part I:
Communications)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1520-6424",
onlinedate = "23 Mar 2007",
}
@Article{Morgan:1986:GDM,
author = "Ronald B. Morgan and David S. Scott",
title = "Generalizations of {Davidson}'s method for computing
eigenvalues of sparse symmetric matrices",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "7",
number = "3",
pages = "817--825",
month = jul,
year = "1986",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "65F15 (65F35 65F50)",
MRnumber = "87g:65056",
bibdate = "Tue Apr 29 19:18:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "See \cite{Davidson:1975:NIC}.",
acknowledgement = ack-nhfb,
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Dept. of Math., Texas Univ., Austin, TX, USA",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "eigenpairs; eigenvalues; eigenvalues and
eigenfunctions; generalised Davidson's method; matrix
algebra; preconditioning techniques; sparse symmetric
matrices",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Moro:1986:LAM,
author = "Giorgio Moro and Jack H. Freed",
editor = "Jane Cullum and Ralph A. Willoughby",
booktitle = "{Large scale eigenvalue problems: proceedings of the
IBM Europe Institute Workshop on Large Scale Eigenvalue
Problems held in Oberlech, Austria, July 8--12, 1985}",
title = "The {Lanczos} Algorithm in Molecular Dynamics:
Calculation of Spectral Densities",
volume = "127",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
bookpages = "viii + 330",
pages = "143--161",
year = "1986",
DOI = "https://doi.org/10.1016/S0304-0208(08)72644-6",
ISBN = "0-444-70074-9 (paperback), 0-08-087238-7 (e-book)",
ISBN-13 = "978-0-444-70074-2 (paperback), 978-0-08-087238-4
(e-book)",
ISSN = "0304-0208",
LCCN = "QA193 .I26 1985",
bibdate = "Fri Jun 10 16:40:55 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Large Scale Eigenvalue Problems, Proceedings of the
IBM Europe Institute Workshop on Large Scale Eigenvalue
Problems",
series = "North-Holland Mathematics Studies",
acknowledgement = ack-nhfb,
xxbookpages = "v + 330",
}
@Article{Sehmi:1986:LAA,
author = "N. S. Sehmi",
title = "The {Lanczos} algorithm applied to {Kron}'s method",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "23",
number = "10",
pages = "1857--1872",
month = oct,
year = "1986",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620231006",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "22 Jun 2005",
}
@Article{Barbour:1987:UFL,
author = "I. M. Barbour and N.-E Behilil and P. E. Gibbs and M.
Rafiq and K. J. M. Moriarty and G. Schierholz",
title = "Updating fermions with the {Lanczos} method",
journal = j-J-COMPUT-PHYS,
volume = "68",
number = "1",
pages = "227--236",
month = jan,
year = "1987",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(87)90053-2",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:33 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999187900532",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Bostic:1987:ILM,
author = "S. Bostic and R. Fulton",
title = "Implementation of the {Lanczos} Method for Structural
Vibration Analysis on a Parallel Computer",
journal = j-COMP-STRUCTURES,
volume = "25",
pages = "395--404",
year = "1987",
CODEN = "CMSTCJ",
ISSN = "0045-7949 (print), 1879-2243 (electronic)",
ISSN-L = "0045-7949",
bibdate = "Fri Jun 10 12:38:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Structures",
journal-URL = "http://www.sciencedirect.com/science/journal/00457949",
}
@Article{Clutton-Brock:1987:GFL,
author = "M. Clutton-Brock",
title = "Generalized {Fej{\'e}r} and {Lanczos} kernels",
journal = j-SIAM-J-MATH-ANA,
volume = "18",
number = "1",
pages = "259--272",
month = jan,
year = "1987",
CODEN = "SJMAAH",
ISSN = "0036-1410 (print), 1095-7154 (electronic)",
ISSN-L = "0036-1410",
MRclass = "41A36 (42A10)",
MRnumber = "88d:41034",
MRreviewer = "W. A. Al-Salam",
bibdate = "Sun Nov 28 19:24:01 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/18/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Mathematical Analysis",
journal-URL = "http://epubs.siam.org/sima",
}
@Article{Coleman:1987:CPA,
author = "John P. Coleman",
title = "Complex polynomial approximation by the {Lanczos} $
\tau $-method: {Dawson}'s integral",
journal = j-J-COMPUT-APPL-MATH,
volume = "20",
number = "??",
pages = "137--151",
month = nov,
year = "1987",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(87)90131-2",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sun Jun 12 08:36:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0377042787901312",
abstract = "The Lanczos $ \tau $-method, with perturbations
proportional to Faber polynomials, is used to obtain
polynomial approximations for Dawson's integral on
circular sectors. An upper bound on the truncation
error is established for one form of the $ \tau
$-method, which gives near-minimax polynomial
approximations, and it is found that this bound
provides a useful estimate of the truncation error. The
Faber series for Dawson's integral on a circular sector
is also investigated. Numerical results show that the $
\tau $-method can produce polynomial approximations as
accurate as the truncated Faber series, with much less
effort than is involved in computing the Faber
coefficients.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@InProceedings{Cooley:1987:HFG,
author = "J. W. Cooley",
editor = "G. E. Crane",
booktitle = "Proceedings of the {ACM Conference on the History of
Scientific and Numeric Computation, Princeton, NJ May
13--15, 1987}",
title = "How the {FFT} gained acceptance",
publisher = pub-ACM,
address = pub-ACM:adr,
bookpages = "viii + 150",
year = "1987",
DOI = "https://doi.org/10.1145/41579.41589",
ISBN = "0-89791-229-2",
ISBN-13 = "978-0-89791-229-7",
LCCN = "QA297 .A32 1987",
bibdate = "Thu Jun 02 18:45:52 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib",
acknowledgement = ack-nhfb,
remark = "This is essentially the same as
\cite{Cooley:1990:HFG}.",
}
@Article{Cybenko:1987:EFL,
author = "George Cybenko",
title = "An explicit formula for {Lanczos} polynomials",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "99--115",
year = "1987",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18 65F30)",
MRnumber = "88d:65071",
MRreviewer = "Vasile I. Ionescu",
bibdate = "Thu Jan 23 11:18:08 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Ericsson:1987:LAF,
author = "Thomas Ericsson and Axel Ruhe",
title = "{L}{\'a}nczos algorithms and field of value rotations
for symmetric matrix pencils",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "733--746",
year = "1987",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15",
MRnumber = "88f:65056",
MRreviewer = "H. R. Schwarz",
bibdate = "Thu Jan 23 11:18:08 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Friedrichs:1987:SPM,
author = "Mark S. Friedrichs and Richard A. Friesner",
title = "Solution of the {Pauli} master equation via the
{Lanczos} algorithm",
journal = j-CHEM-PHYS-LETT,
volume = "137",
number = "3",
pages = "285--290",
day = "12",
month = jun,
year = "1987",
CODEN = "CHPLBC",
DOI = "https://doi.org/10.1016/0009-2614(87)80220-8",
ISSN = "0009-2614 (print), 1873-4448 (electronic)",
ISSN-L = "0009-2614",
bibdate = "Fri Jun 10 18:35:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Chemical Physics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00092614",
}
@TechReport{Golub:1987:SHC,
author = "Gene H. Golub and Dianne P. O'Leary",
title = "Some history of the conjugate gradient and {Lanczos}
algorithms: 1948--1976",
type = "Technical Report",
number = "TR-1859, UMIACS-TR-87-20",
institution = inst-U-MARYLAND-CS,
address = inst-U-MARYLAND-CS:adr,
pages = "51",
month = "??",
year = "1987",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
keywords = "Algorithms --- Bibliography",
}
@TechReport{Grimes:1987:DAL,
author = "R. Grimes and H. Simon",
title = "Dynamic Analysis with the {Lanczos} Algorithm on the
{SCS-40}",
number = "ETA-TR-43",
institution = BCS,
month = jan,
year = "1987",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Miller:1987:TSI,
author = "H. G. Miller and M. C. Steenkamp and C. J. Wright",
title = "A two-step iterative block {Lanczos} algorithm for a
dominant eigenspan",
journal = j-J-COMPUT-PHYS,
volume = "72",
number = "2",
pages = "383--392",
month = oct,
year = "1987",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(87)90089-1",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:37 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0021999187900891",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Nour-Omid:1987:LMH,
author = "Bahram Nour-Omid",
title = "{Lanczos} method for heat conduction analysis",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "24",
number = "1",
pages = "251--262",
month = jan,
year = "1987",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620240117",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "22 Jun 2005",
}
@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/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@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/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{Payne:1987:LAS,
author = "G. L. Payne",
title = "The {Lanczos} algorithm and spline expansions",
journal = j-NUCL-PHYS-A,
volume = "463",
number = "1--2",
pages = "139--144",
day = "16",
month = feb,
year = "1987",
CODEN = "NUPABL",
DOI = "https://doi.org/10.1016/0375-9474(87)90655-5",
ISSN = "0375-9474 (print), 1873-1554 (electronic)",
ISSN-L = "0375-9474",
bibdate = "Fri Jun 10 18:33:28 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Nuclear Physics A",
journal-URL = "http://www.sciencedirect.com/science/journal/03759474",
}
@Article{Saad:1987:LMS,
author = "Youcef Saad",
title = "On the {Lanczos} Method for Solving Symmetric Systems
with Several Right-Hand Sides",
journal = j-MATH-COMPUT,
volume = "48",
number = "178",
pages = "651--662",
month = apr,
year = "1987",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007834",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10 (65F50)",
MRnumber = "878697 (88d:65066)",
bibdate = "Sun Sep 5 09:21:22 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
JSTOR database; MathSciNet database;
Theory/Matrix.bib",
acknowledgement = ack-nhfb,
classcodes = "B0290B (Error analysis in numerical methods); B0290H
(Linear algebra); C4110 (Error analysis in numerical
methods); C4140 (Linear algebra)",
corpsource = "Dept. of Comput. Sci., Yale Univ., New Haven, CT,
USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximation; block; conjugate gradient algorithms;
error analysis; error bound; Galerkin technique; Krylov
subspace; Lanczos method; linear systems; matrix
algebra; orthogonalization; projection process;
right-hand; sides; sparse symmetric linear systems;
symmetric",
kwds = "nla, Lanczos algorithm, linear system",
treatment = "T Theoretical or Mathematical",
}
@Article{Wassam:1987:DLTa,
author = "W. A. {Wassam, Jr.} and Go. Torres-Vega and J.
Neito-Frausto",
title = "Dual {Lanczos} Transformation Theory: Exact Continued
Fraction Expression for Resonant $ \gamma $-ray
Absorption Spectrum of a Harmonically Bound Atom
Executing Classical Motion Described by {Smoluchowski}
Dynamics",
journal = j-CHEM-PHYS-LETT,
volume = "136",
number = "1",
pages = "26--30",
year = "1987",
CODEN = "CHPLBC",
ISSN = "0009-2614 (print), 1873-4448 (electronic)",
ISSN-L = "0009-2614",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
comment = "From the paper: ``\ldots{} with the aid of symbolic
manipulation techniques, we construct a previously
unknown exact continued fraction for the resonany
$\gamma$-ray absorption spectrum \ldots{}''. The system
used is {REDUCE} on a Burroughs.",
fjournal = "Chemical Physics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00092614",
}
@Article{Wassam:1987:DLTb,
author = "W. A. {Wassam, Jr.} and Go. Torres-Vega",
title = "Dual {Lanczos} Transformation Theory: Closed Set of
Algebraic Equations Connecting {Lanczos} Parameters
with Moments in Moment Expansions of Time-Dependent
Quantities",
journal = j-CHEM-PHYS-LETT,
volume = "134",
number = "4",
pages = "355--360",
year = "1987",
CODEN = "CHPLBC",
ISSN = "0009-2614 (print), 1873-4448 (electronic)",
ISSN-L = "0009-2614",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
comment = "From the paper: ``The utility of this set of equations
is illustrated by using them with the aid of symbolic
manipulation on a computer to construct a previously
unknown exact continued fraction for the spectral
density of the incoherent scattering function
\ldots{}.'' The system used is REDUCE on a Burroughs.
Appear enthusiastic about the possibilities for
computer algebra in related fields.",
fjournal = "Chemical Physics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00092614",
}
@Article{Gupta:1988:DBL,
author = "K. K. Gupta and C. L. Lawson",
title = "Development of a block {Lanczos} algorithm for free
vibration analysis of spinning structures",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "26",
number = "5",
pages = "1029--1037",
month = may,
year = "1988",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620260503",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "23 Jun 2005",
}
@Article{Kim:1988:SDA,
author = "Hyoung M. Kim and Roy R. {Craig, Jr.}",
title = "Structural dynamics analysis using an unsymmetric
block {Lanczos} algorithm",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "26",
number = "10",
pages = "2305--2318",
month = oct,
year = "1988",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620261012",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "23 Jun 2005",
}
@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/l/lanczos-cornelius.bib;
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/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
}
@Article{AresdeParga:1989:LP,
author = "Gonz{\'a}lo {Ares de Parga} and Oscar {Chavoya A.} and
Jos{\'e} L. {L{\'o}pez Bonilla}",
title = "{Lanczos} potential",
journal = j-J-MATH-PHYS,
volume = "30",
number = "6",
pages = "1294--1295",
month = jun,
year = "1989",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.528306",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "53C80 (83C60)",
MRnumber = "90h:53090",
bibdate = "Fri Jan 2 07:23:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Coutinho:1989:MST,
author = "Alvaro L. G. A. Coutinho and Luiz Landau and Luiz C.
Wrobel and Nelson F. F. Ebecken",
title = "Modal solution of transient heat conduction utilizing
{Lanczos} algorithm",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "28",
number = "1",
pages = "13--25",
month = jan,
year = "1989",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620280104",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "23 Jun 2005",
}
@Article{Cullum:1989:GNL,
author = "J. Cullum and W. Kerner and R. Willoughby",
title = "A Generalized Nonsymmetric {Lanczos} Procedure",
journal = j-COMP-PHYS-COMM,
volume = "53",
number = "1--3",
pages = "19--48",
month = may,
year = "1989",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(89)90146-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Jun 10 11:59:40 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
kwds = "nla, geig, Lanczos algorithm, nonsymmetric matrix",
}
@Article{Golub:1989:SHC,
author = "Gene H. Golub and Dianne P. O'Leary",
title = "Some History of the Conjugate Gradient and {Lanczos}
Algorithms: 1948--1976",
journal = j-SIAM-REVIEW,
volume = "31",
number = "1",
pages = "50--102",
month = mar,
year = "1989",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1031003",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65-03 (00A15 01A60 65-00 65Fxx 90-03)",
MRnumber = "90b:65003",
bibdate = "Sat Mar 29 09:54:31 MDT 2014",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib;
http://epubs.siam.org/toc/siread/31/1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://www.jstor.org/stable/2030847",
abstract = "The conjugate gradient and Lanczos algorithms for
solving linear systems of equations and eigenproblems
represent very important computational innovations of
the early 1950s. These methods came into wide use only
in the mid-1970s. Shortly thereafter, vector computers
and massive computer memories made it possible to use
these methods to solve problems which could not be
solved in any other way. Since that time, the
algorithms have been further refined and have become a
basic tool for solving a wide variety of problems on a
wide variety of computer architectures. The conjugate
gradient algorithm has also been extended to solve
nonlinear systems of equations and optimization
problems, and this has had tremendous impact on the
computation of unconstrained and constrained
optimization problems. This paper gives some of the
history of the conjugate gradient and Lanczos
algorithms and an annotated bibliography for the period
1948--1976.",
acknowledgement = ack-nhfb,
affiliation = "Stanford Univ",
affiliationaddress = "Stanford, CA, USA",
classification = "723; 921",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "Algorithms; Computer Programming--Algorithms;
Conjugate Gradient Algorithm; Lanczos Algorithm;
Mathematical Techniques; Optimization--Theory; Variable
Metric Algorithms",
mynote = "June 1987 Maryland TR-1859",
onlinedate = "March 1989",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods) \\ G.1.3 Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues \\ G.1.3 Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix
inversion",
}
@Book{Golub:1989:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
volume = "3",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
edition = "Second",
pages = "xix + 642",
year = "1989",
ISBN = "0-8018-3772-3 (hardcover), 0-8018-3739-1 (paperback)",
ISBN-13 = "978-0-8018-3772-2 (hardcover), 978-0-8018-3739-5
(paperback)",
LCCN = "QA188 .G65 1989",
MRclass = "65Fxx (65-02)",
MRnumber = "90d:65055",
MRreviewer = "Perry Smith",
bibdate = "Mon Oct 26 07:31:01 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/bibnet/subjects/domain-decomp.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
price = "US\$14.50",
series = "Johns Hopkins Series in the Mathematical Sciences",
ZMnumber = "0733.65016",
abstract = "Thoroughly revised, updated, and expanded by more than
one third, this new edition of Golub and Van Loan's
landmark book in scientific computing provides the
vital mathematical background and algorithmic skills
required for the production of numerical software. New
chapters on high performance computing use matrix
multiplication to show how to organize a calculation
for vector processors as well as for computers with
shared or distributed memories. Also new are
discussions of parallel vector methods for linear
equations, least squares, and eigenvalue problems.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "book; math; matrices --- data processing; matrices ---
informatique; na; nla",
libnote = "Not yet in my library.",
remark = "See review by G. W. Steward in Mathematics of
Computation, Vol. 56, No. 193 (Jan., 1991),
pp. 380--381.",
shorttableofcontents = "Preface to the Third Edition \\
Software \\
Selected References \\
Matrix Multiplication Problems / 1 \\
Matrix Analysis / 48 \\
General Linear Systems / 87 \\
Special Linear Systems / 133 \\
Orthogonalization and Least Squares / 206 \\
Parallel Matrix Computations / 275 \\
The Unsymmetric Eigenvalue Problem / 308 \\
The Symmetric Eigenvalue Problem / 391 \\
Lanczos Methods / 470 \\
Iterative Methods for Linear Systems / 508 \\
Functions of Matrices / 555 \\
Special Topics / 579 \\
Bibliography / 637 \\
Index / 687",
tableofcontents = "Preface to the First Edition / xi \\
Preface to the Second Edition / xv \\
Using the Book / xvii \\
1: Matrix Multiplication Problems / 1 \\
1.1 Basic Algorithms and Notations / 2 \\
1.2 Exploiting Structure / 16 \\
1.3 Block Matrices and Algorithms / 25 \\
1.4 Aspects of Vector Pipeline Computing / 35 \\
2: Matrix Analysis / 49 \\
2.1 Basic Ideas from Linear Algebra / 49 \\
2.2 Vector Norms / 53 \\
2.3 Matrix Norms / 55 \\
2.4 Finite Precision Matrix Computations / 60 \\
2.5 Orthogonality and the SVD / 70 \\
2.6 Projections and the CS Decomposition / 75 \\
2.7 The Sensitivity of Square Linear Systems / 79 \\
3: General Linear Systems / 86 \\
3.1 Triangular Systems / 86 \\
3.2 Computing the LU Factorization / 92 \\
3.3 Roundoff Analysis of Gaussian Elimination / 104 \\
3.4 Pivoting / 108 \\
3.5 Improving and Estimating Accuracy / 123 \\
4: Special Linear Systems / 133 \\
4.1 The $LDM^T$ and $LDL^T$ Factorizations / 134 \\
4.2 Positive Definite Systems / 139 \\
4.3 Banded Systems / 149 \\
4.4 Symmetric Indefinite Systems / 159 \\
4.5 Block Tridiagonal Systems / 170 \\
4.6 Vandermonde Systems / 178 \\
4.7 Toeplitz Systems / 183 \\
5: Orthogonalization and Least Squares / 193 \\
5.1 Householder and Givens Transformations / 194 \\
5.2 The $Q R$ Factorization / 211 \\
5.3 The Full Rank Least Squares Problem / 221 \\
5.4 Other Orthogonal Factorizations / 233 \\
5.5 The Rank Deficient Least Squares Problem / 241 \\
5.6 Weighting and Iterative Improvement / 250 \\
5.7 A Note on Square and Underdetermined Systems / 256
\\
6: Parallel Matrix Computations / 260 \\
6.1 Distributed Memory Gaxpy / 261 \\
6.2 Shared Memory Gaxpy / 276 \\
6.3 Parallel Matrix Multiplication / 288 \\
6.4 Ring Factorization Procedures / 301 \\
6.5 Mesh Factorization Procedures / 310 \\
6.6 Shared Memory Factorization Methods / 321 \\
7: The Unsymmetric Eigenvalue Problem / 331 \\
7.1 Properties and Decompositions / 332 \\
7.2 Perturbation Theory / 341 \\
7.3 Power Iterations / 351 \\
7.4 Hessenberg and Real Schur Forms / 361 \\
7.5 The Practical $Q R$ Algorithm / 373 \\
7.6 Invariant Subspace Computations / 382 \\
7.7 The $QZ$ Method for $A x = \lambda B x$ / 394 \\
8: The Symmetric Eigenvalue Problem / 409 \\
8.1 Properties, Decompositions, Perturbation Theory /
410 \\
8.2 The Symmetric $Q R$ Algorithm / 418 \\
8.3 Computing the SVD / 427 \\
8.4 Some Special Methods / 437 \\
8.5 Jacobi Methods / 444 \\
8.6 A Divide and Conquer Method / 459 \\
8.7 More Generalized Eigenvalue Problems / 466 \\
9: Lanczos Methods / 475 \\
9.1 Derivation and Convergence Properties / 476 \\
9.2 Practical Lanczos Procedures / 484 \\
9.3 Applications and Extensions / 494 \\
10: Iterative Methods for Linear Systems / 505 \\
10.1 The Standard Iterations / 506 \\
10.2 The Conjugate Gradient Method / 516 \\
10.3 Preconditioned Conjugate Gradient Methods / 527
\\
11: Functions of Matrices / 539 \\
11.1 Eigenvalue Methods / 540 \\
11.2 Approximation Methods / 546 \\
11.3 The Matrix Exponential / 555 \\
12: Special Topics / 561 \\
12.1 Some Constrained Least Squares Problems / 561 \\
12.2 Subset Selection Using the SVD / 571 \\
12.3 Total Least Squares / 576 \\
12.4 Comparing Subspaces Using the SVD / 581 \\
12.5 Some Modified Eigenvalue Problems / 587 \\
12.6 Updating the $Q R$ Factorization / 592 \\
Bibliography / 601 \\
Index / 635",
}
@Article{Greenbaum:1989:BSP,
author = "Anne Greenbaum",
title = "Behavior of Slightly Perturbed {Lanczos} and
Conjugate-Gradient Recurrences",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "113",
pages = "7--63",
year = "1989",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F10 (33A65)",
MRnumber = "90e:65044",
MRreviewer = "Zden{\v{e}}k Dost{\'a}l",
bibdate = "Thu Jan 23 11:18:08 MST 1997",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "nla, conjugate gradients, Lanczos algorithm, rounding
error",
}
@Article{Kress:1989:SSE,
author = "J. D. Kress and S. B. Woodruff and G. A. Parker and R.
T. Pack",
title = "Some strategies for enhancing the performance of the
block {Lanczos} method",
journal = j-COMP-PHYS-COMM,
volume = "53",
number = "1--3",
pages = "109--115",
month = may,
year = "1989",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(89)90151-3",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Jun 10 17:12:30 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Nex:1989:BLA,
author = "C. M. M. Nex",
title = "The block {Lanczos} algorithm and the calculation of
matrix resolvents",
journal = j-COMP-PHYS-COMM,
volume = "53",
number = "1--3",
pages = "141--146",
month = may,
year = "1989",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(89)90155-0",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Jun 10 17:19:40 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Nour-Omid:1989:ALM,
author = "B. Nour-Omid",
title = "Applications of the {Lanczos} method",
journal = j-COMP-PHYS-COMM,
volume = "53",
number = "1--3",
pages = "157--168",
month = may,
year = "1989",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/0010-4655(89)90157-4",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Jun 10 16:47:12 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib",
abstract = "In this paper we are concerned with the application of
the unsymmetric two sided Lanczos method to systems of
first order differential equations and its associated
problems; namely generalized eigenproblems and linear
systems of equations. The unsymmetric Lanczos method is
first used to generate two sets of vectors; the left
and right Lanczos vectors. These Lanczos vectors are
used directly in a method of weighted residual to
reduce the differential equations to a small
unsymmetric tridiagonal system. The advantage of this
method is that the reduced system can be solved
directly thus eliminating the usual computation of the
complex eigenpairs.\par
An algorithm is then derived by simplifying the two
sided Lanczos method for systems of equations with a
symmetric matrix pair. By appropriate choice of the
starting vectors we obtain an implementation of the
Lanczos method that is remarkably close to that in ref.
[9], but generalized to the case with indefinite matrix
coefficients. This modification results in a simple
relation between the left and right Lanczos vectors, a
symmetric tridiagonal, and a diagonal matrix. The
system of differential equations can then be reduced to
one with a symmetric tridiagonal and diagonal
coefficient matrices. The modified algorithm is also
suitable for eigenproblems with symmetric indefinite
matrices and for solution of systems of equations using
indefinite preconditioning matrices.\par
This approach is used to evaluate the vibration
response of a damped beam problem and a space mast
structure with a symmetric damping matrix arising from
velocity feedback control forces. In both problems,
accurate solutions were obtained with as few as 20
Lanczos vectors.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Nour-Omid:1989:LMD,
author = "B. Nour-Omid and M. E. Regelbrugge",
title = "{Lanczos} method for dynamic analysis of damped
structural systems",
journal = j-EARTHQUAKE-ENG-STRUCT-DYN,
volume = "18",
number = "8",
pages = "1091--1104",
month = nov,
year = "1989",
CODEN = "IJEEBG",
DOI = "https://doi.org/10.1002/eqe.4290180802",
ISSN = "0098-8847 (print), 1096-9845 (electronic)",
ISSN-L = "0098-8847",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Earthquake engineering \& structural dynamics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1096-9845",
onlinedate = "29 Nov 2006",
}
@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 = "Fri Nov 11 06:36:51 MST 2005",
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/tex/bib/compphyscomm1980.bib",
URL = "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
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",
}
@PhdThesis{Sadkane:1989:ANM,
author = "M. Sadkane",
title = "Analyse num{\'e}rique de la m{\'e}thode de
{Davidson}",
type = "{Ph.D. thesis}",
school = "UER math{\'e}matiques et Informatique,
l'universit{\'e} de Rennes",
address = "Rennes, France",
year = "1989",
bibdate = "Fri Jun 10 23:37:05 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "See \cite{Davidson:1975:NIC}.",
acknowledgement = ack-nhfb,
}
@Article{Sonneveld:1989:CFL,
author = "Peter Sonneveld",
title = "{CGS}, a fast {Lanczos}-type solver for nonsymmetric
linear systems",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "10",
number = "1",
pages = "36--52",
month = jan,
year = "1989",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "65F50",
MRnumber = "89k:65052",
bibdate = "Tue Apr 29 19:18:28 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
classification = "B0290H (Linear algebra); B0290P (Differential
equations); C4140 (Linear algebra); C4170 (Differential
equations)",
corpsource = "Delft Univ. of Technol., Netherlands",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "bi-conjugate gradients; conjugate gradients algorithm;
convergence rate; elliptic partial differential
equations; iterative methods; Lanczos-type method;
linear algebra; nonsymmetric sparse linear systems;
numerical methods; partial differential equations",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Cooley:1990:HFG,
author = "J. W. Cooley",
title = "How the {FFT} gained acceptance",
crossref = "Nash:1990:HSC",
pages = "133--140",
year = "1990",
bibdate = "Sat Jun 11 16:21:12 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib",
note = "Nowack \cite[p. 395]{Nowack:1994:DFA} quotes Cooley
from this paper: {\em it appears that Lanczos had the
FFT algorithm; and if he had had an electronic
computer, he would have been able to write a program
permitting him to go to arbitrarily high $N$}.",
acknowledgement = ack-nhfb,
remark = "This is essentially the same as
\cite{Cooley:1987:HFG}.",
}
@Article{Ferng:1990:ALM,
author = "W. R. Ferng and G. H. Golub and R. J. Plemmons",
title = "Adaptive {Lanczos} methods for recursive condition
estimation",
journal = j-PROC-SPIE,
volume = "1348",
pages = "326--337",
month = "????",
year = "1990",
CODEN = "PSISDG",
ISSN = "0277-786X (print), 1996-756X (electronic)",
ISSN-L = "0277-786X",
bibdate = "Mon Sep 9 11:37:15 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "This paper proposes an adaptive Lanczos Estimator
scheme for tracking the condition number of the
modified matrix over time. Applications to recursive
least squares computations using the covariance method
with sliding data windows are considered. Comparisons
are made with other adaptive and non-adaptive condition
estimators for recursive least squares problems.
Numerical experiments are reported.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
classification = "B0290H (Linear algebra); B6140 (Signal processing
and detection); C1240 (Adaptive system theory); C1260
(Information theory); C4140 (Linear algebra)",
fjournal = "Proceedings of the SPIE --- The International Society
for Optical Engineering",
keywords = "Adaptive Lanczos Estimator; Covariance method;
Modified matrix; Recursive condition estimation;
Recursive least squares computations; RLS method;
Signal processing; Sliding data windows",
thesaurus = "Adaptive filters; Least squares approximations; Matrix
algebra; Parameter estimation; Signal processing;
Variational techniques",
}
@Article{Kim:1990:CEU,
author = "Hyoung M. Kim and Roy R. {Craig, Jr.}",
title = "Computational enhancement of an unsymmetric block
{Lanczos} algorithm",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "30",
number = "5",
pages = "1083--1089",
day = "5",
month = oct,
year = "1990",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620300509",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "24 Jun 2005",
}
@InProceedings{Lawson:1990:LAP,
author = "Charles L. Lawson and Kajal K. Gupta",
title = "The {Lanczos} Algorithm for a Pure Imaginary
{Hermitian} Matrix",
crossref = "Cox:1990:RNC",
pages = "25--34",
year = "1990",
bibdate = "Tue Nov 2 19:30:33 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Leung:1990:LSM,
author = "A. Y. T. Leung",
title = "A {Lanczos}-Subspace Method for Generalized
Eigenproblems",
journal = j-COMPUT-AIDED-CIVIL-INFRASTRUCT-ENG,
volume = "5",
number = "2",
pages = "129--138",
month = jun,
year = "1990",
CODEN = "CCIEFR",
DOI = "https://doi.org/10.1111/j.1467-8667.1990.tb00048.",
ISSN = "1093-9687 (print), 1467-8667 (electronic)",
ISSN-L = "1093-9687",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer-Aided Civil and Infrastructure Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-8667",
onlinedate = "6 Nov 2008",
}
@Article{Papadrakakis:1990:NIL,
author = "M. Papadrakakis and S. Smerou",
title = "A new implementation of the {Lanczos} method in linear
problems",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "29",
number = "1",
pages = "141--159",
month = jan,
year = "1990",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620290110",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "24 Jun 2005",
}
@Article{Papadrakakis:1990:TNL,
author = "M. Papadrakakis",
title = "A truncated {Newton--Lanczos} method for overcoming
limit and bifurcation points",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "29",
number = "5",
pages = "1065--1077",
month = apr,
year = "1990",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620290511",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "24 Jun 2005",
}
@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/l/lanczos-cornelius.bib;
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/l/lanczos-cornelius.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/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",
mycrossref = "Cox:1990:RNC",
reviewer = "F. Uhlig (Auburn)",
}
@Book{Rivlin:1990:CPA,
author = "Theodore J. Rivlin",
title = "{Chebyshev} Polynomials: From Approximation Theory to
Algebra and Number Theory",
publisher = pub-WILEY,
address = pub-WILEY:adr,
edition = "Second",
pages = "xiii + 249",
year = "1990",
ISBN = "0-471-62896-4",
ISBN-13 = "978-0-471-62896-5",
LCCN = "QA404.5 .R58 1990",
bibdate = "Fri Apr 17 10:09:27 MDT 2009",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
series = "Pure and applied mathematics",
acknowledgement = ack-nhfb,
remark = "A Wiley-Interscience publication.",
subject = "Chebyshev polynomials",
xxURL = "http://www.loc.gov/catdir/description/wiley031/89022721.html;
http://www.loc.gov/catdir/toc/onix01/89022721.html",
}
@InProceedings{Boley:1991:MNL,
author = "D. Boley and G. H. Golub",
title = "A modified non-symmetric {Lanczos} algorithm and
applications",
crossref = "Vaccaro:1991:SSP",
pages = "189--196",
month = "????",
year = "1991",
bibdate = "Mon Sep 9 11:37:15 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Gives a brief description of a non-symmetric Lanczos
algorithm that does not require strict bi-orthogonality
among the generated vectors. Several applications are
mentioned. For example, it is shown how the vectors
generated are algebraically related to `controllable
space' and `observable space' for a related linear
dynamical system. The algorithm described is
particularly appropriate for large sparse problems.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Minnesota, Univ., Minneapolis,
MN, USA",
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
keywords = "Controllable space; Large sparse problems; Linear
dynamical system; Matrix eigenvalue computation;
Modified nonsymmetric Lanczos algorithm; Observable
space",
thesaurus = "Eigenvalues and eigenfunctions; Matrix algebra",
}
@Article{Boley:1991:NLA,
author = "Daniel Boley and Gene Golub",
title = "The nonsymmetric {Lanczos} algorithm and
controllability",
journal = j-SYST-CONTROL-LETT,
volume = "16",
number = "2",
pages = "97--105",
month = feb,
year = "1991",
CODEN = "SCLEDC",
ISSN = "0167-6911 (print), 1872-7956 (electronic)",
ISSN-L = "0167-6911",
MRclass = "93B05 (93B40)",
MRnumber = "92e:93004",
MRreviewer = "Alexander N. Shoshitaishvili",
bibdate = "Fri Dec 20 17:23:54 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Gives a brief description of a nonsymmetric Lanczos
algorithm that does not require strict bi-orthogonality
among the generated vectors. The authors show how the
vectors generated are algebraically related to
reachable space and observable space for a related
linear dynamical system. The algorithm described is
particularly appropriate for large sparse systems.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Comput. Sci. Dept., Minnesota Univ., Minneapolis, MN,
USA",
classification = "C1110 (Algebra); C1120 (Analysis); C1310 (Analysis
and synthesis methods); C1320 (Stability)",
fjournal = "Systems and Control Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01676911",
keywords = "Controllability; Large sparse systems; Linear
dynamical system; Nonsymmetric Lanczos algorithm;
Observability; Observable space; Reachable space;
Vectors",
pubcountry = "Netherlands",
thesaurus = "Algebra; Controllability; Linear systems;
Observability; Vectors",
}
@Article{Boley:1991:NLF,
author = "Daniel L. Boley and Sylvan Elhay and Gene H. Golub and
Martin H. Gutknecht",
title = "Nonsymmetric {Lanczos} and finding orthogonal
polynomials associated with indefinite weights",
journal = j-NUMER-ALGORITHMS,
volume = "1",
number = "1",
pages = "21--43",
month = "????",
year = "1991",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F15 (65F30 65F50 65G05)",
MRnumber = "93f:65033",
MRreviewer = "Alexander S. Babanin",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "The nonsymmetric Lanczos algorithm reduces a general
matrix to tridiagonal by generating two sequences of
vectors which satisfy a mutual bi-orthogonality
property. The process can proceed as long as the two
vectors generated at each stage are not mutually
orthogonal, otherwise the process breaks down. The
authors propose a variant that does not break down by
grouping the vectors into clusters and enforcing the
bi-orthogonality property only between different
clusters, but relaxing the property within clusters.
They show how this variant of the matrix Lanczos
algorithm applies directly to a problem of computing a
set of orthogonal polynomials and associated indefinite
weights with respect to an indefinite inner product,
given the associated moments. The authors discuss the
close relationship between the modified Lanczos
algorithm and the modified Chebyshev algorithm. They
further show the connection between this last problem
and checksum-based error correction schemes for
fault-tolerant computing.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Minnesota Univ., Minneapolis,
MN, USA",
classification = "B0290H (Linear algebra); B6120B (Codes); C4140
(Linear algebra)",
corpsource = "Dept. of Comput. Sci., Minnesota Univ., Minneapolis,
MN, USA",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "checksum-based error correction; error correction
codes; fault-tolerant computing; indefinite inner
product; indefinite weights; matrix algebra; matrix
Lanczos algorithm; modified Chebyshev algorithm;
modified Lanczos algorithm; mutual bi-orthogonality
property; nonsymmetric Lanczos algorithm; orthogonal
polynomials; polynomials; tridiagonal matrix",
pubcountry = "Switzerland",
thesaurus = "Error correction codes; Matrix algebra; Polynomials",
treatment = "T Theoretical or Mathematical",
}
@Article{Brezinski:1991:ABN,
author = "C. Brezinski and M. {Redivo Zaglia} and H. Sadok",
title = "Avoiding breakdown and near-breakdown in {Lanczos}
type algorithms",
journal = j-NUMER-ALGORITHMS,
volume = "1",
number = "3",
pages = "261--284",
month = sep,
year = "1991",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F10 (65F25)",
MRnumber = "92j:65041",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "See erratum \cite{Brezinski:1992:AAB}.",
acknowledgement = ack-nhfb,
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Lab. d'Anal. Numer. et d'Optimisation, Univ. des Sci.
et Tech. de Lille Flandres-Artois, Villeneuve d'Ascq,
France",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "conjugate gradient methods; iterative methods; Lanczos
type algorithms; matrix algebra; method of moments;
method of recursive zoom; near-breakdown; orthogonal
polynomials; rounding errors; systems of linear
equations; zero scalar product",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Chan:1991:TFS,
author = "T. F. Chan and L. {De Pillis} and H. A. van der
Vorst",
title = "A transpose-free squared {Lanczos} algorithm and
application to solving nonsymmetric linear systems",
number = "Preprint 690",
institution = "Utrecht University",
address = "Utrecht, The Netherlands",
year = "1991",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib",
acknowledgement = ack-nhfb,
}
@Article{Ferng:1991:ALM,
author = "William R. Ferng and Gene H. Golub and Robert J.
Plemmons",
title = "Adaptive {Lanczos} methods for recursive condition
estimation",
journal = j-NUMER-ALGORITHMS,
volume = "1",
number = "1",
pages = "1--20",
month = "????",
year = "1991",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F10 (65F20 65F35 93E10 94A12)",
MRnumber = "92h:65053",
MRreviewer = "De Hui Chen",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Estimates for the condition number of a matrix are
useful in many areas of scientific computing,
including: recursive least squares computations,
optimization, eigenanalysis, and general nonlinear
problems solved by linearization techniques where
matrix modification techniques are used. The purpose of
this paper is to propose an adaptive Lanczos estimator
scheme, which the authors call ale, for tracking the
condition number of the modified matrix over time.
Applications to recursive least squares (RLS)
computations using the covariance method with sliding
data windows are considered. ale is fast for relatively
small n-parameter problems arising in RLS methods in
control and signal processing, and is adaptive over
time, i.e., estimates at time t are used to produce
estimates at time t+1. Comparisons are made with other
adaptive and non-adaptive condition estimators for
recursive least squares problems. Numerical experiments
are reported indicating that ale yields a very accurate
recursive condition estimator.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); B6140 (Signal processing and
detection); C1260 (Information theory); C4130
(Interpolation and function approximation); C4140
(Linear algebra)",
corpsource = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Adaptive Lanczos estimator; adaptive Lanczos
estimator; Adaptive Lanczos methods; adaptive Lanczos
methods; Covariance method; covariance method; least
squares approximations; matrix algebra; Matrix
condition number; matrix condition number; Matrix
modification; matrix modification; numerical methods;
Recursive condition estimation; recursive condition
estimation; Recursive least squares computations;
recursive least squares computations; signal
processing; Sliding data windows; sliding data
windows",
pubcountry = "Switzerland",
thesaurus = "Least squares approximations; Matrix algebra;
Numerical methods; Signal processing",
treatment = "T Theoretical or Mathematical",
xxpages = "1--19",
}
@Article{Khelifi:1991:LMA,
author = "Mohamed Khelifi",
title = "{Lanczos} maximal algorithm for unsymmetric eigenvalue
problems",
journal = j-APPL-NUM-MATH,
volume = "7",
number = "2",
pages = "179--193",
month = feb,
year = "1991",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65F15",
MRnumber = "92e:65048",
MRreviewer = "V. L. Makarov",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Kim:1991:CLL,
author = "S. K. Kim and A. T. Chronopoulos",
title = "A class of {Lanczos-like} algorithms implemented on
parallel computers",
journal = j-PARALLEL-COMPUTING,
volume = "17",
number = "6--7",
pages = "763--778",
month = sep,
year = "1991",
CODEN = "PACOEJ",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
MRclass = "65F15 (65F50 65Y05)",
MRnumber = "92f:65045",
bibdate = "Mon Apr 14 12:07:40 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra); C4240P (Parallel programming
and algorithm theory)",
corpsource = "Dept. of Comput. Sci., Minnesota Univ., Minneapolis,
MN, USA",
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
keywords = "64-node NCUBE/seven hypercube; algorithms; conjugate
gradient; CRAY-2; eigenvalues; eigenvalues and
eigenfunctions; eigenvectors; extreme; global
communications; Lanczos-like algorithms; matrix
algebra; message; method; parallel; parallel computers;
parallel properties; passing systems; shared memory
systems; symmetric large sparse matrices;
synchronisation; synchronization point",
treatment = "P Practical",
}
@Article{Rajakumar:1991:LAA,
author = "C. Rajakumar and C. R. Rogers",
title = "The {Lanczos} algorithm applied to unsymmetric
generalized eigenvalue problem",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "32",
number = "5",
pages = "1009--1026",
day = "5",
month = oct,
year = "1991",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620320506",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "27 Jun 2005",
}
@TechReport{Stewart:1991:LLS,
author = "G. W. Stewart",
title = "{Lanczos} and linear systems",
type = "Technical Report",
number = "CS-TR 2641",
institution = "Department of Computer Science, University of
Maryland",
address = "College Park, MD, USA",
pages = "????",
year = "1991",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
mynote = "March",
}
@Article{Ye:1991:CAN,
author = "Qiang Ye",
title = "A convergence analysis for nonsymmetric {Lanczos}
algorithms",
journal = j-MATH-COMPUT,
volume = "56",
number = "194",
pages = "677--691",
month = apr,
year = "1991",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "91m:65115",
MRreviewer = "Zden{\v{e}}k Strako{\v{s}}",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
JSTOR database",
acknowledgement = ack-nhfb,
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Dept. of Math. and Stat., Calgary Univ., Alta.,
Canada",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algorithms; approximation bounds; convergence
analysis; convergence of numerical methods;
eigenfunctions; eigenvalues; eigenvalues and; matrix
algebra; nonsymmetric Lanczos; Ritz; Ritz values;
tridiagonal structure; vectors",
treatment = "T Theoretical or Mathematical",
}
@TechReport{Arioli:1992:BLT,
author = "M. Arioli and Iain S. Duff and D. Ruiz and M.
Sadkane",
title = "Block {Lanczos} techniques for accelerating the {Block
Cimmino} method",
number = "TR/PA/92/70",
institution = inst-CERFACS,
address = inst-CERFACS:adr,
year = "1992",
bibdate = "Sat Apr 16 15:27:17 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Published in \cite{Arioli:1995:BLT}.",
acknowledgement = ack-nhfb,
xxnote = "Check: same report, different titles for
\cite{Amestoy:1992:LACb,Arioli:1992:BLT}??",
}
@Article{Boley:1992:AFT,
author = "Daniel L. Boley and Richard P. Brent and Gene H. Golub
and Franklin T. Luk",
title = "Algorithmic Fault Tolerance Using the {Lanczos}
Method",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "312--332",
month = jan,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (94B05)",
MRnumber = "93f:65034",
MRreviewer = "Herbert J. Bernstein",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Boley:1992:LAH,
author = "Daniel L. Boley and Tong J. Lee and Franklin T. Luk",
title = "The {Lanczos} Algorithm and {Hankel} Matrix
Factorization",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "172",
pages = "109--135",
day = "15",
month = jul,
year = "1992",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Jan 22 09:07:50 MST 1997",
bibsource = "/usr/local/src/bib/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "nla, Hankel matrix, Lanczos algorithm, lud",
}
@Article{Brezinski:1992:AAB,
author = "C. Brezinski and M. {Redivo Zaglia} and H. Sadok",
title = "Addendum to: {``Avoiding breakdown and near-breakdown
in Lanczos type algorithms'' [Numer. Algorithms {\bf 1}
(1991), no. 3, 261--284, MR 92j:65041]}",
journal = j-NUMER-ALGORITHMS,
volume = "2",
number = "2",
pages = "133--136",
month = "????",
year = "1992",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F10 (65F25)",
MRnumber = "1 165 901",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "See \cite{Brezinski:1991:ABN}.",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Brezinski:1992:BFL,
author = "C. Brezinski and M. {Redivo Zaglia} and H. Sadok",
title = "A breakdown-free {Lanczos} type algorithm for solving
linear systems",
journal = j-NUM-MATH,
volume = "63",
number = "1",
pages = "29--38",
month = oct,
year = "1992",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F10 (65F25)",
MRnumber = "93f:65028",
bibdate = "Thu Jan 23 07:49:52 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Dallwig:1992:CCS,
author = "Stefan Dallwig and Norman Fahrer and Christoph
Schlier",
title = "The combination of complex scaling and the {Lanczos}
algorithm",
journal = j-CHEM-PHYS-LETT,
volume = "191",
number = "1--2",
pages = "69--76",
day = "27",
month = mar,
year = "1992",
CODEN = "CHPLBC",
DOI = "https://doi.org/10.1016/0009-2614(92)85370-P",
ISSN = "0009-2614 (print), 1873-4448 (electronic)",
ISSN-L = "0009-2614",
bibdate = "Fri Jun 10 17:09:40 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "We present a symbiosis of three very powerful
mathematical tools: the discrete variable
representation (DVR), complex scaling, and the Lanczos
algorithm, by which we demonstrate that the widespread
negative view on combining the Lanczos algorithm with
the complex coordinate method for large systems may be
too pessimistic. We apply a complex version of the DVR
method suitable for homogeneous operators in the DVR,
such as $ \hat {x} $ and make use of a M{\"o}bius
transform inducing a spectral shift, which enhances
significantly the efficiency of the complex symmetric
matrix adapted Lanczos algorithm. This is done without
any loss of the advantages provided by each method on
its own. A numerical application to a collinear A--B--A
molecule is given.",
acknowledgement = ack-nhfb,
fjournal = "Chemical Physics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/00092614",
}
@TechReport{Eijkhout:1992:QPC,
author = "Victor Eijkhout",
title = "Qualitative Properties of the Conjugate Gradient and
{Lanczos} Methods in a Matrix Framework",
type = "LAPACK Working Note",
number = "51",
institution = inst-UTK-CS,
address = inst-UTK-CS:adr,
month = may,
year = "1992",
bibdate = "Fri Apr 22 17:06:37 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "UT-CS-92-170, May 1992.",
URL = "http://www.netlib.org/lapack/lawns/lawn51.ps;
http://www.netlib.org/lapack/lawnspdf/lawn51.pdf",
acknowledgement = ack-nhfb,
}
@Article{Greenbaum:1992:PBF,
author = "Anne Greenbaum and Zden{\u{e}}k Strako{\u{s}}",
title = "Predicting the Behavior of Finite Precision {Lanczos}
and Conjugate Gradient Computations",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "121--137",
month = jan,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10 (65F15)",
MRnumber = "92j:65043",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
Parallel/par.lin.alg.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
mynote = "Courant Tech. Report No. 538, Jan 1991",
}
@Article{Gupta:1992:DFD,
author = "K. K. Gupta and C. L. Lawson and A. R. Ahmadi",
title = "On development of a finite dynamic element and
solution of associated eigenproblem by a block
{Lanczos} procedure",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "33",
number = "8",
pages = "1611--1623",
day = "30",
month = jun,
year = "1992",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620330805",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "27 Jun 2005",
}
@Article{Gutknecht:1992:CTU,
author = "Martin H. Gutknecht",
title = "A Completed Theory of the Unsymmetric {Lanczos}
Process and Related Algorithms, {Part I}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "2",
pages = "594--639",
month = apr,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10 (30E05 41A21 65F15)",
MRnumber = "93e:65053",
MRreviewer = "E. L. Yip",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Joubert:1992:LMS,
author = "Wayne Joubert",
title = "{Lanczos} Methods for the Solution of Nonsymmetric
Systems of Linear Equations",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "3",
pages = "926--943",
month = jul,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F10 (65F15)",
MRnumber = "93e:65054",
MRreviewer = "Heike Fa{\ss}bender",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Iterative methods in numerical linear algebra (Copper
Mountain, CO, 1990).",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Kuczynski:1992:ELE,
author = "J. Kuczy{\'n}ski and H. Wo{\'z}niakowski",
title = "Estimating the Largest Eigenvalue by the Power and
{Lanczos} Algorithms with a Random Start",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "4",
pages = "1094--1122",
month = oct,
year = "1992",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15",
MRnumber = "93g:65052",
MRreviewer = "Heike Fa{\ss}bender",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Medeiros:1992:NSA,
author = "Djalma Medeiros and G. G. Cabrera",
title = "Numerical study of antiferromagnetic {Heisenberg}
chains for spin {$ S = 1 / 2 $}, using the {Lanczos}
method",
journal = j-MAGN-MAGN-MATER,
volume = "104--107",
number = "part 2",
pages = "799--800",
day = "2",
month = feb,
year = "1992",
CODEN = "JMMMDC",
DOI = "https://doi.org/10.1016/0304-8853(92)90365-U",
ISSN = "0304-8853 (print), 1873-4766 (electronic)",
ISSN-L = "0304-8853",
bibdate = "Fri Jun 10 16:55:53 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Proceedings of the International Conference on
Magnetism, Part II.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Magnetism and Magnetic Materials",
journal-URL = "http://www.sciencedirect.com/science/journal/03048853",
}
@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/l/lanczos-cornelius.bib;
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",
}
@Book{Saad:1992:NML,
author = "Youcef Saad",
title = "Numerical methods for large eigenvalue problems",
publisher = pub-HALSTED,
address = pub-HALSTED:adr,
pages = "xii + 346",
year = "1992",
ISBN = "0-7190-3386-1 (UK), 0-470-21820-7 (US)",
ISBN-13 = "978-0-7190-3386-5 (UK), 978-0-470-21820-4 (US)",
LCCN = "QA188 .S18 1992",
MRclass = "65F15 (65-02 65F50)",
MRnumber = "1177405 (93h:65052)",
MRreviewer = "Cs. J. Heged{\H{u}}s",
bibdate = "Sun Sep 5 09:21:22 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
MathSciNet database",
series = "Algorithms and Architectures for Advanced Scientific
Computing",
acknowledgement = ack-nhfb,
keywords = "eigenvalues; nonsymmetric matrices",
xxaddress = pub-MANCHESTER-UNIV-PRESS:adr,
xxpublisher = pub-MANCHESTER-UNIV-PRESS,
}
@TechReport{Tong:1992:CSP,
author = "Charles H. Tong",
title = "A Comparative Study of Preconditioned {Lanczos}
Methods for Nonsymmetric Linear Systems",
type = "Report",
number = "SAND91-8240",
institution = "Sandia National Laboratories",
address = "Albuquerque, NM, USA",
pages = "????",
month = jan,
year = "1992",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Balasubramanian:1993:ABL,
author = "P. Balasubramanian and J. G. Jagadeesh and H. K. Suhas
and V. Ramamurti",
title = "Application of block {Lanczos} method for analysis of
cyclic symmetric structures",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "36",
number = "2",
pages = "273--285",
day = "30",
month = jan,
year = "1993",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620360207",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "28 Jun 2005",
}
@Article{Brezinski:1993:LTA,
author = "Claude Brezinski and Hassane Sadok",
title = "{Lanczos}-type algorithms for solving systems of
linear equations",
journal = j-APPL-NUM-MATH,
volume = "11",
number = "6",
pages = "443--473",
month = apr,
year = "1993",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65F15",
MRnumber = "94d:65026",
MRreviewer = "Zden{\v{e}}k Strako{\v{s}}",
bibdate = "Sat Feb 8 10:09:54 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Coppersmith:1993:SLE,
author = "Don Coppersmith",
title = "Solving linear equations over {$ {\rm GF}(2) $}: block
{Lanczos} algorithm",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "192",
pages = "33--60",
month = oct,
year = "1993",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F10 (11Y16 94A60)",
MRnumber = "94i:65044",
MRreviewer = "James Weldon Demmel",
bibdate = "Wed Jan 22 17:57:24 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Computational linear algebra in algebraic and related
problems (Essen, 1992).",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Davidson:1993:MMT,
author = "Ernest R. Davidson",
title = "Monster Matrices: Their Eigenvalues and Eigenvectors",
journal = j-COMPUT-PHYS,
volume = "7",
number = "5",
pages = "519--522",
month = sep,
year = "1993",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4823212",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:43 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computphys.bib",
note = "See \cite{Lin:1993:EDM}.",
URL = "https://aip.scitation.org/doi/10.1063/1.4823212",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
keywords = "Davidson--Liu algorithm; Lanczos algorithm;
matrix--vector products; sparse matrices",
}
@Article{Freund:1993:ILAb,
author = "Roland W. Freund and Martin H. Gutknecht and No{\"e}l
M. Nachtigal",
title = "An implementation of the look-ahead {Lanczos}
algorithm for non-{Hermitian} matrices",
journal = j-SIAM-J-SCI-COMP,
volume = "14",
number = "1",
pages = "137--158",
month = jan,
year = "1993",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15",
MRnumber = "93h:65048",
bibdate = "Tue Apr 29 18:15:07 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InCollection{Freund:1993:RALa,
author = "Roland W. Freund and Gene H. Golub and No{\"e}l M.
Nachtigal",
title = "Recent advances in {Lanczos}-based iterative methods
for nonsymmetric linear systems",
crossref = "Hussaini:1993:ATC",
pages = "137--162",
year = "1993",
MRclass = "65F10",
MRnumber = "95f:65066",
MRreviewer = "L. W. Ehrlich",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-sf,
}
@TechReport{Gellai:1993:CLB,
author = "Barbara Gellai",
title = "{Cornelius Lanczos}, a biographical essay",
type = "Report",
institution = "Department of Physics, North Carolina State
University",
address = "Raleigh, NC, USA",
year = "1993",
bibdate = "Thu Jun 09 17:59:19 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Higham:1993:CCL,
author = "Nicholas J. Higham",
editor = "M. Chu and others",
booktitle = "The {Lanczos} Collected Papers with Commentaries",
title = "{Commentary on C. Lanczos, ``Introduction'' to
``Tables of Chebyshev Polynomials $ S_n(x) $ and $
C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
1952, v--xxvi}",
publisher = "????",
address = "????",
year = "1993",
bibdate = "Wed Nov 1 08:00:18 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "To appear.",
acknowledgement = ack-njh,
}
@InProceedings{Jea:1993:LMS,
author = "Kang C. Jea and David M. Young",
title = "{Lanczos}-type methods for solving nonsymmetric linear
systems",
crossref = "Natori:1993:PPS",
pages = "14--24",
year = "1993",
MRclass = "65F10",
MRnumber = "95f:65070",
bibdate = "Wed Jan 17 10:13:02 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib",
acknowledgement = ack-nhfb,
}
@Article{Jones:1993:LAG,
author = "Mark T. Jones and Merrell L. Patrick",
title = "{Lanczos} algorithm for the generalized symmetric
eigenproblem on shared-memory architectures",
journal = j-APPL-NUM-MATH,
volume = "12",
number = "5",
pages = "377--389",
month = jul,
year = "1993",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Sat Feb 8 10:10:32 MST 1997",
bibsource = "Compendex database;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
affiliation = "Argonne Natl Lab",
affiliationaddress = "Argonne, IL, USA",
classification = "723.1; 921; 931.1",
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
journalabr = "Appl Numer Math",
keywords = "Algorithms; Buckling; Computer architecture;
Eigenvalues and eigenfunctions; Generalized symmetric
eigenproblem; Lanczos algorithm; Mathematical models;
Multiprocessing programs; Shared memory architectures;
Structural design; Vibrations (mechanical)",
}
@Article{Koslowski:1993:LCL,
author = "T. Koslowski and W. {Von Niessen}",
title = "Linear combination of {Lanczos} vectors: a
storage-efficient algorithm for sparse matrix
eigenvector computations",
journal = j-J-COMPUT-CHEM,
volume = "14",
number = "7",
pages = "769--774",
month = jul,
year = "1993",
CODEN = "JCCHDD",
DOI = "https://doi.org/10.1002/jcc.540140703",
ISSN = "0192-8651 (print), 1096-987X (electronic)",
ISSN-L = "0192-8651",
bibdate = "Thu Nov 29 14:54:22 MST 2012",
bibsource = "http://www.interscience.wiley.com/jpages/0192-8651;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputchem1990.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Chemistry",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1096-987X",
onlinedate = "7 Sep 2004",
}
@Article{Lancaster:1993:RRL,
author = "Peter Lancaster and Qiang Ye",
title = "{Rayleigh--Ritz} and {Lanczos} Methods for Symmetric
Matrix Pencils",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "185",
pages = "173--201",
month = may,
year = "1993",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A22)",
MRnumber = "94i:65050",
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/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
keywords = "nla, geig, symmetric, Rayleigh--Ritz method, Lanczos
algorithm",
}
@Article{Lin:1993:EDM,
author = "H. Q. Lin and J. E. Gubernatis and Harvey Gould and
Jan Tobochnik",
title = "Exact Diagonalization Methods for Quantum Systems",
journal = j-COMPUT-PHYS,
volume = "7",
number = "4",
pages = "400--??",
month = jul,
year = "1993",
CODEN = "CPHYE2",
DOI = "https://doi.org/10.1063/1.4823192",
ISSN = "0894-1866 (print), 1558-4208 (electronic)",
ISSN-L = "0894-1866",
bibdate = "Wed Apr 10 08:45:42 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computphys.bib",
note = "See \cite{Davidson:1993:MMT}.",
URL = "https://aip.scitation.org/doi/10.1063/1.4823192",
acknowledgement = ack-nhfb,
ajournal = "Comput. Phys",
fjournal = "Computers in Physics",
journal-URL = "https://aip.scitation.org/journal/cip",
keywords = "Lanczos algorithm; matrix--vector products; sparse
matrices",
}
@Article{Mai:1993:MLM,
author = "Tsun-Zee Mai",
title = "Modified {Lanczos} method for solving large sparse
linear systems",
journal = j-COMM-NUMER-METHODS-ENGRG,
volume = "9",
number = "1",
pages = "67--79",
month = jan,
year = "1993",
DOI = "https://doi.org/10.1002/cnm.1640090111",
ISSN = "1069-8299 (print), 1099-0887 (electronic)",
ISSN-L = "1069-8299",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Numerical Methods in Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-0887",
onlinedate = "21 Jun 2005",
}
@Article{Morgan:1993:PLA,
author = "Ronald B. Morgan and David S. Scott",
title = "Preconditioning the {Lanczos} algorithm for sparse
symmetric eigenvalue problems",
journal = j-SIAM-J-SCI-COMP,
volume = "14",
number = "3",
pages = "585--593",
month = may,
year = "1993",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15",
MRnumber = "93k:65032",
bibdate = "Tue Apr 29 18:15:07 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Namasivayam:1993:EAT,
author = "S. Namasivayam and E. L. Ortiz",
title = "Error analysis of the {Tau Method}: dependence of the
approximation error on the choice of perturbation
term",
journal = j-COMPUT-MATH-APPL,
volume = "25",
number = "1",
pages = "89--104",
month = jan,
year = "1993",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(93)90215-H",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:10 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219390215H",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Rajakumar:1993:ABE,
author = "C. Rajakumar and Ashraf Ali",
title = "Acoustic boundary element eigenproblem with sound
absorption and its solution using {Lanczos} algorithm",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "36",
number = "23",
pages = "3957--3972",
day = "15",
month = dec,
year = "1993",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620362303",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "29 Jun 2005",
}
@Article{Smith:1993:LBT,
author = "H. A. Smith and D. C. Sorensen and R. K. Singh",
title = "A {Lanczos}-based technique for exact vibration
analysis of skeletal structures",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "36",
number = "12",
pages = "1987--2000",
day = "30",
month = jun,
year = "1993",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620361203",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "29 Jun 2005",
}
@Article{Stewart:1993:EHS,
author = "G. W. Stewart",
title = "On the Early History of the Singular Value
Decomposition",
journal = j-SIAM-REVIEW,
volume = "35",
number = "4",
pages = "551--566",
month = dec,
year = "1993",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1035134",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "15-03 (01A55 01A60 15A18)",
MRnumber = "94f:15001",
bibdate = "Sat Mar 29 09:55:16 MDT 2014",
bibsource = "Compendex database;
http://epubs.siam.org/toc/siread/35/4;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
abstract = "This paper surveys the contributions of five
mathematicians --- Eugenio Beltrami (1835-1899),
Camille Jordan (1838-1921), James Joseph Sylvester
(1814-1897), Erhard Schmidt (1876-1959), and Hermann
Weyl (1885-1955) --- who were responsible for
establishing the existence of the singular value
decomposition and developing its theory.",
acknowledgement = ack-nhfb,
affiliation = "Univ of Maryland",
affiliationaddress = "College Park, MD, USA",
classification = "921.1; 921.6",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "Algorithms; Computational platforms; Determinants;
Geometry; History; Integral equations; Linear algebra;
Matrix algebra; Matrix decomposition; Quadratic form;
Singular value decomposition",
remark = "See page 556 for Lanczos's contributions to the SVD.",
onlinedate = "December 1993",
}
@Article{Weedon:1993:SHW,
author = "William H. Weedon and Weng Cho Chew and Jiun-Hwa Lin
and Apo Sezginer and Vladimir L. Druskin",
title = "A {$ 2.5 $D} scalar {Helmholtz} wave solution
employing the {Spectral Lanczos Decomposition Method
(SLDM)}",
journal = j-MICROW-OPT-TECHNOL-LETT,
volume = "6",
number = "10",
pages = "587--592",
month = aug,
year = "1993",
CODEN = "MOTLEO",
DOI = "https://doi.org/10.1002/mop.4650061008",
ISSN = "0895-2477 (print), 1098-2760 (electronic)",
ISSN-L = "0895-2477",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Microwave and Optical Technology Letters",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1098-2760",
onlinedate = "22 Jan 2007",
}
@Article{Abdel-Aziz:1994:SUI,
author = "Mohammedi R. Abdel-Aziz",
title = "Safeguarded use of the implicit restarted {Lanczos}
technique for solving non-linear structural
eigensystems",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "37",
number = "18",
pages = "3117--3133",
day = "30",
month = sep,
year = "1994",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620371807",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "29 Jun 2005",
}
@InProceedings{Aliaga:1994:UBC,
author = "Jose I. Aliaga and Vicente Hernandez and Daniel L.
Boley",
title = "Using the Block Clustered Nonsymmetric {Lanczos}
Algorithm to Solve Control Problems for {MIMO} Linear
Systems",
crossref = "Brown:1994:PCL",
pages = "387--389",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
keywords = "MIMO (multiple input, multiple output)",
}
@InProceedings{Anderson:1994:BHE,
author = "Paul R. Anderson",
title = "Black Hole Evaporation and Thermodynamics",
crossref = "Brown:1994:PCL",
pages = "543--544",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:1994:LWC,
author = "Anonymous",
title = "The life and works of {Cornelius Lanczos}. {Cornelius
Lanczos}: a photographic essay",
crossref = "Brown:1994:PCL",
pages = "xvii--xx",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Anonymous:1994:PPB,
author = "Anonymous",
title = "Published papers and books of {Cornelius Lanczos}",
crossref = "Brown:1994:PCL",
pages = "lx--lxv",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Ashtekar:1994:ISC,
author = "Abhay Ashtekar and Donald Marolf and Jos{\'e}
Mour{\~a}o",
title = "Integration on the Space of Connections Modulo Gauge
Transformations",
crossref = "Brown:1994:PCL",
pages = "143--160",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
note = "Plenary presentations, theoretical physics and
astrophysics.",
acknowledgement = ack-nhfb,
}
@InProceedings{Atkins:1994:NRA,
author = "William K. Atkins and William R. Davis",
title = "On a New Relationship among {Lanczos}' {$ H_{\mu
\lambda \kappa } $}, {$ Q_{\mu \lambda } $}, $q$
{Lagrange} Multipliers Leading to Coupled Spin-0 and
Spin-2 Fields Associated with {Riemannian} Geometry",
crossref = "Brown:1994:PCL",
pages = "506--508",
year = "1994",
bibdate = "Sat Jun 18 13:23:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Bai:1994:EAL,
author = "Zhao Jun Bai",
title = "Error analysis of the {Lanczos} algorithm for the
nonsymmetric eigenvalue problem",
journal = j-MATH-COMPUT,
volume = "62",
number = "205",
pages = "209--226",
month = jan,
year = "1994",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "94c:65045",
bibdate = "Tue Mar 25 15:38:13 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Kentucky Univ., Lexington, KY, USA",
classcodes = "B0290H (Linear algebra); B0290B (Error analysis in
numerical methods); C4140 (Linear algebra); C4110
(Error analysis in numerical methods)",
corpsource = "Dept. of Math., Kentucky Univ., Lexington, KY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algorithm; arithmetic; convergence; convergence of
numerical methods; eigenfunctions; eigenvalues and;
error analysis; finite-precision; Lanczos algorithm;
Lanczos vectors; nonsymmetric eigenvalue problem;
Paige's theory; Ritz triplets; Ritz values; symmetric
Lanczos",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Balakrishna:1994:CGF,
author = "B. S. Balakrishna and K. T. Mahahthappa",
title = "Composite Gauge Field Models and Dynamical Symmetry
Breaking",
crossref = "Brown:1994:PCL",
pages = "618--620",
year = "1994",
bibdate = "Sat Jun 18 13:38:48 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{BarberoG:1994:SDG,
author = "J. Fernando {Barbero G.} and Madhavan Varadarajan",
title = "Surprises in $ 2 + 1 $ Dimensional Geometry",
crossref = "Brown:1994:PCL",
pages = "576--578",
year = "1994",
bibdate = "Sat Jun 18 12:28:08 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Beem:1994:CCH,
author = "John K. Beem and Andrzej Krolak",
title = "Censorship and {Cauchy} Horizons",
crossref = "Brown:1994:PCL",
pages = "515--517",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Beffa:1994:PGA,
author = "Gloria Mar{\'\i} Beffa",
title = "{Poisson} Geometry of {Adler--Gel'fand--Dikii}
Manifolds",
crossref = "Brown:1994:PCL",
pages = "635--637",
year = "1994",
bibdate = "Sat Jun 18 13:41:37 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Benzi:1994:EPC,
author = "Michele Benzi and Carl D. Meyer",
title = "An Explicitly Preconditioner for the Conjugate
Gradient Method",
crossref = "Brown:1994:PCL",
pages = "294--296",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Berger:1994:NIC,
author = "B. K. Berger and D. Garfinkle and B.
Grubi{\v{s}}i{\'c} and V. Moncrief and V. Swamy",
title = "Numerical Investigation of Cosmological
Singularities",
crossref = "Brown:1994:PCL",
pages = "532--534",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Berry:1994:BLS,
author = "M. W. Berry",
title = "A Block {Lanczos} {SVD} Method with Adaptive
Reorthogonalization",
crossref = "Brown:1994:PCL",
pages = "329--331",
year = "1994",
bibdate = "Fri Jun 10 11:56:53 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Berry:1994:SLB,
author = "Michael W. Berry",
title = "Software for {Lanczos}-Based Algorithms",
crossref = "Brown:1994:PCL",
pages = "311--312",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Berry:1994:SPD,
author = "Michael W. Berry",
title = "A Survey of Public-Domain {Lanczos}-Based Software",
crossref = "Brown:1994:PCL",
pages = "332--334",
year = "1994",
bibdate = "Fri Jun 10 11:56:53 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Berryman:1994:RII,
author = "James G. Berryman",
title = "Resolution of Iterative Inverses in Seismic
Tomography",
crossref = "Brown:1994:PCL",
pages = "297--299",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
URL = "http://sepwww.stanford.edu/sep/berryman/PS/ltexlanczos.ps",
acknowledgement = ack-nhfb,
}
@InProceedings{Bjorck:1994:IRB,
author = "{\AA}ke Bj{\"o}rck and Eric Grimme and Paul {Van
Dooren}",
title = "An Implicitly Restarted Bidiagonalization Algorithm
for Ill-Posed Systems",
crossref = "Brown:1994:PCL",
pages = "305--307",
year = "1994",
bibdate = "Sat Jun 18 12:15:56 2011",
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}
@InProceedings{Bjorck:1994:LS,
author = "{\AA}ke Bj{\"o}rck",
title = "Least Squares",
crossref = "Brown:1994:PCL",
pages = "301--301",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
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}
@InProceedings{Blondin:1994:CMA,
author = "John Blondin and James Stone",
title = "Computational Magnetohydrodynamics in Astrophysics",
crossref = "Brown:1994:PCL",
pages = "431--451",
year = "1994",
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}
@InProceedings{Boley:1994:KSM,
author = "Daniel L. Boley",
title = "{Krylov} Space Methods in Linear Control and Model
Reduction: {A} Survey",
crossref = "Brown:1994:PCL",
pages = "377--379",
year = "1994",
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}
@InProceedings{Boley:1994:LMC,
author = "Daniel Boley",
title = "{Lanczos} Methods in Control and Signal Processing",
crossref = "Brown:1994:PCL",
pages = "375--376",
year = "1994",
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}
@InProceedings{Brown:1994:BHT,
author = "David Brown",
title = "Black Hole Thermodynamics in a Box",
crossref = "Brown:1994:PCL",
pages = "548--550",
year = "1994",
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}
@InProceedings{Brown:1994:RFS,
author = "David Brown",
title = "Reference Fluids as Standards of Space and Time",
crossref = "Brown:1994:PCL",
pages = "563--565",
year = "1994",
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}
@InProceedings{Bultheel:1994:FOP,
author = "Adhemar Bultheel and Marc {Van Barel}",
title = "Formal Orthogonal Polynomials for an Arbitrary Moment
Matrix and {Lanczos} Type Methods",
crossref = "Brown:1994:PCL",
pages = "273--275",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
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acknowledgement = ack-nhfb,
}
@InProceedings{Butcher:1994:LPA,
author = "John C. Butcher",
title = "{Laguerre} Polynomials: Applications in Numerical
Ordinary Differential Equations",
crossref = "Brown:1994:PCL",
pages = "371--373",
year = "1994",
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}
@InProceedings{Calvetti:1994:CGA,
author = "Daniella Calvetti and Lothar Reichel and Qin Zhang",
title = "Conjugate gradient algorithms for symmetric
inconsistent linear systems",
crossref = "Brown:1994:PCL",
pages = "267--272",
year = "1994",
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}
@Article{Calvetti:1994:IRL,
author = "D. Calvetti and L. Reichel and D. C. Sorensen",
title = "An implicitly restarted {Lanczos} method for large
symmetric eigenvalue problems",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "2",
pages = "1--21",
year = "1994",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:29 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
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acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@InProceedings{Calvetti:1994:MNA,
author = "Daniella Calvetti",
title = "Moments in Numerical Analysis",
crossref = "Brown:1994:PCL",
pages = "265--266",
year = "1994",
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@Article{Carey:1994:LBM,
author = "Cheryl M. M. Carey and Gene H. Golub and Kincho H.
Law",
title = "A {Lanczos}-based method for structural dynamic
reanalysis problems",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "37",
number = "16",
pages = "2857--2883",
day = "30",
month = aug,
year = "1994",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620371610",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
MRclass = "65F15 (15A18)",
MRnumber = "95d:65032",
bibdate = "Mon Jan 15 16:19:27 1996",
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https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "29 Jun 2005",
}
@InProceedings{Carlip:1994:TDQ,
author = "S. Carlip",
title = "Time in $ (2 + 1) $-Dimensional Quantum Gravity",
crossref = "Brown:1994:PCL",
pages = "560--562",
year = "1994",
bibdate = "Sat Jun 18 12:41:44 2011",
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acknowledgement = ack-nhfb,
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@InProceedings{Carlson:1994:OQP,
author = "Carl Carlson and Adam Szczepaniak",
title = "Open Questions in Particle Theory",
crossref = "Brown:1994:PCL",
pages = "603--604",
year = "1994",
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@InProceedings{Carlson:1994:PQC,
author = "Carl E. Carlson",
title = "Perturbative {QCD} Calculations of Heavy Meson
Decays",
crossref = "Brown:1994:PCL",
pages = "605--607",
year = "1994",
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@InProceedings{Chan:1994:CIO,
author = "Raymond Hon-fu Chan and F. R. Lin",
title = "Circulant Integral Operators and Circulant
Preconditioners",
crossref = "Brown:1994:PCL",
pages = "407--409",
year = "1994",
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@InProceedings{Chu:1994:ECA,
author = "Moody Chu and John G. Lewis",
title = "Eigenvalue Computations: Applications",
crossref = "Brown:1994:PCL",
pages = "249--250",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
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author = "Moody Chu and John G. Lewis",
title = "Eigenvalue computations: theory and algorithms",
crossref = "Brown:1994:PCL",
pages = "241--242",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Clarke:1994:CMM,
author = "David A. Clarke",
title = "{CMoC}: {A} Multidimensional {MHD} Algorithm Stable to
the Effects of Velocity Shear",
crossref = "Brown:1994:PCL",
pages = "436--439",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
keywords = "CMoC (the Consistent Method of Characteristics)",
}
@InProceedings{Cooley:1994:DF,
author = "James W. Cooley",
title = "Development of the {FFT}",
crossref = "Brown:1994:PCL",
pages = "393--394",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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@InProceedings{Cooley:1994:LFD,
author = "James W. Cooley",
title = "{Lanczos} and the {FFT}: {A} Discovery Before Its
Time",
crossref = "Brown:1994:PCL",
pages = "3--9",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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note = "Plenary presentations, computational mathematics",
acknowledgement = ack-nhfb,
}
@InProceedings{Craig:1994:AKL,
author = "Roy R. {Craig, Jr.} and Tzu-Jeng Su",
title = "Application of {Krylov\slash Lanczos} Methods to Model
Reduction and Control of Flexible Structures",
crossref = "Brown:1994:PCL",
pages = "380--383",
year = "1994",
bibdate = "Sat Jun 18 13:03:12 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Cui:1994:W,
author = "Charles K. Cui",
title = "Wavelets",
crossref = "Brown:1994:PCL",
pages = "411--412",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Cullum:1994:BLAa,
author = "Jane K. Cullum",
title = "Block {Lanczos} Algorithms for Large Matrix Eigenvalue
Problems: {Part I}. Real Symmetric Case",
crossref = "Brown:1994:PCL",
pages = "313--315",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
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}
@InProceedings{Cullum:1994:BLAb,
author = "Jane K. Cullum",
title = "Block {Lanczos} Algorithms for Large Matrix Eigenvalue
Problems: {Part II}. Nonsymmetric Case",
crossref = "Brown:1994:PCL",
pages = "316--318",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Cullum:1994:LAL,
author = "Jane K. Cullum",
title = "{Lanczos} Algorithms for Large Scale Symmetric and
Nonsymmetric Matrix Eigenvalue Problems",
crossref = "Brown:1994:PCL",
pages = "11--31",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Dai:1994:NSI,
author = "W. Dai and P. R. Woodward",
title = "Numerical Simulations for Ideal Magnetohydrodynamics",
crossref = "Brown:1994:PCL",
pages = "446--448",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Dolan:1994:LPW,
author = "P. Dolan and C. W. Kim",
title = "On the {Lanczos} Potential and its Wave Equation",
crossref = "Brown:1994:PCL",
pages = "497--499",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Dolan:1994:LT,
author = "P. Dolan and A. H. Taub",
title = "{Lanczos} {$H$}-tensor",
crossref = "Brown:1994:PCL",
pages = "488--489",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Drake:1994:EES,
author = "G. W. F. Drake",
title = "Essentially Exact Solutions of the Helium Problem",
crossref = "Brown:1994:PCL",
pages = "251--254",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Dunn:1994:PWE,
author = "C. T. Dunn",
title = "Plasma Waves in the Electron Foreshock",
crossref = "Brown:1994:PCL",
pages = "461--463",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
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}
@InProceedings{Edgar:1994:LTD,
author = "S. Brian Edgar",
title = "The {Lanczos} {$H$}-Tensor, Dimension and Tensor
Identities",
crossref = "Brown:1994:PCL",
pages = "494--496",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
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acknowledgement = ack-nhfb,
}
@InProceedings{El-Daou:1994:WSC,
author = "M. K. El-Daou and E. L. Ortiz",
title = "The Weighting Subspaces of Collocation and the {Tau
Method}",
crossref = "Brown:1994:PCL",
pages = "337--340",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Fernandes:1994:NPS,
author = "Rui L. Fernandes",
title = "A Note on {Poisson} Symmetric Spaces",
crossref = "Brown:1994:PCL",
pages = "638--642",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Finn:1994:OBI,
author = "Lee Samuel Finn",
title = "Observing Binary Inspiral with {LIGO}",
crossref = "Brown:1994:PCL",
pages = "479--481",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
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acknowledgement = ack-nhfb,
keywords = "Laser Interferometer Gravitational-wave Observatory
(LIGO)",
}
@InProceedings{Fischer:1994:CCS,
author = "Arthur E. Fischer and Vincent Moncrief",
title = "Classical and Conformal Superspace, Linearization
Stability, and the Reduction of {Einstein}'s
Equations",
crossref = "Brown:1994:PCL",
pages = "535--542",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Fischer:1994:IPF,
author = "Bernd Fischer and Roland W. Freund",
title = "An Inner Product-Free Conjugate Gradient-Like
Algorithm for {Hermitian} Positive Definite Systems",
crossref = "Brown:1994:PCL",
pages = "288--290",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Florides:1994:TMM,
author = "P. S. Florides",
title = "On the {Tolman} and {M{\o}ller} Mass-Energy Formulae
in {General Relativity}",
crossref = "Brown:1994:PCL",
pages = "503--505",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Frampton:1994:NGB,
author = "Paul H. Frampton",
title = "New Gauge Bosons for Multi-{TEV} pp Scattering",
crossref = "Brown:1994:PCL",
pages = "623--625",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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acknowledgement = ack-nhfb,
}
@InProceedings{Frampton:1994:SP,
author = "Paul Frampton and Tom Kephart and Marc Sher",
title = "Supercollider Physics",
crossref = "Brown:1994:PCL",
pages = "621--622",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
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}
@InProceedings{Frasca:1994:SPE,
author = "Sergio Frasca and Maria Alessandra Papa",
title = "Source Parameter Estimation and Filtering with Local
and Geographical Networks of Resonant Gravitational
Antennas",
crossref = "Brown:1994:PCL",
pages = "485--487",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
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URL = "http://www.roma1.infn.it/rog/array/lancz.html",
acknowledgement = ack-nhfb,
}
@InProceedings{Freund:1994:LAL,
author = "Roland W. Freund",
title = "The Look-Ahead {Lanczos} Process for Nonsymmetric
Matrices and its Applications",
crossref = "Brown:1994:PCL",
pages = "33--47",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
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URL = "ftp://netlib.att.com/netlib/att/cs/doc/94/4-06.ps.Z",
acknowledgement = ack-nhfb,
}
@InProceedings{Freund:1994:LTA,
author = "Roland W. Freund",
title = "{Lanczos}-Type Algorithms for Structured
Non-{Hermitian} Eigenvalue Problems",
crossref = "Brown:1994:PCL",
pages = "243--245",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
URL = "ftp://netlib.att.com/netlib/att/cs/doc/94/4-05.ps.Z",
acknowledgement = ack-nhfb,
scope = "linal",
}
@InProceedings{Galick:1994:ESL,
author = "Albert T. Galick",
title = "Efficient Solution of Large Sparse Eigenvalue Problems
in Microelectronic Simulation",
crossref = "Brown:1994:PCL",
pages = "258--260",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
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}
@Article{Gambolati:1994:CLO,
author = "Giuseppe Gambolati and Mario Putti",
title = "A comparison of {Lanczos} and optimization methods in
the partial solution of sparse symmetric
eigenproblems",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "37",
number = "4",
pages = "605--621",
day = "28",
month = feb,
year = "1994",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620370405",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "24 Jun 2005",
}
@InProceedings{Gander:1994:LCQ,
author = "Walter Gander and Gene H. Golub and Urs von Matt",
title = "Large Constrained Quadratic Problems",
crossref = "Brown:1994:PCL",
pages = "308--310",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
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}
@InProceedings{Ganguli:1994:IGL,
author = "G. Ganguli",
title = "Interdependence of Global and Local Physics in the
Magnetotail",
crossref = "Brown:1994:PCL",
pages = "470--472",
year = "1994",
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@InProceedings{Garfinkle:1994:CC,
author = "David Garfinkle",
title = "Cosmic censorship",
crossref = "Brown:1994:PCL",
pages = "513--514",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Garfinkle:1994:EPP,
author = "David Garfinkle and Steven Giddings and Andrew
Strominger",
title = "Entropy of Pair Production of Charged Black Holes",
crossref = "Brown:1994:PCL",
pages = "551--553",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Geers:1994:NSW,
author = "D. Glenn Geers and I. M. Bassett",
title = "Numerical Solution of the Wave Equation in an Optical
Fibre",
crossref = "Brown:1994:PCL",
pages = "255--257",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Gellai:1994:CLB,
author = "Barbara Gellai",
title = "{Cornelius Lanczos}: a biographical essay",
crossref = "Brown:1994:PCL",
pages = "xxi--xlviii",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Gotay:1994:SMP,
author = "Mark J. Gotay and Peter J. Olver",
title = "Symplectic Methods in Physics",
crossref = "Brown:1994:PCL",
pages = "633--634",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Greenbaum:1994:GCA,
author = "Anne Greenbaum and Lloyd N. Trefethen",
title = "{GMRES\slash CR} and {Arnoldi\slash Lanczos} as Matrix
Approximation Problems",
journal = j-SIAM-J-SCI-COMP,
volume = "15",
number = "2",
pages = "359--368",
month = mar,
year = "1994",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F10 (65F15)",
MRnumber = "MR1261459 (95e:65029)",
MRreviewer = "Zden{\v{e}}k Dost{\'a}l",
bibdate = "Tue Apr 29 18:25:50 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib",
note = "Iterative methods in numerical linear algebra (Copper
Mountain Resort, CO, 1992).",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@InProceedings{Greenbaum:1994:LCG,
author = "Anne Greenbaum",
title = "The {Lanczos} and Conjugate Gradient Algorithms in
Finite Precision Arithmetic",
crossref = "Brown:1994:PCL",
pages = "49--60",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Grimes:1994:SBL,
author = "Roger G. Grimes and John G. Lewis and Horst D. Simon",
title = "A Shifted Block {Lanczos} Algorithm for Solving Sparse
Symmetric Generalized Eigenproblems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "15",
number = "1",
pages = "228--272",
month = jan,
year = "1994",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479888151111",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (65F50 73K12 73V20)",
MRnumber = "94k:65054",
MRreviewer = "Colette Lebaud",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/15/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/15111",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Grubisic:1994:VDN,
author = "Boro Grubi{\v{s}}i{\'c}",
title = "Velocity Dominance near a Crushing Singularity",
crossref = "Brown:1994:PCL",
pages = "524--526",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
URL = "http://xxx.lanl.gov/abs/gr-qc/9404056",
acknowledgement = ack-nhfb,
}
@InProceedings{Gsponer:1994:LER,
author = "Andr{\'e} A. Gsponer and Jean-Pierre Hurni",
title = "{Lanczos}'s Equation to Replace {Dirac}'s Equation?",
crossref = "Brown:1994:PCL",
pages = "509--512",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Guarracino:1994:PBL,
author = "Mario Rosario Guarracino and Francesca Perla",
title = "A Parallel Block {Lanczos} Algorithm for Distributed
Memory Architectures",
journal = j-PARALLEL-ALGORITHMS-APPL,
volume = "4",
number = "3--4",
pages = "211--221",
month = "????",
year = "1994",
CODEN = "PAAPEC",
DOI = "https://doi.org/10.1080/10637199408915465",
ISSN = "1063-7192",
ISSN-L = "1026-7689",
bibdate = "Fri Jul 11 06:45:41 MDT 2008",
bibsource = "http://pixel.dma.unina.it/ResearchNLA_mc.html;
http://ventotene.dma.unina.it/mathsoft_ing.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.informaworld.com/smpp/content~content=a777314732",
acknowledgement = ack-nhfb,
fjournal = "Parallel Algorithms and Applications",
journal-URL = "http://www.tandfonline.com/loi/gpaa20",
}
@Article{Gutknecht:1994:CTU,
author = "Martin H. Gutknecht",
title = "A Completed Theory of the Unsymmetric {Lanczos}
Process and Related Algorithms, {Part II}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "15",
number = "1",
pages = "15--58",
month = jan,
year = "1994",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479890188803",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F30",
MRnumber = "95d:65039",
MRreviewer = "E. L. Yip",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/15/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/18880",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Gutknecht:1994:LPP,
author = "Martin H. Gutknecht",
title = "The {Lanczos} process and {Pad{\'e}} approximation",
crossref = "Brown:1994:PCL",
pages = "61--75",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
kwds = "nla, Lanczos algorithm, Krylov sequence, Pade
approximation",
}
@InProceedings{Halliwell:1994:DFQ,
author = "Jonathan J. Halliwell",
title = "Decoherence and the Foundations of Quantum Mechanics",
crossref = "Brown:1994:PCL",
pages = "589--590",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Halliwell:1994:QMH,
author = "J. J. Halliwell",
title = "Quantum-Mechanical Histories and the {Uncertainty
Principle}: An Information-Theoretic Approach",
crossref = "Brown:1994:PCL",
pages = "600--602",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Hammon:1994:LTG,
author = "K. S. Hammon and L. K. Norris",
title = "The {Lanczos} {$H$}-tensor and Generalized Affine
Geometry",
crossref = "Brown:1994:PCL",
pages = "500--502",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Hartle:1994:QDQ,
author = "James B. Hartle",
title = "Quasiclassical Domains in a Quantum Universe",
crossref = "Brown:1994:PCL",
pages = "161--172",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Hendrikx:1994:MIE,
author = "Koen Hendrikx and Marc {Van Burel} and Adhemar
Bultheel",
title = "{MatMan}: An Interactive Environment for Using and
Testing Linear Algebra Software",
crossref = "Brown:1994:PCL",
pages = "326--328",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
keywords = "Matlab; MatMan (Matrix Manipulator)",
}
@InProceedings{Husain:1994:CCN,
author = "Viqar Husain",
title = "Conserved Currents for Non-Linear Gravitons",
crossref = "Brown:1994:PCL",
pages = "582--584",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Isenberg:1994:CPG,
author = "James Isenberg",
title = "{Cauchy} Problem of {General Relativity}",
crossref = "Brown:1994:PCL",
pages = "527--528",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Jaimoukha:1994:MRL,
author = "Imad M. Jaimoukha and Ebrahim M. Kasenally",
title = "Model reduction of large scale systems via the
{Arnoldi} process",
crossref = "Brown:1994:PCL",
pages = "384--386",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Ji:1994:LV,
author = "Chueng-Ryong Ji",
title = "The Lightcone Vacuum",
crossref = "Brown:1994:PCL",
pages = "615--617",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Jones:1994:SGE,
author = "Mark T. Jones and Paul E. Plassman",
title = "Software for the Generalized Eigenproblem on
Distributed Memory Architectures",
crossref = "Brown:1994:PCL",
pages = "322--325",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Karlberg:1994:GQF,
author = "Lennart Karlberg and Hans Wallin",
title = "General quadrature formulas and {Pad{\'e} type
approximants}",
crossref = "Brown:1994:PCL",
pages = "368--370",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Karolyhazy:1994:GEB,
author = "F. Karolyhazy",
title = "Gravitation and the Eventual Breakdown of the
Quantummechanical Superposition Principle",
crossref = "Brown:1994:PCL",
pages = "597--599",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Kephart:1994:GNS,
author = "Thomas W. Kephart",
title = "Gravity, Naturalness, and the Strong {CP} Problem",
crossref = "Brown:1994:PCL",
pages = "626--628",
year = "1994",
bibdate = "Sat Jun 18 13:40:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Khajah:1994:UHP,
author = "H. G. Khajah and E. L. Ortiz",
title = "Ultra-high precision computations",
journal = j-COMPUT-MATH-APPL,
volume = "27",
number = "7",
pages = "41--57",
month = apr,
year = "1994",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(94)90148-1",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 19:11:20 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122194901481",
abstract = "We describe a machine independent Fortran subroutine
which performs the four basic arithmetic operations
with a degree of accuracy prescribed by the user.
Tables of Chebyshev expansions of orders 48 and 50 for
some basic mathematical functions are obtained as a
result of applying this subroutine in conjunction with
the recursive formulation of the Tau Method. A recently
devised technique for the sharp determination of upper
and lower error bounds for Tau Method approximations
enables us to find the degree $n$ required to achieve a
prescribed accuracy $ \epsilon $ over a given interval
$ [a, b] $. A number of practical illustrations are
given.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., Imperial Coll. of Sci., Technol. and
Med., London, UK",
classification = "C6140D (High level languages); C7310 (Mathematics)",
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "$\cos(\pi x)$; $\sin(\pi x)$; $z \exp(z) \Ei(-z)$;
$\erf(x) / x$; $\exp(-x^2)$; $\exp(x)$; $x \exp(x^2)
erfc(x)$; Arithmetic operations; Chebyshev expansions;
Lower error bounds; Machine independent Fortran
subroutine; Mathematical functions; Tau method; Upper
error bounds",
pubcountry = "UK",
thesaurus = "FORTRAN; Mathematics computing",
}
@InProceedings{Kiefer:1994:SGP,
author = "Claus Kiefer",
title = "Semiclassical Gravity and the Problem of Time",
crossref = "Brown:1994:PCL",
pages = "566--569",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Klimas:1994:VSF,
author = "Alex Klimas",
title = "{Vlasov} Simulation with Filamentation Removed",
crossref = "Brown:1994:PCL",
pages = "458--460",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Knizhnerman:1994:SLD,
author = "Leonid Knizhnerman and Vladimir Druskin and Qing-Huo
Liu and Fikri J. Kuchuk",
title = "Spectral {Lanczos} decomposition method for solving
single-phase fluid flow porous media",
journal = j-NUMER-METHODS-PARTIAL-DIFFER-EQU,
volume = "10",
number = "5",
pages = "569--580",
month = sep,
year = "1994",
CODEN = "NMPDEB",
DOI = "https://doi.org/10.1002/num.1690100504",
ISSN = "0749-159x (print), 1098-2426 (electronic)",
ISSN-L = "0749-159X",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Methods for Partial Differential Equations",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1098-2426",
onlinedate = "20 Jun 2005",
}
@InProceedings{Krauss-Varban:1994:SGW,
author = "D. Krauss-Varban and N. Omidi and M. E. McKean",
title = "Shock-Generated Waves as a Source of Magnetosheath
Turbulence",
crossref = "Brown:1994:PCL",
pages = "464--466",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Krolak:1994:NSS,
author = "Andrzej Kr{\'o}lak and Andrzej Czyrka and Janusz Gaber
and Wies{\l}aw Rudnicki",
title = "On the Nature and Strength of Singularities in the
{Szekeres} Quasispherical Collapse",
crossref = "Brown:1994:PCL",
pages = "518--520",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Kuchar:1994:PTQ,
author = "Karl V. Kucha{\v{r}}",
title = "The Problem of Time in Quantum Gravity",
crossref = "Brown:1994:PCL",
pages = "555--556",
year = "1994",
bibdate = "Sat Jun 18 12:39:04 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Kucharek:1994:IPI,
author = "H. Kucharek and M. Scholer",
title = "Interstellar Pick-up Ions at the Heliospheric
Termination Shock",
crossref = "Brown:1994:PCL",
pages = "473--475",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Kuczynski:1994:PBE,
author = "J. Kuczy{\'n}ski and H. Wo{\'z}niakowski",
title = "Probabilistic Bounds on the Extremal Eigenvalues and
Condition Number by the {Lanczos} Algorithm",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "15",
number = "2",
pages = "672--691",
month = apr,
year = "1994",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479892230456",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (65F10)",
MRnumber = "95d:65033",
MRreviewer = "Marc Van Barel",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/15/2;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/23045",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Lax:1994:CLH,
author = "Peter D. Lax",
title = "{Cornelius Lanczos} (1893--1974), and the {Hungarian}
phenomenon in science and mathematics",
crossref = "Brown:1994:PCL",
pages = "xlix--lii",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Lee:1994:HSM,
author = "L. C. Lee and Y. Lin",
title = "A Hybrid Simulation of Magnetopause",
crossref = "Brown:1994:PCL",
pages = "467--469",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Lewandowski:1994:DGT,
author = "Jerzy Lewandowski",
title = "Differential Geometry for the Space of Connections
Modulo Gauge Transformations",
crossref = "Brown:1994:PCL",
pages = "573--575",
year = "1994",
bibdate = "Sat Jun 18 12:28:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
xxtitle = "Differential Geometry on {$\bar{\mathcal{A} /
\mathcal{G}}$}",
}
@InProceedings{Lewis:1994:PSO,
author = "John G. Lewis and Roger G. Grimes",
title = "Preserving Semi-Orthogonality in Practice",
crossref = "Brown:1994:PCL",
pages = "319--321",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Louko:1994:GSW,
author = "Jorma Louko and Donald Marolf",
title = "Global Structure of {Witten}'s $ 2 + 1 $ Gravity on {$
\mathbf {R} \times T^2 $}",
crossref = "Brown:1994:PCL",
pages = "579--581",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Mann:1994:CQP,
author = "R. B. Mann",
title = "Classical and Quantum Properties of {Liouville} Black
Holes",
crossref = "Brown:1994:PCL",
pages = "545--547",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@TechReport{Marques:1994:SPC,
author = "Osni A. Marques and Vincent Toumazou",
title = "Spectral Portrait Computation by a {Lanczos} Method
(Normal Equation Version)",
type = "Technical Report",
number = "TR/PA/95/02",
institution = "CERFACS",
address = "Toulouse, France",
pages = "????",
month = dec,
year = "1994",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Marx:1994:RCL,
author = "George Marx",
title = "The roots of {Cornelius Lanczos}",
crossref = "Brown:1994:PCL",
pages = "liii--lvii",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Masson:1994:EST,
author = "David R. Masson",
title = "Explicit Spectral Theory: From {Chebyshev} to
{Askey--Wilson}",
crossref = "Brown:1994:PCL",
pages = "359--364",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Matsumoto:1994:CMJ,
author = "R. Matsumoto and K. Shibata and T. Yokoyama",
title = "Computational Magnetohydrodynamics of Jets, Loops, and
Flares in Astrophysics",
crossref = "Brown:1994:PCL",
pages = "443--445",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Nagy:1994:IIR,
author = "James G. Nagy",
title = "Iterative Image Restoration Using {FFT}-Based
Preconditioners",
crossref = "Brown:1994:PCL",
pages = "401--403",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Ng:1994:FFB,
author = "Michael Kwok-Po Ng",
title = "Fast {FFT}-based Conjugate Gradient Algorithm for the
Applications in Signal Processing",
crossref = "Brown:1994:PCL",
pages = "404--406",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Nowack:1994:DFA,
author = "Robert Nowack",
title = "Development of the {FFT} and Applications in
Geophysics",
crossref = "Brown:1994:PCL",
pages = "395--397",
year = "1994",
bibdate = "Sat Jun 11 16:15:19 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib",
URL = "http://web.ics.purdue.edu/~nowack/nowackpubs-dir/Lanczos-nowackfft1994.pdf",
abstract = "The development of the fast Fourier transform, or FFT,
has had a major impact on most scientific fields. One
of the earliest ``recent'' discoveries of the FTT was
by Danielson and Lanczos in 1942, although the method
was made widespread through the work of Cooley and
Tukey in 1965. In the geophysical sciences, the FFT has
been utilized in a wide variety of applications
including forward modeling, data processing and
inversion methods.",
acknowledgement = ack-nhfb,
}
@InProceedings{Opfer:1994:NID,
author = "G. Opfer",
title = "On the Number of Integer Dilation Matrices Used in
Wavelet Theory",
crossref = "Brown:1994:PCL",
pages = "426--428",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Ortiz:1994:CP,
author = "Eduardo L. Ortiz",
title = "{Chebyshev} Polynomials",
crossref = "Brown:1994:PCL",
pages = "357--358",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Ortiz:1994:TM,
author = "Eduardo L. Ortiz",
title = "{Tau Method}",
crossref = "Brown:1994:PCL",
pages = "335--336",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Ortiz:1994:TMN,
author = "Eduardo L. Ortiz",
title = "The {Tau Method} and the Numerical Solution of
Differential Equations: Past and Recent Research",
crossref = "Brown:1994:PCL",
pages = "77--81",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Paige:1994:KSP,
author = "C. C. Paige",
title = "{Krylov} Subspace Processes, {Krylov} Subspace
Methods, and Iteration Polynomials",
crossref = "Brown:1994:PCL",
pages = "83--92",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@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/l/lanczos-cornelius.bib;
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",
acknowledgement = ack-nhfb,
}
@InProceedings{Pearle:1994:PWC,
author = "Philip Pearle",
title = "Putting wavefunction collapse ``in the equations and
not just the talk''",
crossref = "Brown:1994:PCL",
pages = "594--596",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Petiot:1994:GIE,
author = "D. Petiot and Y. (Yasushi) Takahashi",
title = "Gauge Invariant Energy-Momentum Tensor in Spinor
Electrodynamics",
crossref = "Brown:1994:PCL",
pages = "173--186",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Pini:1994:TFL,
author = "G. Pini",
title = "Transpose-Free {Lanczos}-Type Schemes on Transputer
Network",
journal = j-PARALLEL-ALGORITHMS-APPL,
volume = "3",
number = "3--4",
pages = "249--260",
month = "????",
year = "1994",
CODEN = "PAAPEC",
DOI = "https://doi.org/10.1080/10637199408962541",
ISSN = "1063-7192",
ISSN-L = "1026-7689",
bibdate = "Fri Jul 11 06:45:41 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.informaworld.com/smpp/content~content=a779167060",
acknowledgement = ack-nhfb,
fjournal = "Parallel Algorithms and Applications",
journal-URL = "http://www.tandfonline.com/loi/gpaa20",
}
@InProceedings{Piran:1994:RBN,
author = "Tsvi Piran",
title = "$ \gamma $-Ray Bursts and Neutron Star Mergers",
crossref = "Brown:1994:PCL",
pages = "187--199",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Plemmons:1994:FSP,
author = "Robert J. Plemmons",
title = "The {FFT} in Signal Processing",
crossref = "Brown:1994:PCL",
pages = "399--400",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Prestin:1994:DPT,
author = "J{\"u}rgen Prestin and Ewald Quak",
title = "Decay Properties of Trigonometric Wavelets",
crossref = "Brown:1994:PCL",
pages = "413--415",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Rappoport:1994:TMC,
author = "Juri M. Rappoport",
title = "The {Tau-Method} and the Computation of the {Bessel}
Functions of the Complex Order",
crossref = "Brown:1994:PCL",
pages = "353--355",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Rimini:1994:SLA,
author = "Alberto Rimini",
title = "The Spontaneous Localization Approach to Quantum
Measurement",
crossref = "Brown:1994:PCL",
pages = "591--593",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Ron:1994:FSB,
author = "Amos Ron and Zuowei Shen",
title = "Frames and Stable Bases for Subspaces of {$ L_2
(\mathbb {R}^d) $} the Duality Principle of
{Weyl--Heisenberg} Sets",
crossref = "Brown:1994:PCL",
pages = "422--425",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Rozsa:1994:GBM,
author = "P{\'a}l R{\'o}zsa and Francesco Romani and Roberto
Bevilacqua",
title = "On Generalized Band Matrices and Their Inverses",
crossref = "Brown:1994:PCL",
pages = "109--121",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Rudnicki:1994:GST,
author = "Wies{\l}aw Rudnicki",
title = "Generic Space-times, Strong Curvature Singularities
and Cosmic Censorship",
crossref = "Brown:1994:PCL",
pages = "521--523",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@TechReport{Saad:1994:TEBa,
author = "Y. Saad",
title = "Theoretical Error Bounds and General Analysis of a Few
{Lanczos}-Type Algorithms",
number = "UMSI 94-90",
institution = "University of Minnesota Supercomputer Institute",
address = "Minneapolis, MN 55415, USA",
year = "1994",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib",
acknowledgement = ack-nhfb,
thanks = "This work was supported by NSF under grants number
DMR-9217287 and CCR-9214116 and by the Minnesota
Supercomputer Institute.",
}
@InProceedings{Saad:1994:TEBb,
author = "Yousef Saad",
title = "Theoretical Error Bounds and General Analysis of a Few
{Lanczos}-Type Algorithms",
crossref = "Brown:1994:PCL",
pages = "123--134",
year = "1994",
MRclass = "65F10 (65G05)",
MRnumber = "1298227 (95f:65071)",
bibdate = "Sun Sep 5 09:21:22 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Scholer:1994:NSC,
author = "Manfred Scholer and Dan Winske",
title = "Numerical Simulations of Collisionless Space Plasmas",
crossref = "Brown:1994:PCL",
pages = "453--454",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Seidel:1994:SEE,
author = "Edward Seidel",
title = "Solving {Einstein}'s Equations on Supercomputers",
crossref = "Brown:1994:PCL",
pages = "529--531",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Sher:1994:SS,
author = "Mark Sher",
title = "Supersymmetry at Supercolliders",
crossref = "Brown:1994:PCL",
pages = "629--631",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Sidi:1994:AVV,
author = "Avram Sidi",
title = "Application of Vector-Valued Rational Approximations
to the Matrix Eigenvalue Problem and Connections with
{Krylov} Subspace Methods",
crossref = "Brown:1994:PCL",
pages = "246--248",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Sidi:1994:UBC,
author = "Avram Sidi and Yair Shapira",
title = "Upper Bounds for Convergence Rates of Vector
Extrapolation Methods on Linear Systems with Initial
Iterations",
crossref = "Brown:1994:PCL",
pages = "285--287",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Sleijpen:1994:BES,
author = "G. L. G. Sleijpen and D. R. Fokkema and H. A. van der
Vorst",
title = "{BiCGstab}($ \ell $ ): An Efficient and Surprisingly
Stable Solver of Nonsymmetric Linear Equations",
crossref = "Brown:1994:PCL",
pages = "291--293",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Smith:1994:DDK,
author = "H. A. Smith and D. C. Sorensen and R. K. Singh",
title = "To discussion by {D. Kennedy} and {F. W. Williams} on
{{\em A Lanczos-based technique for exact vibration
analysis of skeletal structures}}",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "37",
number = "18",
pages = "3199--3201",
day = "30",
month = sep,
year = "1994",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1620371813",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "29 Jun 2005",
}
@InProceedings{Smolin:1994:NVL,
author = "L. Smolin",
title = "New Variables and Loop Quantization",
crossref = "Brown:1994:PCL",
pages = "571--572",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Springer:1994:BDC,
author = "R. P. Springer and M. N. Butler and M. J. Savage",
title = "The Baryon Decuplet in Chiral Perturbation Theory",
crossref = "Brown:1994:PCL",
pages = "611--614",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Stachel:1994:LEC,
author = "John Stachel",
title = "{Lanczos}'s Early Contributions to {Relativity} and
His Relationship with {Einstein}",
crossref = "Brown:1994:PCL",
pages = "201--221",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Stein:1994:MSP,
author = "R. F. Stein and Klaus Galsgaard and {\AA}ke Nordlund",
title = "{MHD} Simulations on Parallel Computers",
crossref = "Brown:1994:PCL",
pages = "440--442",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Stewart:1994:LLS,
author = "G. W. Stewart",
title = "{Lanczos} and linear systems",
crossref = "Brown:1994:PCL",
pages = "135--139",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Stone:1994:CCM,
author = "James M. Stone",
title = "The Challenge of Computational {MHD} in Astrophysics",
crossref = "Brown:1994:PCL",
pages = "433--435",
year = "1994",
bibdate = "Sat Jun 18 13:10:44 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Szczepaniak:1994:HMF,
author = "Adam Szczepaniak",
title = "Heavy Meson Form Factor and Constituent Quark
Structure",
crossref = "Brown:1994:PCL",
pages = "608--610",
year = "1994",
bibdate = "Sat Jun 18 13:36:43 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Taasan:1994:MTL,
author = "Shlomo Ta'asan and Sorin Costiner",
title = "Multilevel Techniques for Large Sparse Eigenvalue
Problems",
crossref = "Brown:1994:PCL",
pages = "261--263",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Tassone:1994:ASI,
author = "F. Tassone and F. Mauri and R. Car",
title = "Acceleration schemes for ab initio molecular-dynamics
simulations and electronic-structure calculations",
journal = j-PHYS-REV-B-CMMP,
volume = "50",
number = "15",
pages = "10561--10573",
month = "????",
year = "1994",
CODEN = "PRBMDO",
DOI = "https://doi.org/10.1103/PhysRevB.50.10561",
ISSN = "1098-0121",
ISSN-L = "1098-0121",
bibdate = "Mon Jun 13 10:08:11 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.aps.org/doi/10.1103/PhysRevB.50.10561",
acknowledgement = ack-nhfb,
fjournal = "Physical Review B: Condensed Matter and Materials Physics",
journal-URL = "http://prb.aps.org/browse",
keywords = "Car--Pinello eigensolution preconditioning",
}
@InProceedings{Taub:1994:LTG,
author = "A. H. Taub",
title = "The {Lanczos} Tensor in Gauge Theoretic Form",
crossref = "Brown:1994:PCL",
pages = "491--493",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Teitelboim:1994:TRB,
author = "Claudio Teitelboim",
title = "Topological Roots of Black Hole Entropy",
crossref = "Brown:1994:PCL",
pages = "223--230",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Thiemann:1994:CQM,
author = "T. Thiemann",
title = "Canonical Quantization of a Minisuperspace Model for
Gravity Using Self-Dual Variables",
crossref = "Brown:1994:PCL",
pages = "585--587",
year = "1994",
bibdate = "Sat Jun 18 13:31:03 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Todd:1994:RCL,
author = "John Todd",
title = "Reminiscences of {Cornelius Lanczos}",
crossref = "Brown:1994:PCL",
pages = "lviii--lix",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Torre:1994:PTO,
author = "C. G. Torre",
title = "The Problems of Time and Observables: Some Recent
Mathematical Results",
crossref = "Brown:1994:PCL",
pages = "557--559",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Treumann:1994:WCW,
author = "Rudolf Treumann",
title = "What Can We Learn from Numerical Simulations?",
crossref = "Brown:1994:PCL",
pages = "455--457",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{vanderVorst:1994:CBA,
author = "Henk A. van der Vorst",
title = "A Comparison between {ART}, {CG} and {SIRT}",
crossref = "Brown:1994:PCL",
pages = "302--304",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{vanderVorst:1994:IML,
author = "Henk A. van der Vorst",
title = "Iterative Methods for Linear Systems",
crossref = "Brown:1994:PCL",
pages = "277--277",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{vanPutten:1994:FMC,
author = "Maurice H. P. M. van Putten",
title = "On the Formation of Magnetically Collimated
Relativistic Jets",
crossref = "Brown:1994:PCL",
pages = "449--452",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Vuik:1994:GLM,
author = "C. Vuik",
title = "{GMRES}-like Methods with Variable Preconditioners",
crossref = "Brown:1994:PCL",
pages = "282--284",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Wald:1994:VPL,
author = "Robert M. Wald",
title = "Variational Principles, Local Symmetries, and Black
Hole Entropy",
crossref = "Brown:1994:PCL",
pages = "231--237",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Wang:1994:LSE,
author = "Lin-Wang Wang and Alex Zunger",
title = "Large scale electronic structure calculations using
the {Lanczos} method",
journal = j-COMPUT-MATER-SCI,
volume = "2",
number = "2",
pages = "326--340",
month = mar,
year = "1994",
CODEN = "CMMSEM",
DOI = "https://doi.org/10.1016/0927-0256(94)90115-5",
ISSN = "0927-0256 (print), 1879-0801 (electronic)",
ISSN-L = "0927-0256",
bibdate = "Fri Jun 10 17:03:28 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Computational Materials Science",
journal-URL = "http://www.sciencedirect.com/science/journal/09270256",
}
@InProceedings{Wells:1994:MAW,
author = "R. O. {Wells, Jr.}",
title = "Multiscale Applications of Wavelets to Solutions of
Partial Differential Equations",
crossref = "Brown:1994:PCL",
pages = "416--417",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Wickerhauser:1994:AWF,
author = "Mladen Victor Wickerhauser",
title = "An Adapted Waveform Functional Calculus",
crossref = "Brown:1994:PCL",
pages = "418--421",
year = "1994",
bibdate = "Sat Jun 18 13:03:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Will:1994:DGR,
author = "Clifford M. Will",
title = "Detection of Gravitational Radiation from
Astrophysical Sources",
crossref = "Brown:1994:PCL",
pages = "477--478",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@InProceedings{Xu:1994:ALA,
author = "Guanghan Xu and Young Man Cho and Thomas Kailath",
title = "An Application of the {Lanczos} Algorithm in Signal
Processing and System Identification",
crossref = "Brown:1994:PCL",
pages = "390--392",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Xu:1994:FEP,
author = "Guanghan Xu and Thomas Kailath",
title = "Fast Estimation of Principal Eigenspace Using
{Lanczos} Algorithm",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "15",
number = "3",
pages = "974--994",
month = jul,
year = "1994",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479890183848",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (65J10)",
MRnumber = "95c:65064",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/15/3;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/18384",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Ye:1994:BFV,
author = "Qiang Ye",
title = "A breakdown-free variation of the nonsymmetric
{Lanczos} algorithms",
journal = j-MATH-COMPUT,
volume = "62",
number = "205",
pages = "179--207",
month = jan,
year = "1994",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15",
MRnumber = "94c:65049",
MRreviewer = "Cs. J. Heged\H us",
bibdate = "Sat Jan 11 13:29:06 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Young:1994:LAB,
author = "David M. Young and Jen-Yuan Chen",
title = "{LANGMRES}: An Alternative to the Biconjugate Gradient
Method for Solving Large Sparse Nonsymmetric Linear
Systems",
crossref = "Brown:1994:PCL",
pages = "279--281",
year = "1994",
bibdate = "Sat Jun 11 17:22:09 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
}
@Article{Anonymous:1995:BRP,
author = "Anonymous",
title = "Book Review: {{\em Proceedings of the Cornelius
Lanczos International Centenary Conference}, J. D.
Brown, M. T. Chu, D. C. Ellison and R. J. Plemmons,
Eds., SIAM, Philadelphia, PA, 1994, lxv + 644 pp}",
journal = j-J-APPROX-THEORY,
volume = "82",
number = "3",
pages = "479--479",
month = sep,
year = "1995",
CODEN = "JAXTAZ",
DOI = "https://doi.org/10.1006/jath.1995.1104",
ISSN = "0021-9045 (print), 1096-0430 (electronic)",
ISSN-L = "0021-9045",
bibdate = "Fri Jun 10 17:17:03 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Approximation Theory",
journal-URL = "http://www.sciencedirect.com/science/journal/00219045",
}
@Article{Arioli:1995:BLT,
author = "Mario Arioli and Iain S. Duff and Daniel Ruiz and
Miloud Sadkane",
title = "{Block Lanczos} techniques for accelerating the {Block
Cimmino} method",
journal = j-SIAM-J-SCI-COMP,
volume = "16",
number = "6",
pages = "1478--1511",
month = nov,
year = "1995",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/0916086",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F50 (65F10 65F35 65Y05)",
MRnumber = "MR1355505 (96m:65051)",
MRreviewer = "K. N. Sigmon",
bibdate = "Mon Jan 2 09:11:24 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Baheux:1995:NIL,
author = "C. Baheux",
title = "New implementations of {Lanczos} method",
journal = j-J-COMPUT-APPL-MATH,
volume = "57",
number = "1--2",
pages = "3--15",
day = "20",
month = feb,
year = "1995",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/0377-0427(93)E0230-J",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Fri Jun 10 16:19:16 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
remark = "Proceeding of the Fourth International Symposium on
Orthogonal Polynomials and their Applications",
}
@Article{Boyd:1995:CPI,
author = "John P. Boyd",
title = "A {Chebyshev} Polynomial Interval-Searching Method
(``{Lanczos} Economization'') for Solving a Nonlinear
Equation with Application to the Nonlinear Eigenvalue
Problem",
journal = j-J-COMPUT-PHYS,
volume = "118",
number = "1",
pages = "1--8",
month = apr,
year = "1995",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1995.1075",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:01 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999185710753",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@TechReport{Braconnier:1995:CFV,
author = "Thierry Braconnier and Nicholas J. Higham",
title = "Computing the Field of Values and Pseudospectra Using
the {Lanczos} Method with Continuation",
type = "Numerical Analysis Report",
number = "279",
institution = inst-MCCM,
address = inst-MCCM:adr,
pages = "20",
month = nov,
year = "1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Submitted to " # j-BIT,
bibdate = "Fri Jun 10 12:38:34 2011",
acknowledgement = ack-nhfb,
}
@InProceedings{Guarracino:1995:PMB,
author = "M. R. Guarracino and F. Perla",
title = "A parallel modified block {Lanczos} algorithm for
distributed memory architectures",
crossref = "IEEE:1995:PEW",
pages = "424--431",
year = "1995",
bibdate = "Sun Dec 22 10:20:45 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
affiliation = "Dipartimento di Matematica e Applicazioni, Naples
Univ., Italy",
classification = "C4140 (Linear algebra); C4240P (Parallel programming
and algorithm theory); C6110P (Parallel programming)",
keywords = "Block column wrap-around matrices; Block Lanczos
algorithm; Distributed memory architectures;
Eigenproblems; Load-balancing; Parallel block Lanczos
algorithm; Parallel software",
thesaurus = "Distributed memory systems; Eigenvalues and
eigenfunctions; Matrix algebra; Parallel algorithms",
}
@Article{Huckle:1995:LRM,
author = "Thomas Huckle",
title = "Low-rank modification of the unsymmetric {Lanczos}
algorithm",
journal = j-MATH-COMPUT,
volume = "64",
number = "212",
pages = "1577--1588",
month = oct,
year = "1995",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10",
MRnumber = "95m:65052",
MRreviewer = "Colette Lebaud",
bibdate = "Tue Mar 25 15:38:13 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Angewandte Math. und Stat., Wurzburg Univ.,
Germany",
classcodes = "C4140 (Linear algebra); C4130 (Interpolation and
function approximation)",
corpsource = "Inst. fur Angewandte Math. und Stat., Wurzburg Univ.,
Germany",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algebra; BCG; convergence behavior; eigenvalue
estimation; eigenvalues and eigenfunctions; iterative
methods; Lanczos based iterative solver; Lanczos
vectors; linear equations; low rank modification;
matrix; orthogonality; QMR; rank 1 modified matrix;
serious breakdown; start vectors; unsymmetric Lanczos
algorithm",
treatment = "T Theoretical or Mathematical",
}
@Article{Jia:1995:CGL,
author = "Zhong Xiao Jia",
title = "The Convergence of Generalized {Lanczos} Methods for
Large Unsymmetric Eigenproblems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "16",
number = "3",
pages = "843--862",
month = jul,
year = "1995",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479893246753",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15",
MRnumber = "96d:65062",
MRreviewer = "Colette Lebaud",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/16/3;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/24675",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@PhdThesis{Lehoucq:1995:AIIa,
author = "Richard Bruno Lehoucq",
title = "Analysis and implementation of an implicitly restarted
{Arnoldi} iteration",
school = "Rice University",
address = "Houston, TX, USA",
pages = "193",
year = "1995",
LCCN = "????",
bibdate = "Thu Jun 9 11:13:14 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://hdl.handle.net/1911/16844;
http://scholarship.rice.edu/bitstream/handle/1911/16844/9610667.PDF",
abstract = "The Arnoldi algorithm, or iteration, is a
computationally attractive technique for computing a
few eigenvalues and associated invariant subspace of
large, often sparse, matrices. The method is a
generalization of the Lanczos process and reduces to
that when the underlying matrix is symmetric. This
thesis presents an analysis of Sorensen's Implicitly
Re-started Arnoldi iteration, (scIRA-iteration), by
exploiting its relationship with the scQR algorithm.
The goal of this thesis is to present numerical
techniques that attempt to make the scIRA-iteration as
robust as the implicitly shifted scQR algorithm. The
benefit is that the Arnoldi iteration only requires the
computation of matrix vector products w = Av at each
step. It does to rely on the dense matrix similarity
transformations required by the EISPACK and LAPACK
software packages. Five topics form the contribution of
this dissertation. The first topic analyzes re-starting
the Arnoldi iteration in an implicit or explicit
manner. The second topic is the numerical stability of
an scIRA-iteration. The forward instability of the scQR
algorithm and the various schemes used to re-order the
Schur form of a matrix are fundamental to this
analysis. A sensitivity analysis of the Hessenberg
decomposition is presented. The practical issues
associated with maintaining numerical orthogonality
among the Arnoldi/Lanczos basis vectors is the third
topic. The fourth topic is deflation techniques for an
scIRA-iteration. The deflation strategies introduced
make it possible to compute multiple or clustered
eigenvalues with a single vector re-start method. The
block Arnoldi/Lanczos methods commonly used are not
required. The final topic is the convergence typical of
an scIRA-iteration. Both formal theory and heuristics
are provided for making choices that will lead to
improved convergence of an scIRA-iteration.",
acknowledgement = ack-nhfb,
}
@TechReport{Lehoucq:1995:AIIb,
author = "R. B. Lehoucq",
title = "Analysis and Implementation of an Implicitly Restarted
{Arnoldi} Iteration",
institution = "Defense Technical Information Center",
address = "Ft. Belvoir, VA, USA",
pages = "145",
month = oct,
year = "1995",
LCCN = "????",
bibdate = "Thu Jun 9 11:13:14 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://handle.dtic.mil/100.2/ADA445625",
abstract = "The Arnoldi algorithm, or iteration, is a
computationally attractive technique for computing a
few eigenvalues and associated invariant subspace of
large, often sparse, matrices. The method is a
generalization of the Lanczos process and reduces to
that when the underlying matrix is symmetric. This
thesis presents an analysis of Sorensen's Implicitly
Re-started Arnoldi iteration, (IRA-iteration), by
exploiting its relationship with the QR algorithm. The
goal of this thesis is to present numerical techniques
that attempt to make the IRA-iteration as robust as the
implicitly shifted QR algorithm. The benefit is that
the Arnoldi iteration only requires the computation of
matrix vector products (pi = Av) at each step. It does
not rely on the dense matrix similarity transformations
required by the EISPACK and LAPACK software packages.
Five topics form the contribution of this dissertation.
The first topic analyzes re-starting the Arnoldi
iteration in an implicit or explicit manlier. The
second topic is the numerical stability of an
IRA-iteration. The forward instability of the QR
algorithm and the various schemes used to re-order the
Schur form of a matrix are fundamental to this
analysis. A sensitivity analysis of the Hessenberg
decomposition is presented. The practical issues
associated with maintaining numerical orthogonality
among the Arnoldi/Lanczos basis vectors is the third
topic. The fourth topic is deflation techniques for an
IRA-iteration. The deflation strategies introduced make
it possible to compute multiple or clustered
eigenvalues with a single vector re-start method. The
block Arnoldi/Lanczos methods commonly used are not
required. The final topic is the convergence typical of
an IRA-iteration. Both formal theory and heuristics are
provided for making choices that will lead to improved
convergence of an IRA-iteration.",
acknowledgement = ack-nhfb,
remark = "Additional contract number is DAAL03-91-C-0047.",
subject = "Theoretical Mathematics; Operations Research;
Algorithms; Eigenvalues; Heuristic methods; Numerical
methods and procedures; Computer programs;
Decomposition; Orthogonality; Instability; Stability;
Forward areas; Numerical analysis; Theses",
}
@TechReport{Marques:1995:SPC,
author = "Osni A. Marques and Vincent Toumazou",
title = "Spectral Portrait Computation by a {Lanczos} Method
(Augmented Matrix Version)",
type = "Technical Report",
number = "TR/PA/95/05",
institution = "CERFACS",
address = "Toulouse, France",
pages = "????",
month = feb,
year = "1995",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Montgomery:1995:BLA,
author = "Peter L. Montgomery",
title = "A Block {Lanczos} Algorithm for Finding Dependencies
over {{\em GF\/}$ (2) $}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "921",
pages = "106--??",
year = "1995",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Feb 5 11:49:38 MST 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t0921.htm;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/0921/09210106.htm;
http://link.springer-ny.com/link/service/series/0558/papers/0921/09210106.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@TechReport{Sorensen:1995:IRAa,
author = "Danny C. Sorensen",
title = "Implicitly Restarted {Arnoldi\slash Lanczos} Methods
for Large Scale Eigenvalue Calculation",
type = "Report",
number = "??",
institution = "Department of Computational and Applied Mathematics,
Rice University",
address = "Houston, TX 77251-1829",
day = "25",
month = oct,
year = "1995",
bibdate = "Thu Jun 09 11:39:01 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://people.sc.fsu.edu/~jburkardt/pdf/arpack_ref.pdf",
acknowledgement = ack-nhfb,
}
@InProceedings{Sorensen:1995:IRAb,
author = "D. C. Sorensen",
title = "Implicitly restarted {Arnoldi\slash Lanczos} methods
and large scale {SVD} applications",
crossref = "Moonen:1995:SSP",
pages = "21--31",
year = "1995",
DOI = "https://doi.org/10.1016/B978-044482107-2/50003-0",
bibdate = "Fri Jun 10 17:21:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Szularz:1995:MCL,
author = "M. Szularz and J. Weston and K. Murphy and M. Clint",
title = "Monitoring the Convergence of the {Lanczos} Algorithm
in Parallel Computing Environments",
journal = j-PARALLEL-ALGORITHMS-APPL,
volume = "6",
number = "4",
pages = "287--302",
month = sep,
year = "1995",
CODEN = "PAAPEC",
DOI = "https://doi.org/10.1080/10637199508915516",
ISSN = "1063-7192",
ISSN-L = "1026-7689",
bibdate = "Fri Jul 11 06:45:42 MDT 2008",
bibsource = "http://www.infc.ulst.ac.uk/~jweston/jw.papers.html;
http://www.infc.ulst.ac.uk/~jweston/jw.progress.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.informaworld.com/smpp/content~content=a772403915",
acknowledgement = ack-nhfb,
fjournal = "Parallel Algorithms and Applications",
journal-URL = "http://www.tandfonline.com/loi/gpaa20",
}
@Article{TorresdelCastillo:1995:LPS,
author = "G. F. {Torres del Castillo}",
title = "{Lanczos} potential for some type {$D$} space-times",
journal = j-J-MATH-PHYS,
volume = "36",
number = "1",
pages = "195--200",
month = jan,
year = "1995",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.531300",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "83C20 (83C22)",
MRnumber = "96b:83025",
MRreviewer = "J. D. Finley, III",
bibdate = "Fri Jan 2 07:23:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{vanderVeen:1995:BLP,
author = "H. I. van der Veen and K. Vuik",
title = "Bi-{Lanczos} with partial orthogonalization",
journal = j-COMP-STRUCTURES,
volume = "56",
number = "4",
pages = "605--613",
day = "17",
month = aug,
year = "1995",
CODEN = "CMSTCJ",
DOI = "https://doi.org/10.1016/0045-7949(94)00565-K",
ISSN = "0045-7949 (print), 1879-2243 (electronic)",
ISSN-L = "0045-7949",
bibdate = "Fri Jun 10 16:45:35 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Computers and Structures",
journal-URL = "http://www.sciencedirect.com/science/journal/00457949",
}
@Article{Zhang:1995:TMAa,
author = "J. Zhang and J. A. Belward",
title = "Tau-method approximations for the {Bessel} function {$
Y_0 (z) $}",
journal = j-COMPUT-MATH-APPL,
volume = "30",
number = "7",
pages = "5--14",
month = oct,
year = "1995",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(95)00120-N",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:21 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219500120N",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Zhang:1995:TMAb,
author = "J. Zhang",
title = "Tau-method approximations for the {Bessel} function {$
Y_1 (z) $}",
journal = j-COMPUT-MATH-APPL,
volume = "30",
number = "7",
pages = "15--19",
month = oct,
year = "1995",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(95)00121-E",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:21 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/089812219500121E",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
remark = "From p. 18 (conclusions section), ``We may use this
method to approximate the Bessel functions of other
integer orders. \ldots{} It is therefore advisable to
use the recurrence relations of the Bessel functions to
compute function values for $ n > 1 $ \ldots''. [This
is a similar limitation as with Chebyshev and minimax
polynomial approximations: they are valid only for a
single order the Bessel function.]",
}
@Article{Braconnier:1996:CFV,
author = "Thierry Braconnier and Nicholas J. Higham",
title = "Computing the Field of Values and Pseudospectra Using
the {Lanczos} Method with Continuation",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "3",
pages = "422--440",
month = sep,
year = "1996",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01731925",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F15",
MRnumber = "97d:65015",
bibdate = "Wed Jan 4 18:52:24 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
note = "International Linear Algebra Year (Toulouse, 1995).",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=3&spage=422",
acknowledgement = ack-njh # " and " # ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Braun:1996:ECL,
author = "M. Braun and S. A. Sofianos and D. G. Papageorgiou and
I. E. Lagaris",
title = "An Efficient {Chebyshev--Lanczos} Method for Obtaining
Eigensolutions of the {Schr{\"o}dinger} Equation on a
Grid",
journal = j-J-COMPUT-PHYS,
volume = "126",
number = "2",
pages = "315--327",
month = jul,
year = "1996",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1996.0140",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:10 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999196901400",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Brezinski:1996:MVL,
author = "C. Brezinski",
title = "The Methods of {Vorobyev} and {Lanczos}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "234",
number = "1--3",
pages = "21--41",
day = "??",
month = feb,
year = "1996",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F30 (41A05)",
MRnumber = "96i:65027",
MRreviewer = "Marc Van Barel",
bibdate = "Sat May 29 08:35:13 MDT 1999",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1996&volume=234&issue=1-3&aid=9400081",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Cullum:1996:AVN,
author = "Jane Cullum",
title = "{Arnoldi} versus nonsymmetric {Lanczos} algorithms for
solving matrix eigenvalue problems",
journal = j-BIT-NUM-MATH,
volume = "36",
number = "3",
pages = "470--493",
month = sep,
year = "1996",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01731928",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F15",
MRnumber = "97f:65027",
bibdate = "Wed Jan 4 18:52:24 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
note = "International Linear Algebra Year (Toulouse, 1995).",
URL = "http://www.mai.liu.se/BIT/contents/bit36.html;
http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=3&spage=470",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Freund:1996:SSL,
author = "Roland W. Freund and No{\"e}l M. Nachtigal",
title = "Software for simplified {Lanczos} and {QMR}
algorithms",
journal = j-APPL-NUM-MATH,
volume = "19",
number = "3",
pages = "319--341",
day = "15",
month = jan,
year = "1996",
CODEN = "ANMAEL",
DOI = "https://doi.org/10.1016/0168-9274(95)00089-5",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
MRclass = "65Fxx",
MRnumber = "1 374 355",
bibdate = "Wed Jul 28 14:36:16 MDT 1999",
bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1996&volume=19&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Special issue on iterative methods for linear
equations (Atlanta, GA, 1994).",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1996&volume=19&issue=3&aid=637",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Gallivan:1996:RLA,
author = "K. Gallivan and E. Grimme and P. {Van Dooren}",
title = "A rational {Lanczos} algorithm for model reduction",
journal = j-NUMER-ALGORITHMS,
volume = "12",
number = "1--2",
pages = "33--63",
month = apr,
year = "1996",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F15 (65G05)",
MRnumber = "1 423 547",
bibdate = "Wed Feb 7 07:37:21 MST 2001",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
ZMnumber = "870.65053",
acknowledgement = ack-nhfb,
classification = "C1310 (Control system analysis and synthesis
methods); C1340B (Multivariable control systems); C4130
(Interpolation and function approximation)",
corpsource = "Coordinated Sci. Lab., Illinois Univ., Urbana, IL,
USA",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "convergence; exact expression; interpolant;
interpolation; Lanczos type approach; large scale
linear systems; large-scale systems; model reduction
method; multi point Pade approximant; nonsymmetric
Lanczos method; rational interpolant; rational
interpolation; rational Lanczos; rational Lanczos
algorithm; rational Lanczos method; reduced order
systems; single point Lanczos approaches; state space
systems; state-space methods",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@InProceedings{Garzon:1996:PIL,
author = "E. M. Garzon and I. Garcia",
title = "Parallel Implementation of the {Lanczos} Method for
Sparse Matrices: Analysis of Data Distributions",
crossref = "ACM:1996:FCP",
pages = "294--300",
year = "1996",
bibdate = "Wed Mar 18 12:33:18 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
annote = "Also known as ICS'96. Held as part of the Federated
computing research conference (FCRC'96)",
keywords = "ACM; architecture; computer; FCRC; ICS; SIGARCH;
supercomputing",
}
@Article{Grimme:1996:MRS,
author = "E. J. Grimme and D. C. Sorensen and P. {Van Dooren}",
title = "Model reduction of state space systems via an
implicitly restarted {Lanczos} method",
journal = j-NUMER-ALGORITHMS,
volume = "12",
number = "1--2",
pages = "1--31",
month = apr,
year = "1996",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F15 (65G05)",
MRnumber = "1 423 546",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
classification = "C1310 (Control system analysis and synthesis
methods); C1340B (Multivariable control systems); C4140
(Linear algebra)",
corpsource = "Coordinated Sci. Lab., Illinois Univ., Urbana, IL,
USA",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "eigenvalues; eigenvalues and eigenfunctions; implicit
restarting; implicitly restarted Lanczos method;
inexpensive implicit restarts; Lanczos generated model;
large scale systems; large-scale systems; model
reduction technique; nonsymmetric Lanczos method;
reduced order systems; SISO; state space systems;
state-space methods; unstable partial realization",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@InCollection{Higham:1996:CCL,
author = "Nicholas J. Higham",
editor = "M. Chu and others",
booktitle = "The {Lanczos} Collected Papers with Commentaries",
title = "{Commentary on C. Lanczos, ``Introduction'' to
``Tables of Chebyshev Polynomials $ S_n(x) $ and $
C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
1952, v--xxvi}",
publisher = "????",
address = "????",
pages = "??--??",
year = "1996",
bibdate = "Fri Jun 10 12:38:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "To appear",
acknowledgement = ack-nhfb,
}
@Article{Isaacson:1996:BRP,
author = "Eugene Isaacson",
title = "Book Reviews: {{\em Proceedings of the Cornelius
Lanczos international centenary conference}}, by {J.
David Brown}, {Moody T. Chu}, {Donald C. Ellison} and
{Robert J. Plemmons}",
journal = j-MATH-COMPUT,
volume = "65",
number = "213",
pages = "423--435",
month = jan,
year = "1996",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Mon Jul 26 12:07:20 1999",
bibsource = "http://www.ams.org/mcom/1996-65-213;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00666-7&u=/mcom/1996-65-213/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
xxpages = "429--443",
}
@InProceedings{Leyk:1996:ILM,
author = "Z. Leyk and M. R. Osborne",
title = "Implementation of the {Lanczos} Method for Solving
Eigenproblems on the {VPP500} Supercomputer",
crossref = "May:1996:CTA",
pages = "487--494",
year = "1996",
bibdate = "Wed Mar 18 12:33:18 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Marx:1996:MMG,
author = "George Marx",
title = "The myth of the {Martians} and the golden age of
{Hungarian} science",
journal = j-SCI-EDUC-SPRINGER,
volume = "5",
number = "3",
pages = "225--234",
month = jul,
year = "1996",
CODEN = "SCEDE9",
DOI = "https://doi.org/10.1007/BF00414313",
ISSN = "0926-7220 (print), 1573-1901 (electronic)",
ISSN-L = "0926-7220",
bibdate = "Mon Jun 19 11:33:04 MDT 2017",
bibsource = "http://link.springer.com/journal/11191/5/3;
https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/szilard-leo.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/teller-edward.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/tex/bib/sci-educ-springer.bib",
URL = "http://adsabs.harvard.edu/abs/1996Sc%26Ed...5..225M",
abstract = "Enrico Fermi was a man with outstanding talents, he
had many interests outside his own particular field. He
was credited with asking famous questions. There are
long preambles to Fermi's questions like this: --- `The
universe is vast, containing myriads of stars, many of
them not unlike our Sun. Many of these stars are likely
to have planets circling around them. A fair fraction
of these planets will have liquid water on their
surface and a gaseous atmosphere. The energy pouring
down from a star will cause the synthesis of organic
compounds, turning the ocean into a thin, warm soup.
These chemicals will join each other to produce a
self-reproducing system. The simplest living things
will multiply, and evolve by natural selection and
become more complicated. And eventually active,
thinking creatures will emerge. Civilization, science
and technology will follow. Then, yearning for fresh
worlds, they will travel to neighboring planets, and
later to planets of nearby stars. Eventually they
should spread out all over the Galaxy. These highly
exceptional and talented people could hardly overlook
such a beautiful place as our Earth'. And so Fermi came
to his overwhelming question, --- `If all this has been
happening, they should have arrived here by now, so
where are they?' It was Leo Szilard, a man with an
impish sense of humor who supplied the perfect reply to
Fermi's rhetoric: `They are among us', he said, `but
they call themselves Hungarians'.",
acknowledgement = ack-nhfb,
fjournal = "Science \& Education (Springer)",
journal-URL = "http://link.springer.com/journal/11191",
keywords = "Albert Szent-Gyorgyi; Andrew Graf (later Grove);
Arthur Koestler; Baron Jozsef E{\"o}tv{\"o}s; Baron
Roland E{\"o}tv{\"o}s; Charles Simonyi; Cornelius
Lanczos; Dennis Gabor; Edward Teller; Enrico Fermi;
Ervin Bauer (husband of Szilard's sister); Eugene
Wigner; George de Hevesy; George Soros; George von
B{\'e}k{\'e}sy; John G. Kemeny; John von Neumann; Leo
Szilard; Leslie Groves; life in the Universe; Martians;
Michael Polanyi; Peter Lax; Robert B{\'a}r{\'a}ny;
Theodore von Karman; Valentine Telegdi; Zoltan Bay",
remark = "Based on the author's book \booktitle{The Voice of the
Martians}, Roland E{\"o}tv{\"o}s Physical Society,
Budapest, 1994. From page 226: ``The usage of {\em y\/}
instead of {\em i\/} at the end of the [Hungarian]
family name indicates a nobleman, like {\em von\/} in
German or {\em de\/} in Italian.''",
}
@Article{Murphy:1996:CPE,
author = "K. Murphy and M. Clint and M. Szularz and J. Weston",
title = "The Computation of Partial Eigensolutions on a
Distributed Memory Machine Using a Modified {Lanczos}
Method",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1124",
pages = "22--??",
year = "1996",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Oct 29 14:12:39 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@MastersThesis{Radke:1996:MII,
author = "Richard Joseph Radke",
title = "A {Matlab} implementation of the {Implicitly Restarted
Arnoldi Method} for solving large-scale eigenvalue
problems",
school = "Rice University",
address = "Houston, TX, USA",
pages = "94",
year = "1996",
LCCN = "????",
bibdate = "Thu Jun 9 11:13:14 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://hdl.handle.net/1911/14054;
http://scholarship.rice.edu/bitstream/handle/1911/14054/1379511.PDF",
abstract = "This thesis describes a Matlab implementation of the
Implicitly Restarted Arnoldi Method for computing a few
selected eigenvalues of large structured matrices.
Shift-and-invert methods allow the calculation of the
eigenvalues nearest any point in the complex plane, and
polynomial acceleration techniques aid in computing
eigenvalues of operators which are defined by m-files
instead of Matlab matrices. These new Matlab functions
will be incorporated into the upcoming version 5 of
Matlab and will greatly extend Matlab's capability to
deal with many real-world eigenvalue problems that were
intractable in version 4. The thesis begins with a
discussion of the Implicitly Restarted Arnoldi Method.
The bulk of the thesis is a user's manual for the
Matlab functions which implement this algorithm. The
user's guide not only describes the functions' syntax
and structure but also discusses some of the
difficulties that were overcome during their
development. The thesis concludes with several examples
of the functions applied to realistic test problems
which illustrate the versatility and power of this new
tool.",
acknowledgement = ack-nhfb,
advisor = "Danny C. Sorensen",
}
@Article{Schuele:1996:PLA,
author = "J. Schuele",
title = "Parallel {Lanczos} Algorithm on a {CRAY-T3D} Combining
{PVM} and {SHMEM} Routines",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1156",
pages = "158--??",
month = "????",
year = "1996",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Dec 21 09:47:26 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@InProceedings{Schule:1996:PLA,
author = "J. Schule",
title = "Parallel {Lanczos} algorithm on a {CRAY-T3D} combining
{PVM} and {SHMEM} routines",
crossref = "Bode:1996:PVM",
pages = "158--165",
year = "1996",
bibdate = "Wed Apr 16 06:39:19 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
classification = "A7130 (Metal-insulator transitions); A7155J
(Localization in disordered structures); C4140 (Linear
algebra); C6110P (Parallel programming); C7320 (Physics
and chemistry computing)",
corpsource = "Inst. for Sci. Comput., Braunschweig, Germany",
keywords = "Anderson model; Anderson-; arithmetic; coarse-grain;
Cray computers; CRAY-; cubic tungsten bronzes; data
distribution; dynamic group; effectiveness;
eigenfunctions; eigenvalues and; eigenvector
calculation; fine-grain; finite precision; Hamiltonian
matrix; HF calculations; Hubbard model; iterations;
iterative; Krylov sequence; load imbalance; machines;
master-slave paradigm; matrix algebra; membership;
metal-insulator transition; methods; Mott-Hubbard
model; NaWO$_3$; parallel algorithms; parallel Lanczos
algorithm; parallelisation strategies; parallelism;
physics computing; PVM; resource allocation; rounding
errors; roundoff errors; SHMEM routines; sodium
compounds; software development costs; stochastic
distributions; subroutines; T3D; tridiagonalisation;
unrestricted Hartree-Fock approach; virtual",
pubcountry = "Germany",
treatment = "P Practical",
}
@Article{Singh:1996:ASL,
author = "R. K. Singh and H. A. Smith and D. C. Sorensen",
title = "Application of $k$-Step {Lanczos} Method to Extract
the Interior Eigenvalues of Skeletal Systems",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "39",
number = "4",
pages = "705--716",
day = "28",
month = feb,
year = "1996",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/(SICI)1097-0207(19960229)39",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "4 Dec 1998",
}
@TechReport{Sorensen:1996:IRAa,
author = "D. C. (Danny C.) Sorensen",
title = "Implicitly restarted {Arnoldi\slash Lanczos} methods
for large scale eigenvalue calculations",
number = "198342 (NASA), 96-40 (ICASE)",
institution = "National Aeronautics and Space Administration, Langley
Research Center",
address = "Hampton, VA, USA",
pages = "????",
year = "1996",
LCCN = "????",
bibdate = "Thu Jun 9 11:04:11 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "NASA contractor report; ICASE report",
acknowledgement = ack-nhfb,
remark = "Shipping list number 98-1098-M.",
subject = "Computer programming. Computer systems performance.
Linear operators. Software engineering. Numerical
analysis. Applications of mathematics. Computer
programming; Linear operators; Software engineering;
Numerical analysis; Applications of mathematics",
}
@TechReport{Sorensen:1996:IRAb,
author = "Danny C. Sorensen",
title = "Implicitly Restarted {Arnoldi}",
institution = "Defense Technical Information Center",
address = "Ft. Belvoir, VA, USA",
pages = "37",
month = may,
year = "1996",
LCCN = "????",
bibdate = "Thu Jun 9 11:04:11 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://handle.dtic.mil/100.2/ADA313185",
abstract = "Eigenvalues and eigenfunctions of linear operators are
important to many areas of applied mathematics. The
ability to approximate these quantities numerically is
becoming increasingly important in a wide variety of
applications. This increasing demand has fueled
interest in the development of new methods and software
for the numerical solution of large-scale algebraic
eigenvalue problems. In turn, the existence of these
new methods and software, along with the dramatically
increased computational capabilities now available, has
enabled the solution of problems that would not even
have been posed five or ten years ago. Until very
recently, software for large-scale nonsymmetric
problems was virtually non-existent. Fortunately, the
situation is improving rapidly. The purpose of this
article is to provide an overview of the numerical
solution of large-scale algebraic eigenvalue problems.
The focus will be on a class of methods called Krylov
subspace projection methods. The well-known Lanczos
method is the premier member of this class. The Arnoldi
method generalizes the Lanczos method to the
nonsymmetric case. A recently developed variant of the
Arnoldi/Lanczos scheme called the Implicitly Restarted
Arnoldi Method is presented here in some depth. This
method is highlighted because of its suitability as a
basis for software development.",
acknowledgement = ack-nhfb,
subject = "Theoretical Mathematics. Computations. Eigenvalues.
Computer programs. Algebra. Numerical analysis.
Eigenvectors. Problem solving. Solutions(general)
Asymmetry. Approximation(mathematics) Linearity.
Operators(mathematics) Applied mathematics",
}
@Article{Szularz:1996:HPE,
author = "M. Szularz and J. Weston and M. Clint and K. Murphy",
title = "A Highly Parallel Explicitly Restarted {Lanczos}
Algorithm",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1184",
pages = "651--??",
year = "1996",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Aug 22 11:59:49 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Webster:1996:PBL,
author = "Frank Webster and Gen-Ching Lo",
title = "Projective Block {Lanczos} Algorithm for Dense,
{Hermitian} Eigensystems",
journal = j-J-COMPUT-PHYS,
volume = "124",
number = "1",
pages = "146--161",
day = "1",
month = mar,
year = "1996",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1996.0050",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:07 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999196900509",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Ye:1996:ABL,
author = "Qiang Ye",
title = "An adaptive block {Lanczos} algorithm",
journal = j-NUMER-ALGORITHMS,
volume = "12",
number = "1--2",
pages = "97--110",
month = apr,
year = "1996",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F15",
MRnumber = "1 423 550",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
classification = "C1110 (Algebra); C4130 (Interpolation and function
approximation); C4140 (Linear algebra); C4240
(Programming and algorithm theory)",
corpsource = "Dept. of Appl. Math., Manitoba Univ., Winnipeg, Man.,
Canada",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "adaptive algorithm; adaptive block Lanczos algorithm;
adaptive estimation; algorithm theory; block size;
clustered eigenvalue; clustered eigenvalues;
eigenvalues and eigenfunctions; iteration; iterative
methods; matrix algebra; misconvergence; multiple
eigenvalues; residual bounds; Ritz value",
pubcountry = "Switzerland",
treatment = "T Theoretical or Mathematical",
}
@Article{Zhang:1996:NTM,
author = "J. Zhang",
title = "A note on the tau-method approximations for the
{Bessel} functions {$ Y_0 (z) $} and {$ Y_1 (z) $}",
journal = j-COMPUT-MATH-APPL,
volume = "31",
number = "9",
pages = "63--70",
month = may,
year = "1996",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/0898-1221(96)00043-0",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:28 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0898122196000430",
abstract = "This paper is to complete and improve the work
reported in [1,2], using the Lanczos $ \tau $-method
(in Coleman's version) to approximate the Bessel
functions $ Y_0 (z) $ and $ Y_1 (z) $. We introduce
symbolic representations of the scaled Faber
polynomials on any fan-shaped section of the complex
plane. These Faber polynomials are used as the
perturbation terms in the $ \tau $-method. Numerical
comparison among the power series, the Chebyshev series
and the $ \tau $-method are conducted to show the
accuracy improvement achieved by this new version of
the $ \tau $-method. Some concluding remarks and
suggestions on future research are given.",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
keywords = "Automated $\tau$-method; Bessel functions; Chebyshev
series; Symbolic Faber polynomials",
}
@Article{Aliaga:1997:PIG,
author = "J. I. Aliaga and V. Hernandez and J. L. Perez",
title = "A Parallel Implementation of the General {Lanczos}
Method on the {Cray T3D}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1215",
pages = "168--??",
year = "1997",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Fri Aug 22 11:59:49 MDT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Basermann:1997:CGL,
author = "A. Basermann",
title = "Conjugate Gradient and {Lanczos} Methods for Sparse
Matrices on Distributed Memory Multiprocessors",
journal = j-J-PAR-DIST-COMP,
volume = "45",
number = "1",
pages = "46--52",
day = "25",
month = aug,
year = "1997",
CODEN = "JPDCER",
DOI = "https://doi.org/10.1006/jpdc.1997.1364",
ISSN = "0743-7315 (print), 1096-0848 (electronic)",
ISSN-L = "0743-7315",
bibdate = "Thu Mar 9 09:19:03 MST 2000",
bibsource = "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.idealibrary.com/links/doi/10.1006/jpdc.1997.1364/production;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1997.1364/production/pdf;
http://www.idealibrary.com/links/doi/10.1006/jpdc.1997.1364/production/ref",
acknowledgement = ack-nhfb,
fjournal = "Journal of Parallel and Distributed Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/07437315",
}
@Article{Benner:1997:IRS,
author = "Peter Benner and Heike Fa{\ss}bender",
title = "An Implicitly Restarted Symplectic {Lanczos} Method
for the {Hamiltonian} Eigenvalue Problem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "263",
number = "1--3",
pages = "75--111",
day = "15",
month = sep,
year = "1997",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18); 65Fxx (15A18)",
MRnumber = "98f:65039; 1 453 966",
MRreviewer = "Lars Eld{\'e}n",
bibdate = "Fri May 28 11:36:55 MDT 1999",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1997&volume=263&issue=1-3&aid=9600524",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Bergqvist:1997:LPK,
author = "G{\"o}ran Bergqvist",
title = "A {Lanczos} potential in {Kerr} geometry",
journal = j-J-MATH-PHYS,
volume = "38",
number = "6",
pages = "3142--3154",
month = jun,
year = "1997",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.532040",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
MRclass = "83C15",
MRnumber = "98a:83020",
MRreviewer = "Simonetta Frittelli",
bibdate = "Fri Jan 2 07:23:17 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Besalu:1997:IMS,
author = "Emili Besal{\'u} and Ramon Carb{\'o} Dorca",
title = "An iterative method to solve the algebraic eigenvalue
problem",
journal = j-J-MATH-CHEM,
volume = "21",
number = "4",
pages = "395--412",
month = "????",
year = "1997",
CODEN = "JMCHEG",
DOI = "https://doi.org/10.1023/A:1019103309814",
ISSN = "0259-9791 (print), 1572-8897 (electronic)",
ISSN-L = "0259-9791",
bibdate = "Fri Jun 10 22:18:16 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "An iterative method based on perturbation theory in
matrix form is described as a procedure to obtain the
eigenvalues and eigenvectors of square matrices.
Practical vector notation and elementary schematic
algorithm codes are given. The particular programming
characteristics of the present computational scheme are
based upon eigenvector corrections, obtained through a
simple Rayleigh--Schr{\"o}dinger perturbation theory
algorithm. The proposed methodological processes can be
used to evaluate the eigensystem of large matrices.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Chemistry",
journal-URL = "http://link.springer.com/journal/10910",
}
@InBook{Bultheel:1997:LA,
author = "Adhemar Bultheel and Marc van Barel",
booktitle = "Linear algebra, rational approximation, and orthogonal
polynomials",
title = "{Lanczos} algorithm",
chapter = "3",
volume = "6",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
bookpages = "xvii + 446",
pages = "99--133",
year = "1997",
ISBN = "0-444-82872-9",
ISBN-13 = "978-0-444-82872-9",
LCCN = "QA242 .B88 1997",
bibdate = "Fri Jun 10 16:50:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
series = "Studies in computational mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0601/97040610-d.html",
acknowledgement = ack-nhfb,
subject = "Euclidean algorithm; algebras, linear; Pad{\'e}
approximant; orthogonal polynomials",
}
@Article{Bunchaft:1997:SEL,
author = "M. E. Froes Bunchaft",
title = "Some extensions of the {Lanczos--Ortiz} theory of
canonical polynomials in the {Tau Method}",
journal = j-MATH-COMPUT,
volume = "66",
number = "218",
pages = "609--621",
month = apr,
year = "1997",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65L05 (65L10)",
MRnumber = "1 397 440",
bibdate = "Fri Jul 16 10:38:42 MDT 1999",
bibsource = "http://www.ams.org/mcom/1997-66-218;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00816-8&u=/mcom/1997-66-218/",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Chen:1997:DEL,
author = "Rongqing Chen and Hua Guo",
title = "Determination of Eigenstates via {Lanczos}-Based
Forward Substitution and Filter-Diagonalization",
journal = j-J-COMPUT-PHYS,
volume = "136",
number = "2",
pages = "494--502",
day = "15",
month = sep,
year = "1997",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1997.5777",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:20 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999197957776",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Chien:1997:LTM,
author = "C.-S. Chien and Z.-L. Weng and C.-L. Shen",
title = "{Lanczos}-type Methods for Continuation Problems",
journal = j-NUM-LIN-ALG-APPL,
volume = "4",
number = "1",
pages = "23--41",
month = jan # "\slash " # feb,
year = "1997",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/(SICI)1099-1506(199701/02)4",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "65H10",
MRnumber = "97m:65099",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.interscience.wiley.com/journalfinder.html",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=15001012;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=15001012&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "31 Dec 1998",
}
@Article{Day:1997:EIN,
author = "David Day",
title = "An Efficient Implementation of the Nonsymmetric
{Lanczos} Algorithm",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "18",
number = "3",
pages = "566--589",
month = jul,
year = "1997",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479895292503",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15",
MRnumber = "1 453 541",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/18/3;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/29250",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Eberly:1997:RLA,
author = "Wayne Eberly and Erich Kaltofen",
title = "On randomized {Lanczos} algorithms",
crossref = "Kuchlin:1997:IJM",
pages = "176--183",
year = "1997",
bibdate = "Wed Mar 11 18:24:16 MST 1998",
bibsource = "http://www.acm.org/pubs/toc/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/258726/p176-eberly/",
acknowledgement = ack-nhfb,
}
@Article{Ferng:1997:NNL,
author = "William R. Ferng and Kun-Yi Lin and Wen-Wei Lin",
title = "A novel nonsymmetric $ {K \_ } $-{L}{\'a}nczos
algorithm for the generalized nonsymmetric $ {K \_ }
$-eigenvalue problems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "252",
number = "1--3",
pages = "81--105",
day = "??",
month = feb,
year = "1997",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15",
MRnumber = "97k:65090",
MRreviewer = "Marc Van Barel",
bibdate = "Fri May 28 11:36:31 MDT 1999",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1997&volume=252&issue=1-3&aid=9600670",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Graves-Morris:1997:LAL,
author = "P. R. Graves-Morris",
title = "A ``look-around {Lanczos}'' algorithm for solving a
system of linear equations",
journal = j-NUMER-ALGORITHMS,
volume = "15",
number = "3--4",
pages = "247--274",
month = jan,
year = "1997",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F10 (65B05 65F50)",
MRnumber = "98m:65042",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Hanke:1997:SCR,
author = "Martin Hanke",
title = "Superlinear convergence rates for the {Lanczos} method
applied to elliptic operators",
journal = j-NUM-MATH,
volume = "77",
number = "4",
pages = "487--499",
month = oct,
year = "1997",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F15 (65N25)",
MRnumber = "1 473 393",
bibdate = "Sat Jun 6 06:08:59 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.springer.de/link/service/journals/00211/bibs/7077004/70770487.htm;
http://science.springer.de/nmee/bibs/7077004/70770487.htm",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InCollection{Higham:1997:CCL,
author = "Nicholas J. Higham",
editor = "William R. Davis and others",
booktitle = "Cornelius Lanczos Collected Published Papers with
Commentaries",
title = "{Commentary on C. Lanczos, ``Introduction'' to
``Tables of Chebyshev Polynomials $ S_n(x) $ and $
C_n(x) $'', Nat.\ Bur.\ Stand., Appl.\ Math.\ Series 9,
1952, v--xxvi}",
volume = "VI(3)",
publisher = "????",
address = "????",
pages = "557--559",
year = "1997",
bibdate = "Wed Aug 13 08:39:47 GMT 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "To appear.",
acknowledgement = ack-njh,
mynote = "Volume VI, Part 3, pp. 557--559.",
}
@Article{Karlsson:1997:DSA,
author = "H. O. Karlsson and G. L. Bendazzoli and O. Goscinski
and S. Evangelisti",
title = "Density of States of Alternant Cyclic Polyenes
{(CH)$_N$} by a Direct {Lanczos} Method",
journal = j-IJQC,
volume = "63",
number = "3",
pages = "719--728",
day = "5",
month = jun,
year = "1997",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/(SICI)1097-461X(1997)63",
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fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
journalabr = "Int J Quant Chem",
onlinedate = "6 Dec 1998",
}
@TechReport{Lehoucq:1997:IRA,
author = "R. B. Lehoucq and J. A. Scott",
title = "Implicitly restarted {Arnoldi} methods and eigenvalues
of the discretized {Navier--Stokes} equations",
type = "Report",
number = "RAL-TR-97-058",
institution = "Council for the Central Laboratory of the Research
Councils",
address = "Chilton, UK",
pages = "41",
year = "1997",
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http://epubs.cclrc.ac.uk/work-details?w=26902",
acknowledgement = ack-nhfb,
}
@Article{Murphy:1997:PCP,
author = "K. Murphy and M. Clint and M. Szularz and J. Weston",
title = "The Parallel Computation of Partial Eigensolutions
Using a Modified {Lanczos} Method",
journal = j-PARALLEL-ALGORITHMS-APPL,
volume = "11",
number = "3--4",
pages = "299--323",
month = "????",
year = "1997",
CODEN = "PAAPEC",
DOI = "https://doi.org/10.1080/10637199708915600",
ISSN = "1063-7192",
ISSN-L = "1026-7689",
MRclass = "65F15 (65Y05)",
MRnumber = "MR1477393 (98e:65030)",
bibdate = "Fri Jul 11 06:45:43 MDT 2008",
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URL = "http://www.informaworld.com/smpp/content~content=a772742296",
acknowledgement = ack-nhfb,
fjournal = "Parallel Algorithms and Applications",
journal-URL = "http://www.tandfonline.com/loi/gpaa20",
remark = "Also cited as v12 n9 pp 299--323 1998.",
}
@Article{Ortiz:1997:ATA,
author = "Eduardo L. Ortiz and T. J. Rivlin",
title = "Approximation theory and applications. {Preface}: a
collection of papers to commemorate the {Cornelius
Lanczos} centennial",
journal = j-COMPUT-MATH-APPL,
volume = "33",
number = "1--2",
pages = "xiii--xiv",
month = jan,
year = "1997",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/S0898-1221(96)00214-3",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Fri Jun 10 17:49:16 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib",
note = "Dedicated to Cornelius Lanczos (1893--1974).",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Ortiz:1997:PCP,
author = "E. L. Ortiz and T. J. Rivlin",
title = "Preface: a collection of papers to commemorate the
{Cornelius Lanczos} centennial",
journal = j-COMPUT-MATH-APPL,
volume = "33",
number = "1--2",
pages = "xiii--xiv",
month = jan,
year = "1997",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/S0898-1221(96)00214-3",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:48:34 MST 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0898122196002143",
acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Rottner:1997:NSF,
author = "Th. Rottner and I. Lenhardt and G. Alefeld and K.
Schweizerhof",
title = "Nonlinear structural finite element analysis using the
preconditioned {Lanczos} method on serial and parallel
computers",
journal = j-BIT-NUM-MATH,
volume = "37",
number = "3",
pages = "759--769",
month = sep,
year = "1997",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65N30 (65F10 65Y05)",
MRnumber = "1 483 685",
bibdate = "Fri Nov 13 07:00:34 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
note = "Direct methods, linear algebra in optimization,
iterative methods (Toulouse, 1995/1996).",
URL = "http://www.mai.liu.se/BIT/contents/bit37.html",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Szularz:1997:RPL,
author = "M. Szularz and J. Weston and M. Clint",
title = "Robust Parallel {Lanczos} Methods for Clustered
Eigenvalues",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1300",
pages = "710--??",
year = "1997",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 28 08:51:33 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Yang:1997:EIIb,
author = "T. Yang",
title = "Efficient Implementation of the Improved Unsymmetric
{Lanczos} Process on Massively Distributed Memory
Computers",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1277",
pages = "145--??",
year = "1997",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Apr 28 08:51:33 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Andersson:1998:CFA,
author = "F. Andersson and S. Brian Edgar",
title = "Curvature-free asymmetric metric connections and
{Lanczos} potentials in {Kerr--Schild} spacetimes",
journal = j-J-MATH-PHYS,
volume = "39",
number = "5",
pages = "2859--2861",
month = may,
year = "1998",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.532425",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Sat Aug 15 13:36:35 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Bai:1998:EEP,
author = "Zhaojun Bai and Qiang Ye",
title = "Error estimation of the {Pad{\'e}} approximation of
transfer functions via the {Lanczos} process",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "7",
pages = "1--17",
year = "1998",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:29 MDT 2010",
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note = "Large scale eigenvalue problems (Argonne, IL, 1997)",
URL = "http://etna.mcs.kent.edu/vol.7.1998/pp1-17.dir/pp1-17.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Benner:1998:SEP,
author = "Peter Benner and Heike Fa{\ss}bender",
title = "The symplectic eigenvalue problem, the butterfly form,
the {$ S R $} algorithm, and the {Lanczos} method",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "275/276",
number = "1--3",
pages = "19--47",
day = "15",
month = may,
year = "1998",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18)",
MRnumber = "1 628 381",
bibdate = "Fri May 28 09:34:09 MDT 1999",
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https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Proceedings of the Sixth Conference of the
International Linear Algebra Society (Chemnitz,
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http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1998&volume=275-276&issue=1-3&aid=6047",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Bjorck:1998:SCG,
author = "{\AA}ke Bj{\"o}rck and Tommy Elfving and Zden{\v{e}}k
Strako{\v{s}}",
title = "Stability of Conjugate Gradient and {Lanczos} Methods
for Linear Least Squares Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "19",
number = "3",
pages = "720--736",
month = jul,
year = "1998",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S089547989631202X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Dec 4 12:14:09 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/19/3;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/31202",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Brezinski:1998:TFL,
author = "C. Brezinski and M. Redivo-Zaglia",
title = "Transpose-free {Lanczos-type} algorithms for
nonsymmetric linear systems",
journal = j-NUMER-ALGORITHMS,
volume = "17",
number = "1--2",
pages = "67--103",
month = mar,
year = "1998",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65Fxx",
MRnumber = "1 628 482",
bibdate = "Mon Sep 29 08:36:53 MDT 2003",
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http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
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http://ipsapp007.kluweronline.com/content/getfile/5058/31/5/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Chan:1998:TFF,
author = "Tony F. Chan and Lisette {de Pillis} and Henk van der
Vorst",
title = "Transpose-free formulations of {Lanczos}-type methods
for nonsymmetric linear systems",
journal = j-NUMER-ALGORITHMS,
volume = "17",
number = "1--2",
pages = "51--66",
month = mar,
year = "1998",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F10, 65Fxx",
MRnumber = "MR1628478 (99d:65101)",
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http://www.math.psu.edu/dna/contents/na.html;
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acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{DeSamblanx:1998:NLI,
author = "Gorik {De Samblanx} and Adhemar Bultheel",
title = "Nested {Lanczos}: Implicitly restarting an unsymmetric
{Lanczos} algorithm",
journal = j-NUMER-ALGORITHMS,
volume = "18",
number = "1",
pages = "31--50",
month = sep,
year = "1998",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Sep 29 08:36:54 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/13/3/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/13/3/fulltext.pdf",
ZMnumber = "924.65031",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Dolan:1998:LPV,
author = "P. Dolan and B. D. Muratori",
title = "The {Lanczos} potential for vacuum space--times with
an {Ernst} potential",
journal = j-J-MATH-PHYS,
volume = "39",
number = "10",
pages = "5406--5420",
month = oct,
year = "1998",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.532580",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 20 08:18:05 MDT 2000",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Druskin:1998:UNL,
author = "V. Druskin and A. Greenbaum and L. Knizhnerman",
title = "Using Nonorthogonal {Lanczos} Vectors in the
Computation of Matrix Functions",
journal = j-SIAM-J-SCI-COMP,
volume = "19",
number = "1",
pages = "38--54",
month = jan,
year = "1998",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827596303661",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Dec 4 14:47:53 MST 1998",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/19/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30366",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Fokkema:1998:JDS,
author = "Diederik R. Fokkema and Gerard L. G. Sleijpen and Henk
A. van der Vorst",
title = "{Jacobi--Davidson} Style {QR} and {QZ} Algorithms for
the Reduction of Matrix Pencils",
journal = j-SIAM-J-SCI-COMP,
volume = "20",
number = "1",
pages = "94--125",
month = jan,
year = "1998",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827596300073",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15",
MRnumber = "MR1639102 (99e:65061)",
bibdate = "Sat Dec 31 06:28:14 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/20/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib;
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URL = "http://epubs.siam.org/sam-bin/dbq/article/30007;
http://epubs.siam.org/sam-bin/dbq/toc/SISC/20/1",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Groetsch:1998:LGD,
author = "C. W. Groetsch",
title = "{Lanczos}' Generalized Derivative",
journal = j-AMER-MATH-MONTHLY,
volume = "105",
number = "4",
pages = "320--326",
month = apr,
year = "1998",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
MRclass = "26A24",
MRnumber = "1 614 875",
bibdate = "Tue Jun 22 10:29:34 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.maa.org/pubs/monthly_apr98_toc.html",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
}
@Article{Guiang:1998:QDL,
author = "Chona S. Guiang and Robert E. Wyatt",
title = "Quantum Dynamics with {Lanczos} Subspace Propagation:
Application to a Laser-Driven Molecular System",
journal = j-IJQC,
volume = "67",
number = "5",
pages = "273--285",
month = "????",
year = "1998",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/(SICI)1097-461X(1998)67",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.interscience.wiley.com/journalfinder.html",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=29906;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=29906&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
onlinedate = "6 Dec 1998",
}
@Article{Horoi:1998:EIL,
author = "M. Horoi and R. Enbody",
title = "Efficient Implementation of a {Lanczos} Eigenvalue
Solver on a {Cray T3E-900}",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1401",
pages = "907--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Oct 10 14:40:24 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Jia:1998:GBL,
author = "Zhongxiao Jia",
title = "Generalized block {Lanczos} methods for large
unsymmetric eigenproblems",
journal = j-NUM-MATH,
volume = "80",
number = "2",
pages = "239--266",
month = aug,
year = "1998",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Tue Jan 5 07:23:12 MST 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.springer.de/link/service/journals/00211/bibs/8080002/80800239.htm;
http://link.springer.de/link/service/journals/00211/papers/8080002/80800239.pdf;
http://link.springer.de/link/service/journals/00211/papers/8080002/80800239.ps.gz",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Book{Lehoucq:1998:AUG,
author = "Richard B. Lehoucq and Chao-Chih Yang and Danny C.
Sorensen",
title = "{ARPACK} users' guide: solution of large-scale
eigenvalue problems with implicitly restarted {Arnoldi}
methods",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xv + 142",
year = "1998",
ISBN = "0-89871-407-9",
ISBN-13 = "978-0-89871-407-4",
LCCN = "QA193.L44 1998",
bibdate = "Thu Jun 9 11:13:14 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "This book is a guide to understanding and using the
software package ARPACK to solve large algebraic
eigenvalue problems. The software described is based on
the implicitly restarted Arnoldi method, which has been
heralded as one of the three most important advances in
large scale eigenanalysis in the past ten years. The
book explains the acquisition, installation,
capabilities, and detailed use of the software for
computing a desired subset of the eigenvalues and
eigenvectors of large (sparse) standard or generalized
eigenproblems. It also discusses the underlying theory
and algorithmic background at a level that is
accessible to the general practitioner.",
acknowledgement = ack-nhfb,
subject = "Arnoldi method; eigenvalue problem; ARPACK",
tableofcontents = "List of figures \\
List of tables \\
Preface \\
1. Introduction to ARPACK \\
Important features \\
Getting started \\
Reverse communication interface \\
Availability \\
Installation \\
Documentation \\
Dependence on LAPACK and BLAS \\
Expected performance \\
P\_ARPACK \\
Contributed additions \\
Trouble shooting and problems \\
2. Getting started with ARPACK \\
Directory structure and contents \\
Getting started \\
An example for a symmetric eigenvalue problem \\
3. General use of ARPACK \\
Naming conventions, precisions, and types \\
Shift and invert spectral transformation mode \\
Reverse communication structure for shift-invert \\
Using the computational modes \\
Computational modes for real symmetric problems \\
Postprocessing for eigenvectors using dseupd \\
Computational modes for real nonsymmetric problems \\
Postprocessing for eigenvectors using dneupd \\
Computational modes for complex problems \\
Postprocessing for eigenvectors using zneupd \\
4. The implicitly restarted Arnoldi method \\
Structure of the eigenvalue problem \\
Krylov subspaces and projection methods \\
The Arnoldi factorization \\
Restarting the Arnoldi method \\
The generalized eigenvalue problem \\
Stopping criterion \\
5. Computational routines \\
ARPACK subroutines \\
LAPACK routines used by ARPACK \\
BLAS routines used by ARPACK \\
Appendix A. Templates and driver routines \\
Symmetric Drivers \\
Real nonsymmetric drivers \\
Complex divers \\
Band drivers \\
The singular value decomposition \\
Appendix B. Tracking the progress of ARPACK \\
Obtaining trace output \\
Check-pointing ARPACK \\
Appendix C. The XYaupd ARPACK routines \\
DSAUPD \\
DNAUPD \\
ZNAUPD \\
Bibliography \\
Index",
}
@Article{Leyk:1998:ELE,
author = "Zbigniew Leyk and Henryk Wo{\'z}niakowski",
title = "Estimating a largest eigenvector by {Lanczos} and
polynomial algorithms with a random start",
journal = j-NUM-LIN-ALG-APPL,
volume = "5",
number = "3",
pages = "147--164",
month = may # "\slash " # jun,
year = "1998",
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onlinedate = "4 May 1999",
}
@Article{Li:1998:ETM,
author = "Henian Li and Allan Woodbury and Peter Aitchison",
title = "Eigenvalue translation method for stabilizing an
unsymmetric {Lanczos} reduction process",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "43",
number = "2",
pages = "221--239",
day = "30",
month = sep,
year = "1998",
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Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "18 Dec 1998",
}
@Article{Li:1998:MOB,
author = "Henian Li and Peter Aitchison and Allan Woodbury",
title = "Methods for overcoming breakdown problems in the
{Unsymmetric Lanczos Reduction} method",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "42",
number = "3",
pages = "389--408",
day = "15",
month = jun,
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Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "4 Dec 1998",
}
@Article{Meerbergen:1998:TCB,
author = "Karl Meerbergen",
title = "A theoretical comparison between inner products in the
shift-invert {Arnoldi} method and the spectral
transformation {Lanczos} method",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "7",
pages = "90--103",
year = "1998",
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fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Ressel:1998:QSL,
author = "Klaus J. Ressel and Martin H. Gutknecht",
title = "{QMR} Smoothing for {Lanczos}-Type Product Methods
Based on Three-Term Recurrences",
journal = j-SIAM-J-SCI-COMP,
volume = "19",
number = "1",
pages = "55--73",
month = jan,
year = "1998",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827596304812",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
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fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Simoncini:1998:MAA,
author = "V. Simoncini",
title = "A matrix analysis of {Arnoldi} and {Lanczos} methods",
journal = j-NUM-MATH,
volume = "81",
number = "1",
pages = "125--141",
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year = "1998",
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acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Teitelbaum:1998:EAL,
author = "Jeremy Teitelbaum",
title = "{Euclid}'s algorithm and the {Lanczos} method over
finite fields",
journal = j-MATH-COMPUT,
volume = "67",
number = "224",
pages = "1665--1678",
month = oct,
year = "1998",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "11Y16 (11T99 65F50 94A60)",
MRnumber = "1 474 657",
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acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@InProceedings{Wu:1998:NLM,
author = "Kesheng Wu and A. Canning and H. D. Simon",
title = "A New {Lanczos} Method for Electronic Structure
Simulation",
crossref = "ACM:1998:SHP",
pages = "35--40",
year = "1998",
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acknowledgement = ack-nhfb,
}
@Article{Wu:1998:TRL,
author = "K. Wu and H. D. Simon",
title = "Thick-Restart {Lanczos} Method for Symmetric
Eigenvalue Problems",
journal = j-LECT-NOTES-COMP-SCI,
volume = "1457",
pages = "43--??",
year = "1998",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Sat Oct 10 14:40:24 MDT 1998",
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acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Article{Yu:1998:ELG,
author = "Hua-Gen Yu and Sean C. Smith",
title = "The Elimination of {Lanczos} Ghosting Effects by
{MINRES} Filter Diagonalization",
journal = j-J-COMPUT-PHYS,
volume = "143",
number = "2",
pages = "484--494",
day = "1",
month = jul,
year = "1998",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1998.5971",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
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acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Bai:1999:AAB,
author = "Zhaojun Bai and David Day and Qiang Ye",
title = "{ABLE}: An Adaptive Block {Lanczos} Method for
Non-{Hermitian} Eigenvalue Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "20",
number = "4",
pages = "1060--1082",
year = "1999",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479897317806",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
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acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Brezinski:1999:NLA,
author = "C. Brezinski and M. Redivo Zaglia and H. Sadok",
title = "New look-ahead {Lanczos}-type algorithms for linear
systems",
journal = j-NUM-MATH,
volume = "83",
number = "1",
pages = "53--85",
month = jul,
year = "1999",
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acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Calvetti:1999:BLM,
author = "D. Calvetti and L. Reichel",
title = "A block-{Lanczos} method for large continuation
problems",
journal = j-NUMER-ALGORITHMS,
volume = "21",
number = "1--4",
pages = "109--118",
month = dec,
year = "1999",
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http://ipsapp007.kluweronline.com/content/getfile/5058/20/15/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Calvetti:1999:ECL,
author = "D. Calvetti and G. H. Golub and L. Reichel",
title = "Estimation of the {$L$}-curve via {Lanczos}
bidiagonalization",
journal = j-BIT-NUM-MATH,
volume = "39",
number = "4",
pages = "603--619",
month = dec,
year = "1999",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1022383005969",
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journal-URL = "http://link.springer.com/journal/10543",
}
@InProceedings{Frommer:1999:VEBa,
author = "Andreas Frommer and Andre Weinberg",
title = "Verified Error Bounds for Linear Systems through the
{Lanczos} Process",
crossref = "Csendes:1999:DRC",
pages = "255--267",
year = "1999",
bibdate = "Fri Nov 21 08:27:10 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Frommer:1999:VEBb,
author = "A. Frommer and A. Weinberg",
title = "Verified Error Bounds for Linear Systems Through the
{Lanczos} Process",
journal = j-RELIABLE-COMPUTING,
volume = "5",
number = "3",
pages = "255--267",
year = "1999",
CODEN = "RCOMF8",
ISSN = "1385-3139 (print), 1573-1340 (electronic)",
ISSN-L = "1385-3139",
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acknowledgement = ack-nhfb,
fjournal = "Reliable Computing = Nadezhnye vychisleniia",
journal-URL = "http://link.springer.com/journal/11155",
remark = "Papers from Scientific computing, computer arithmetic
and validated numerics (SCAN '98), September 1998,
Budapest, Hungary.",
}
@Article{Gallivan:1999:RAP,
author = "Kyle Gallivan and Paul {Van Dooren}",
title = "Rational approximations of pre-filtered transfer
functions via the {Lanczos} algorithm",
journal = j-NUMER-ALGORITHMS,
volume = "20",
number = "4",
pages = "331--342",
month = dec,
year = "1999",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Sep 29 08:36:58 MDT 2003",
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acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@InProceedings{Golub:1999:LSS,
author = "Gene H. Golub and Zhenyue Zhang and Hongyuan Zha",
booktitle = "Advances in numerical mathematics: Proceedings of the
Fourth Japan-China Joint Seminar on Numerical
Mathematics (Chiba, 1998)",
title = "Large sparse symmetric eigenvalue problems with
homogeneous linear constraints: the {Lanczos} process
with inner-outer iterations",
volume = "12",
publisher = "Gakk{\=o}tosho",
address = "Tokyo, Japan",
pages = "21--34",
year = "1999",
MRclass = "65F15 (65F30 65F50)",
MRnumber = "1 763 339",
bibdate = "Fri Jun 10 12:38:34 2011",
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series = "GAKUTO Internat. Ser. Math. Sci. Appl.",
acknowledgement = ack-nhfb,
}
@Article{Gould:1999:STR,
author = "Nicholas I. M. Gould and Stefano Lucidi and Massimo
Roma and Philippe L. Toint",
title = "Solving the Trust-Region Subproblem using the
{Lanczos} Method",
journal = j-SIAM-J-OPT,
volume = "9",
number = "2",
pages = "504--525",
month = mar,
year = "1999",
CODEN = "SJOPE8",
DOI = "https://doi.org/10.1137/S1052623497322735",
ISSN = "1052-6234 (print), 1095-7189 (electronic)",
ISSN-L = "1052-6234",
MRclass = "90C20 (65F10 65K05 90C30)",
MRnumber = "MR1686795 (2000b:90046)",
MRreviewer = "Horst Hollatz",
bibdate = "Tue Sep 30 16:21:28 MDT 2003",
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URL = "http://epubs.siam.org/sam-bin/dbq/article/32273",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Optimization",
journal-URL = "http://epubs.siam.org/siopt",
}
@Article{Im:1999:NLT,
author = "C. K. Im and S. P. Chang",
title = "Non-linear transient heat transfer analysis based on
{Lanczos} co-ordinates using pseudo-force method",
journal = j-COMM-NUMER-METHODS-ENGRG,
volume = "15",
number = "9",
pages = "629--639",
month = sep,
year = "1999",
DOI = "https://doi.org/10.1002/(SICI)1099-0887(199909)15",
ISSN = "1069-8299 (print), 1099-0887 (electronic)",
ISSN-L = "1069-8299",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Numerical Methods in Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-0887",
onlinedate = "29 Sep 1999",
}
@Article{Kim:1999:CEA,
author = "Man-Cheol Kim and In-Won Lee",
title = "A computationally efficient algorithm for the solution
of eigenproblems for large structures with
non-proportional damping using {Lanczos} method",
journal = j-EARTHQUAKE-ENG-STRUCT-DYN,
volume = "28",
number = "2",
pages = "157--172",
month = feb,
year = "1999",
CODEN = "IJEEBG",
DOI = "http://tinyurl.com/h8ktxdu",
ISSN = "0098-8847 (print), 1096-9845 (electronic)",
ISSN-L = "0098-8847",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Earthquake engineering \& structural dynamics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1096-9845",
onlinedate = "27 Jan 1999",
xxDOI = "https://doi.org/10.1002/(SICI)1096-9845(199902)28:2<157::AID-EQE809>3.0.CO%3B2-2",
}
@TechReport{Lehoucq:1999:CIR,
author = "Richard B. Lehoucq",
title = "On the Convergence of an Implicitly Restarted
{Arnoldi} Method",
type = "Report",
number = "SAND99-1756j",
institution = "United States Department of Energy",
address = "Washington, DC, USA",
pages = "13",
year = "1999",
LCCN = "????",
bibdate = "Thu Jun 9 11:13:14 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.osti.gov/servlets/purl/9021-L2vVMI/webviewable/",
abstract = "We show that Sorensen's [35] implicitly restarted
Arnoldi method (including its block extension) is
simultaneous iteration with an implicit projection step
to accelerate convergence to the invariant subspace of
interest. By using the geometric convergence theory for
simultaneous iteration due to Watkins and Elsner [43],
we prove that an implicitly restarted Arnoldi method
can achieve a super-linear rate of convergence to the
dominant invariant subspace of a matrix. Moreover, we
show how an IRAM computes a nested sequence of
approximations for the partial Schur decomposition
associated with the dominant invariant subspace of a
matrix.",
acknowledgement = ack-nhfb,
subject = "Eigenvalues; Convergence; Iterative Methods; Matrix
Elements; General And Miscellaneous//mathematics,
Computing, And Information Science",
}
@Article{Li:1999:AUL,
author = "Henian Li and Allan Woodbury and Peter Aitchison",
title = "Application of the unsymmetric {Lanczos} method to
radionuclide decay-chain transport in porous media",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "44",
number = "3",
pages = "355--372",
day = "30",
month = jan,
year = "1999",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/(SICI)1097-0207(19990130)44",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "7 Jan 1999",
}
@Article{Liu:1999:ASS,
author = "K. M. Liu and C. K. Pan",
title = "The automatic solution to systems of ordinary
differential equations by the tau method",
journal = j-COMPUT-MATH-APPL,
volume = "38",
number = "9--10",
pages = "197--210",
month = nov,
year = "1999",
CODEN = "CMAPDK",
DOI = "https://doi.org/10.1016/S0898-1221(99)00275-8",
ISSN = "0898-1221 (print), 1873-7668 (electronic)",
ISSN-L = "0898-1221",
bibdate = "Wed Mar 1 21:49:04 MST 2017",
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acknowledgement = ack-nhfb,
fjournal = "Computers and Mathematics with Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/08981221",
}
@Article{Paige:1999:SAL,
author = "Christopher C. Paige and Paul {Van Dooren}",
title = "Sensitivity analysis of the {Lanczos} reduction",
journal = j-NUM-LIN-ALG-APPL,
volume = "6",
number = "1",
pages = "29--50",
month = jan # "\slash " # feb,
year = "1999",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/(SICI)1099-1506(199901/02)6",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
MRclass = "65Fxx",
MRnumber = "1 684 651",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
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Computing, Part I (Milovy, 1997).",
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http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=62002985&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "22 Jun 1999",
}
@Article{Rao:1999:DSS,
author = "R. Venugopala Rao and N. S. V. Kameswara Rao",
title = "Dynamic soil--structure interaction analysis using
{Lanczos} vectors with adaptive time integration
technique",
journal = j-INT-J-NUMER-ANAL-METHODS-GEOMECH,
volume = "23",
number = "11",
pages = "1141--1158",
month = sep,
year = "1999",
CODEN = "IJNGDZ",
DOI = "http://tinyurl.com/hph4zbp",
ISSN = "0363-9061 (print), 1096-9853 (electronic)",
ISSN-L = "0363-9061",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical and Analytical
Methods in Geomechanics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1096-9853",
onlinedate = "31 Aug 1999",
xxDOI = "https://doi.org/10.1002/(SICI)1096-9853(199909)23:11<1141::AID-NAG997>3.0.CO%3B2-V",
}
@Article{Santoro:1999:LCN,
author = "Fabrizio Santoro and Carlo Petrongolo",
title = "{Lanczos} Calculation of the {$ \tilde {\rm X}^2 {\rm
A}_1 / \tilde {\rm A}^2 {\rm B}_2 $} Nonadiabatic
{Franck-Condon} Absorption Spectrum of {NO$_2$}",
journal = j-ADV-QUANTUM-CHEM,
volume = "36",
pages = "323--340",
year = "1999",
CODEN = "AQCHA9",
ISSN = "0065-3276",
bibdate = "Sat Dec 30 12:41:21 2000",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
OCR scan conversion; Science Citation Index database
(1980--2000)",
acknowledgement = ack-nhfb,
fjournal = "Advances in Quantum Chemistry",
journal-URL = "http://www.sciencedirect.com/science/bookseries/00653276",
journalabr = "Advan Quantum Chem",
toc = "1. Introduction 324;\\
2. Method 324;\\
3. Results 328;\\
4. Conclusions 338;\\
References 340",
}
@Article{Shen:1999:NGL,
author = "Jianhong Shen",
title = "Notes: On the Generalized ``{Lanczos}' Generalized
Derivative''",
journal = j-AMER-MATH-MONTHLY,
volume = "106",
number = "8",
pages = "766--767",
month = oct,
year = "1999",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Thu Dec 30 11:29:00 MST 1999",
bibsource = "http://www.maa.org/pubs/monthly.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "https://www.jstor.org/journals/00029890.htm",
mailto = "mailto:jhshen@math.ucla.edu",
}
@Article{Sun:1999:AAL,
author = "Din-Kow Sun",
title = "{ALPS}: An adaptive {Lanczos--Pad{\'e}} spectral
solution of mixed-potential integral equation",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "169",
number = "3--4",
pages = "425--432",
day = "12",
month = feb,
year = "1999",
CODEN = "CMMECC",
DOI = "https://doi.org/10.1016/S0045-7825(98)00167-4",
ISSN = "0045-7825 (print), 1879-2138 (electronic)",
ISSN-L = "0045-7825",
bibdate = "Fri Jun 10 17:04:52 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Methods in Applied Mechanics and
Engineering",
journal-URL = "http://www.sciencedirect.com/science/journal/00457825",
}
@Article{Szularz:1999:ERL,
author = "M. Szularz and J. Weston and M. Clint",
title = "Explicitly restarted {Lanczos} algorithms in an {MPP}
environment",
journal = j-PARALLEL-COMPUTING,
volume = "25",
number = "5",
pages = "613--631",
day = "1",
month = may,
year = "1999",
CODEN = "PACOEJ",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Fri Aug 6 10:16:06 MDT 1999",
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URL = "http://www.elsevier.com/cas/tree/store/parco/sub/1999/25/5/1397.pdf",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@Article{Szularz:1999:RTL,
author = "M. Szularz and J. Weston and M. Clint",
title = "Restarting Techniques for the {Lanczos} Algorithm and
Their Implementation in Parallel Computing
Environments: Architectural Influences",
journal = j-PARALLEL-ALGORITHMS-APPL,
volume = "14",
number = "1",
pages = "57--77",
month = "????",
year = "1999",
CODEN = "PAAPEC",
DOI = "https://doi.org/10.1080/10637199808947378",
ISSN = "1063-7192",
ISSN-L = "1026-7689",
MRclass = "65F10 (65Y05)",
MRnumber = "MR1689055",
bibdate = "Fri Jul 11 06:45:43 MDT 2008",
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URL = "http://www.informaworld.com/smpp/content~content=a777980765",
ZMnumber = "01799927",
acknowledgement = ack-nhfb,
fjournal = "Parallel Algorithms and Applications",
journal-URL = "http://www.tandfonline.com/loi/gpaa20",
}
@Article{Witte:1999:LAE,
author = "N. S. Witte and D. Bessis",
title = "The {Lanczos} algorithm for extensive many-body
systems in the thermodynamic limit",
journal = j-J-MATH-PHYS,
volume = "40",
number = "10",
pages = "4975--4994",
month = oct,
year = "1999",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.533010",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 20 08:10:39 MDT 2000",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Wu:1999:TRL,
author = "K. Wu and A. Canning and H. D. Simon and L.-W Wang",
title = "Thick-Restart {Lanczos} Method for Electronic
Structure Calculations",
journal = j-J-COMPUT-PHYS,
volume = "154",
number = "1",
pages = "156--173",
day = "1",
month = sep,
year = "1999",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.1999.6306",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 07:55:37 MST 2012",
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acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Yeung:1999:MBV,
author = "Man-Chung Yeung and Tony F. Chan",
title = "{ML$ (k) $BiCGSTAB}: {A} {BiCGSTAB} Variant Based on
Multiple {Lanczos} Starting Vectors",
journal = j-SIAM-J-SCI-COMP,
volume = "21",
number = "4",
pages = "1263--1290",
month = jul,
year = "1999",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827597321581",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Oct 27 13:32:22 MDT 2000",
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https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/32158",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Aliaga:2000:LTM,
author = "J. I. Aliaga and D. L. Boley and R. W. Freund and V.
Hern{\'a}ndez",
title = "A {Lanczos}-type method for multiple starting
vectors",
journal = j-MATH-COMPUT,
volume = "69",
number = "232",
pages = "1577--1601",
month = oct,
year = "2000",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Nov 1 11:50:08 MST 2000",
bibsource = "http://www.ams.org/mcom/2000-69-232;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
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http://www.ams.org/mcom/2000-69-232/S0025-5718-99-01163-1/S0025-5718-99-01163-1.tex",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Andersson:2000:SCL,
author = "F. Andersson and S. B. Edgar",
title = "Spin coefficients as {Lanczos} scalars: {Underlying}
spinor relations",
journal = j-J-MATH-PHYS,
volume = "41",
number = "5",
pages = "2990--3001",
month = may,
year = "2000",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.533285",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Oct 20 08:28:46 MDT 2000",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Baglama:2000:DLD,
author = "J. Baglama",
title = "Dealing with linear dependence during the iterations
of the restarted block {Lanczos} methods",
journal = j-NUMER-ALGORITHMS,
volume = "25",
number = "1--4",
pages = "23--36",
month = sep,
year = "2000",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F30",
MRnumber = "1 827 143",
bibdate = "Mon Sep 29 08:37:05 MDT 2003",
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note = "Mathematical journey through analysis, matrix theory
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http://ipsapp007.kluweronline.com/content/getfile/5058/3/23/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Benner:2000:IRS,
author = "Peter Benner and Heike Fassbender",
title = "An Implicitly Restarted Symplectic {Lanczos} Method
for the Symplectic Eigenvalue Problem",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "3",
pages = "682--713",
year = "2000",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479898343115",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Oct 27 07:23:39 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/34311",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Borici:2000:LAI,
author = "Artan Bori{\c{c}}i",
title = "A {Lanczos} Approach to the Inverse Square Root of a
Large and Sparse Matrix",
journal = j-J-COMPUT-PHYS,
volume = "162",
number = "1",
pages = "123--131",
day = "20",
month = jul,
year = "2000",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1006/jcph.2000.6529",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:11:56 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S002199910096529X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Cipra:2000:BCE,
author = "Barry A. Cipra",
title = "The Best of the {20th Century}: Editors Name Top 10
Algorithms",
journal = j-SIAM-NEWS,
volume = "33",
number = "4",
pages = "1--2",
month = may,
year = "2000",
ISSN = "0036-1437",
ISSN-L = "0036-1437",
bibdate = "Thu Sep 03 19:34:45 2020",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
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https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
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https://www.math.utah.edu/pub/tex/bib/fortran3.bib",
URL = "https://archive.siam.org/pdf/news/637.pdf",
acknowledgement = ack-nhfb,
fjournal = "SIAM News",
journal-URL = "http://www.siam.org/news/",
keywords = "1946: Monte Carlo method (John von Neumann, Stan Ulam,
and Nick Metropolis); 1947: simplex method for linear
programming (George Dantzig); 1950: Krylov subspace
iteration methods and conjugate gradient (Magnus
Hestenes, Eduard Stiefel, and Cornelius Lanczos); 1951:
decompositional approach to matrix computations (Alston
Householder); 1957: Fortran optimizing compiler (John
Backus); 1959--1961: QR algorithm (J. G. F. Francis);
1962: Quicksort (Tony Hoare); 1965: Fast Fourier
Transform (James Cooley and John Tukey); 1977: integer
relation detection algorithm (Helaman Ferguson and
Rodney Forcade); 1987: fast multipole algorithm (Leslie
Greengard and Vladimir Rokhlin)",
subject-dates = "Alston Scott Householder (5 May 1904--4 July 1993);
Cornelius Lanczos (2 February 1893--25 June 1974);
Eduard Stiefel (21 April 1909--25 November 1978);
George Bernard Dantzig (8 November 1914--13 May 2005);
James William Cooley (1926--June 29, 2016); John Warner
Backus (3 December 1924--17 March 2007); John Wilder
Tukey (16 June 1915--26 July 2000); Magnus Rudolph
Hestenes (13 February 1906--31 May 1991); Neumann
J{\'a}nos (28 December 1903--8 February 1957); Nicholas
Constantine Metropolis (11 June 1915--17 October 1999);
Stanis{\l}aw Marcin Ulam (13 April 1909--13 May 1984)",
}
@Article{Cizek:2000:SLC,
author = "M. {\c{C}}i{\v{z}}ek and J. Hor{\'a}{\v{c}}ek and
H.-D. Meyer",
title = "{Schwinger--Lanczos} for calculation of off-shell
{T}-matrix elements and {Wynn}'s epsilon algorithm",
journal = j-COMP-PHYS-COMM,
volume = "131",
number = "1--2",
pages = "41--51",
day = "1",
month = sep,
year = "2000",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/S0010-4655(00)00076-X",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Jun 10 16:24:59 2011",
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https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Fassbender:2000:EAS,
author = "Heike Fassbender",
title = "Error analysis of the symplectic {Lanczos} method for
the symplectic eigenvalue problem",
journal = j-BIT-NUM-MATH,
volume = "40",
number = "3",
pages = "471--496",
month = sep,
year = "2000",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1022315729226",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:04 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=40&issue=3;
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https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
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acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Fischer:2000:NSE,
author = "Patrick Fischer",
title = "Numerical solution of eigenvalue problems by means of
a wavelet-based {Lanczos} decomposition",
journal = j-IJQC,
volume = "77",
number = "2",
pages = "552--562",
month = "????",
year = "2000",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/(SICI)1097-461X(2000)77",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
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acknowledgement = ack-nhfb,
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
onlinedate = "10 Mar 2000",
}
@Article{Golub:2000:LSS,
author = "Gene H. Golub and Zhenyue Zhang and Hongyuan Zha",
title = "Large sparse symmetric eigenvalue problems with
homogeneous linear constraints: the {Lanczos} process
with inner-outer iterations",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "309",
number = "1--3",
pages = "289--306",
day = "15",
month = apr,
year = "2000",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Oct 9 10:54:41 MDT 2000",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
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http://www.elsevier.nl/gej-ng/10/30/19/126/25/39/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Gutknecht:2000:LAP,
author = "Martin H. Gutknecht and Klaus J. Ressel",
title = "Look-Ahead Procedures for {Lanczos}-Type Product
Methods Based on Three-Term {Lanczos} Recurrences",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "21",
number = "4",
pages = "1051--1078",
year = "2000",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479896306744",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Oct 27 07:23:32 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/21/4;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/30674",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Gutknecht:2000:LTM,
author = "M. H. Gutknecht",
title = "On {Lanczos-Type} Methods for {Wilson} Fermions",
crossref = "Frommer:2000:NCL",
pages = "48--65",
year = "2000",
bibdate = "Tue Feb 05 09:57:08 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
cnnumber = "CN036426100",
}
@Article{Hicks:2000:LGD,
author = "D. L. Hicks and L. M. Liebrock",
title = "{Lanczos}' generalized derivative: Insights and
Applications",
journal = j-APPL-MATH-COMP,
volume = "112",
number = "1",
pages = "63--73",
day = "1",
month = jun,
year = "2000",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/S0096-3003(99)00048-X",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Thu Oct 19 16:32:12 MDT 2000",
bibsource = "http://www.elsevier.com/locate/issn/00963003;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.nl/gej-ng/29/17/20/86/21/26/abstract.html;
http://www.elsevier.nl/gej-ng/29/17/20/86/21/26/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Kuijlaars:2000:WEF,
author = "A. B. J. Kuijlaars",
title = "Which Eigenvalues Are Found by the {Lanczos} Method?",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "1",
pages = "306--321",
year = "2000",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S089547989935527X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Oct 27 07:23:35 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/35527",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Ng:2000:PLM,
author = "Michael K. Ng",
title = "Preconditioned {Lanczos} Methods for the Minimum
Eigenvalue of a Symmetric Positive Definite {Toeplitz}
Matrix",
journal = j-SIAM-J-SCI-COMP,
volume = "21",
number = "6",
pages = "1973--1986",
month = nov,
year = "2000",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827597330169",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Oct 27 13:32:27 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/6;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/33016",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Simon:2000:LRM,
author = "Horst D. Simon and Hongyuan Zha",
title = "Low-Rank Matrix Approximation Using the {Lanczos}
Bidiagonalization Process with Applications",
journal = j-SIAM-J-SCI-COMP,
volume = "21",
number = "6",
pages = "2257--2274",
month = nov,
year = "2000",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827597327309",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Fri Oct 27 13:32:27 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/6;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/32730",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{UC:2000:NSL,
author = "{The UKQCD Collaboration} and Eamonn Cahill and Alan
Irving and Christopher Johnston and James Sexton",
title = "Numerical stability of {Lanczos} methods",
journal = j-NUCL-PHYS-B-PROC-SUPPL,
volume = "83--84",
number = "??",
pages = "825--827",
month = apr,
year = "2000",
CODEN = "NPBSE7",
DOI = "https://doi.org/10.1016/S0920-5632(00)91816-4",
ISSN = "0920-5632 (print), 1873-3832 (electronic)",
ISSN-L = "0920-5632",
bibdate = "Fri Jun 10 16:59:32 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Proceedings of the XVIIth International Symposium on
Lattice Field Theory.",
acknowledgement = ack-nhfb,
fjournal = "Nuclear Physics B, Proceedings Supplements",
journal-URL = "http://www.sciencedirect.com/science/journal/09205632",
}
@Article{vanDorsselaer:2000:CPB,
author = "Jos L. M. van Dorsselaer and Michiel E. Hochstenbach
and Henk A. van der Vorst",
title = "Computing probabilistic bounds for extreme eigenvalues
of symmetric matrices with the {Lanczos} method",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "3",
pages = "837--852",
year = "2000",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479800366859",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15A42)",
MRnumber = "MR1799527 (2001j:65061)",
MRreviewer = "Jin Yun Yuan",
bibdate = "Sat Dec 31 06:28:14 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib;
MathSciNet database",
URL = "http://epubs.siam.org/sam-bin/dbq/article/36685",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Voss:2000:SEL,
author = "Heinrich Voss",
title = "A symmetry exploiting {Lanczos} method for symmetric
{Toeplitz} matrices",
journal = j-NUMER-ALGORITHMS,
volume = "25",
number = "1--4",
pages = "377--385",
month = sep,
year = "2000",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F15",
MRnumber = "1 827 166",
bibdate = "Mon Sep 29 08:37:05 MDT 2003",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
MathSciNet database",
note = "Mathematical journey through analysis, matrix theory
and scientific computation (Kent, OH, 1999).",
URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/3/10/abstract.htm;
http://ipsapp007.kluweronline.com/content/getfile/5058/3/10/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Wu:2000:TRL,
author = "Kesheng Wu and Horst Simon",
title = "Thick-Restart {Lanczos} Method for Large Symmetric
Eigenvalue Problems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "2",
pages = "602--616",
year = "2000",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479898334605",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Oct 27 07:23:37 MDT 2000",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/2;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/33460",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Antoulas:2001:LLI,
author = "A. C. Antoulas and D. C. Sorensen",
title = "{Lyapunov}, {Lanczos}, and inertia",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "326",
number = "1--3",
pages = "137--150",
day = "15",
month = mar,
year = "2001",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Mar 19 19:03:24 MST 2001",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/148/24/32/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/148/24/32/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Bai:2001:PPL,
author = "Zhaojun Bai and Roland W. Freund",
title = "A partial {Pad{\'e}-via-Lanczos} method for
reduced-order modeling",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "332--334",
number = "1",
pages = "139--164",
day = "1",
month = aug,
year = "2001",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Jul 25 17:54:46 MDT 2001",
bibsource = "http://www.elsevier.com/locate/laa;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.nl/gej-ng/10/30/19/157/25/34/abstract.html;
http://www.elsevier.nl/gej-ng/10/30/19/157/25/34/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Bai:2001:SBL,
author = "Zhaojun Bai and Roland W. Freund",
title = "A Symmetric Band {Lanczos} Process Based on Coupled
Recurrences and Some Applications",
journal = j-SIAM-J-SCI-COMP,
volume = "23",
number = "2",
pages = "542--562",
month = mar,
year = "2001",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827500371773",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed Jul 25 09:55:57 MDT 2001",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/23/2;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/37177",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Cooper:2001:ESO,
author = "A. Cooper and M. Szularz and J. Weston",
title = "External selective orthogonalization for the {Lanczos}
algorithm in distributed memory environments",
journal = j-PARALLEL-COMPUTING,
volume = "27",
number = "7",
pages = "913--923",
month = jun,
year = "2001",
CODEN = "PACOEJ",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Wed Jul 18 06:31:16 MDT 2001",
bibsource = "http://www.elsevier.com/locate/issn/01678191;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.nl/gej-ng/10/35/21/47/31/27/abstract.html;
http://www.elsevier.nl/gej-ng/10/35/21/47/31/27/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@InCollection{Craig:2001:KLM,
author = "R. R. {Craig, Jr.}",
title = "{Krylov--Lanczos} Methods",
crossref = "Braun:2002:EV",
pages = "691--698",
year = "2001",
DOI = "https://doi.org/10.1006/rwvb.2001.0011",
bibdate = "Fri Jun 10 17:29:30 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Fierro:2001:LHT,
author = "Ricardo D. Fierro",
title = "{Lanczos}, {Householder} transformations, and implicit
deflation for fast and reliable dominant singular
subspace computation",
journal = j-NUM-LIN-ALG-APPL,
volume = "8",
number = "4",
pages = "245--264",
month = jun,
year = "2001",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.240",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "26 Mar 2001",
}
@Unpublished{Godfrey:2001:NCC,
author = "P. Godfrey",
title = "A Note on the Computation of the Convergent {Lanczos}
Complex Gamma Approximation",
year = "2001",
bibdate = "Mon Nov 24 21:04:40 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Unpublished Web file.",
URL = "http://my.fit.edu/~gabdo/gamma.txt",
acknowledgement = ack-nhfb,
}
@Article{Hanke:2001:LBM,
author = "Martin Hanke",
title = "On {Lanczos} based methods for the regularization of
discrete ill-posed problems",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "5",
pages = "1008--1018",
month = dec,
year = "2001",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1021941328858",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:05 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=5;
http://www.mai.liu.se/BIT/contents/bit41.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=5&spage=1008",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Honecker:2001:LSF,
author = "A. Honecker",
title = "{Lanczos} study of the $ {S} = 1 / 2 $ frustrated
square-lattice anti-ferromagnet in a magnetic field",
journal = j-CAN-J-PHYS,
volume = "79",
number = "??",
pages = "1557--1563",
month = "????",
year = "2001",
CODEN = "CJPHAD",
DOI = "https://doi.org/10.1139/p01-095",
ISSN = "0008-4204 (print), 1208-6045 (electronic)",
ISSN-L = "0008-4204",
bibdate = "Fri Jun 10 13:29:02 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Canadian Journal of Physics = Journal canadien de
physique",
journal-URL = "http://www.nrcresearchpress.com/journal/cjp",
}
@Article{Meerbergen:2001:CPR,
author = "K. Meerbergen",
title = "Changing poles in the rational {Lanczos} method for
the {Hermitian} eigenvalue problem",
journal = j-NUM-LIN-ALG-APPL,
volume = "8",
number = "1",
pages = "33--52",
month = jan # "\slash " # feb,
year = "2001",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/1099-1506(200101/02)8",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.interscience.wiley.com/journalfinder.html",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract/76501452/START;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=76501452&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "5 Dec 2000",
}
@Article{Meerbergen:2001:LMS,
author = "Karl Meerbergen",
title = "The {Lanczos} method with semi-definite inner
product",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "5",
pages = "1069--1078",
month = dec,
year = "2001",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1023/A:1021953631584",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:05 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=5;
http://www.mai.liu.se/BIT/contents/bit41.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=5&spage=1069",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Morigi:2001:RCL,
author = "S. Morigi and F. Sgallari",
title = "A regularizing {$L$}-curve {Lanczos} method for
underdetermined linear systems",
journal = j-APPL-MATH-COMP,
volume = "121",
number = "1",
pages = "55--73",
day = "25",
month = may,
year = "2001",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Tue Jul 17 08:45:13 MDT 2001",
bibsource = "http://www.elsevier.com/locate/issn/00963003;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.nl/gej-ng/10/9/12/105/21/25/abstract.html;
http://www.elsevier.nl/gej-ng/10/9/12/105/21/25/article.pdf",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Murga:2001:NAC,
author = "Leonel F. Murga and Mary Jo Ondrechen",
title = "Numerical Aspects of the Calculation of Second
Hyperpolarizabilities Using the Finite Field Method
Coupled with a Simple {Lanczos} Algorithm",
journal = j-J-COMPUT-CHEM,
volume = "22",
number = "4",
pages = "468--474",
month = mar,
year = "2001",
CODEN = "JCCHDD",
DOI = "https://doi.org/10.1002/1096-987X(200103)22",
ISSN = "0192-8651 (print), 1096-987X (electronic)",
ISSN-L = "0192-8651",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputchem2000.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Chemistry",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1096-987X",
onlinedate = "14 Feb 2001",
}
@InCollection{OLeary:2001:IMS,
author = "Dianne P. O'Leary",
title = "Iteration Method for the Solution of the Eigenvalue
Problem of Linear Differential and Integral Operators",
crossref = "Lide:2001:CEM",
pages = "77--80",
year = "2001",
bibdate = "Wed Oct 25 15:17:38 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/taussky-todd-olga.bib",
URL = "https://nvlpubs.nist.gov/nistpubs/sp958-lide/077-080.pdf",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991); Olga Taussky-Todd (30 August 1906--7 October
1995)",
}
@Article{vanDorsselaer:2001:CPB,
author = "Jos L. M. van Dorsselaer and Michiel E. Hochstenbach
and Henk A. van der Vorst",
title = "Computing Probabilistic Bounds for Extreme Eigenvalues
of Symmetric Matrices with the {Lanczos} Method",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "22",
number = "3",
pages = "837--852",
month = jul,
year = "2001",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Wed Oct 23 08:36:30 MDT 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/36685",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Voss:2001:VIL,
author = "Heinrich Voss",
title = "A variant of the inverted {Lanczos} method",
journal = j-BIT-NUM-MATH,
volume = "41",
number = "5",
pages = "1111--1120",
month = "????",
year = "2001",
CODEN = "BITTEL, NBITAB",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Thu Oct 16 08:15:34 2003",
bibsource = "http://www.mai.liu.se/BIT/contents/bit41.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@MastersThesis{Wang:2001:IRA,
author = "Xianyao Wang",
title = "The {Implicitly Restarted Arnoldi (IRA)} method for
eigenanalysis of large power systems",
type = "Thesis ({M.S.})",
school = "University of Missouri--Rolla",
address = "Rolla, MO, USA",
pages = "x + 91",
year = "2001",
bibdate = "Thu Jun 9 11:13:14 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Weaire:2001:BRL,
author = "Denis Weaire",
title = "Book Review: {{\booktitle{A life's work in exile
Cornelius Lanczos: collected published papers with
commentaries}}. North Carolina State University, 1999
ISBN 0-929493-01-X}",
journal = j-EUROPHYS-NEWS,
volume = "32",
number = "1",
pages = "27--27",
month = jan # "\slash " # feb,
year = "2001",
CODEN = "EUPNAS",
ISSN = "0531-7479 (print), 1432-1092 (electronic)",
ISSN-L = "0531-7479",
bibdate = "Mon May 21 16:45:39 2018",
URL = "https://www.europhysicsnews.org/articles/epn/pdf/2001/01/epn2001-32-1.pdf",
acknowledgement = ack-nhfb,
fjournal = "Europhysics News",
journal-URL = "http://www.europhysicsnews.org",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
}
@Article{Calvetti:2002:CCB,
author = "D. Calvetti and P. C. Hansen and L. Reichel",
title = "{$L$}-curve curvature bounds via {Lanczos}
bidiagonalization",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "14",
pages = "20--35",
year = "2002",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:29 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://etna.mcs.kent.edu/vol.14.2002/pp20-35.dir/pp20-35.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Calvetti:2002:LBE,
author = "D. Calvetti and L. Reichel",
title = "{Lanczos}-Based Exponential Filtering for Discrete
Ill-Posed Problems",
journal = j-NUMER-ALGORITHMS,
volume = "29",
number = "1--3",
pages = "45--65",
month = mar,
year = "2002",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Thu Apr 11 06:41:52 MDT 2002",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://ipsapp008.lwwonline.com/content/getfile/5058/38/4/abstract.htm;
http://ipsapp008.lwwonline.com/content/getfile/5058/38/4/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Cooper:2002:ALE,
author = "A. Cooper and M. Szularz and J. Weston",
title = "Analysis of the {Lanczos} Error Bounds and Its
Application to the Explicitly Restarted {Lanczos}
Algorithm",
journal = j-LECT-NOTES-COMP-SCI,
volume = "2328",
pages = "410--??",
year = "2002",
CODEN = "LNCSD9",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
ISSN-L = "0302-9743",
bibdate = "Tue Sep 10 19:09:33 MDT 2002",
bibsource = "http://link.springer-ny.com/link/service/series/0558/tocs/t2328.htm;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://link.springer-ny.com/link/service/series/0558/bibs/2328/23280410.htm;
http://link.springer-ny.com/link/service/series/0558/papers/2328/23280410.pdf",
acknowledgement = ack-nhfb,
fjournal = "Lecture Notes in Computer Science",
journal-URL = "http://link.springer.com/bookseries/558",
}
@Book{Cullum:2002:LAL,
author = "Jane K. Cullum and Ralph A. Willoughby",
title = "{Lanczos} algorithms for large symmetric eigenvalue
computations",
volume = "41",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xx + 268",
year = "2002",
ISBN = "0-89871-523-7 (paperback)",
ISBN-13 = "978-0-89871-523-1 (paperback)",
LCCN = "QA193 .C84 2002",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
series = "Classics in applied mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0664/2002075847-d.html;
http://www.loc.gov/catdir/enhancements/fy0664/2002075847-t.html",
acknowledgement = ack-nhfb,
remark = "Originally published: Boston:Birkh{\"a}user, 1985-, in
series: Progress in scientific computing ; v. 3. v. 1.
Theory.",
subject = "Symmetric matrices; Data processing; Eigenvalues",
}
@Article{Cullum:2002:TSA,
author = "Jane Cullum and Tong Zhang",
title = "Two-Sided {Arnoldi} and Nonsymmetric {Lanczos}
Algorithms",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "24",
number = "2",
pages = "303--319",
year = "2002",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479898339013",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue Oct 22 18:08:00 MDT 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/24/2;
https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/33901",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Fasino:2002:LTA,
author = "Dario Fasino and Luca Gemignani",
title = "A {Lanczos}-type algorithm for the {$ Q R $}
factorization of regular {Cauchy} matrices",
journal = j-NUM-LIN-ALG-APPL,
volume = "9",
number = "4",
pages = "305--319",
month = jun,
year = "2002",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.275",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.interscience.wiley.com/journalfinder.html",
URL = "http://www3.interscience.wiley.com/cgi-bin/abstract/92012855/START;
http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=92012855&PLACEBO=IE.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "25 Mar 2002",
}
@InBook{Hazewinkel:2002:EM,
editor = "Michiel Hazewinkel",
booktitle = "Encyclopaedia of mathematics",
title = "Tau method",
pages = "??--??",
publisher = pub-SV,
address = pub-SV:adr,
year = "2002",
ISBN = "1-4020-0609-8",
ISBN-13 = "978-1-4020-0609-8",
LCCN = "QA5 20",
bibdate = "Mon Jun 13 12:57:15 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://eom.springer.de/t/t130040.htm",
acknowledgement = ack-nhfb,
remark = "The article notes that Tau-Method approximations are
of the order of the best uniform or rational polynomial
approximations. While they are not difficult to
evaluate, they are more difficult to generate in the
first place, and it seems uncertain whether they offer
any advantages over the easier-to-compute Chebyshev or
minimax approximations that are available in some
symbolic-algebra systems.",
subject = "Mathematics; Encyclopedias",
}
@Article{Huhtanen:2002:HLM,
author = "Marko Huhtanen",
title = "A {Hermitian} {Lanczos} Method for Normal Matrices",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "23",
number = "4",
pages = "1092--1108",
year = "2002",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479800398468",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Apr 12 05:26:56 MDT 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/23/4;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/39846",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Odekunle:2002:SBV,
author = "M. R. Odekunle",
title = "Solution of boundary value problems by
{Lanczos--Legendre} reduction method",
journal = j-APPL-MATH-COMP,
volume = "131",
number = "2--3",
pages = "321--327",
day = "25",
month = sep,
year = "2002",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Jan 9 08:40:42 MST 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Phatak:2002:ECB,
author = "Aloke Phatak and Frank de Hoog",
title = "Exploiting the connection between {PLS}, {Lanczos}
methods and conjugate gradients: alternative proofs of
some properties of {PLS}",
journal = j-J-CHEMOM,
volume = "16",
number = "7",
pages = "361--367",
month = jul,
year = "2002",
CODEN = "JOCHEU",
DOI = "https://doi.org/10.1002/cem.728",
ISSN = "0886-9383 (print), 1099-128x (electronic)",
ISSN-L = "0886-9383",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Chemometrics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-128X",
onlinedate = "17 Jun 2002",
}
@Article{Rollin:2002:VZL,
author = "Stefan R{\"o}llin and Martin H. Gutknecht",
title = "Variations of {Zhang}'s {Lanczos}-type product
method",
journal = j-APPL-NUM-MATH,
volume = "41",
number = "1",
pages = "119--133",
month = apr,
year = "2002",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Mon Feb 25 12:44:11 MST 2002",
bibsource = "http://www.elsevier.com/locate/issn/01689274;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.elsevier.com/gej-ng/10/10/28/86/27/35/abstract.html",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Stewart:2002:ARQ,
author = "G. W. Stewart",
title = "Adjusting the {Rayleigh} Quotient in Semiorthogonal
{Lanczos} Methods",
journal = j-SIAM-J-SCI-COMP,
volume = "24",
number = "1",
pages = "201--207",
month = jan,
year = "2002",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827501388984",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Tue Oct 22 18:24:38 MDT 2002",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/24/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/38898",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{VanIseghem:2002:VOL,
author = "Jeannette {Van Iseghem}",
title = "Vector-Orthogonality and {Lanczos}-Type Methods",
journal = j-NUMER-ALGORITHMS,
volume = "29",
number = "1--3",
pages = "267--279",
month = mar,
year = "2002",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Thu Apr 11 06:41:52 MDT 2002",
bibsource = "http://www.kluweronline.com/issn/1017-1398;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://ipsapp008.lwwonline.com/content/getfile/5058/38/15/abstract.htm;
http://ipsapp008.lwwonline.com/content/getfile/5058/38/15/fulltext.pdf",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Baglama:2003:IIR,
author = "J. Baglama and D. Calvetti and L. Reichel",
title = "{IRBL}: An Implicitly Restarted Block-{Lanczos} Method
for Large-Scale {Hermitian} Eigenproblems",
journal = j-SIAM-J-SCI-COMP,
volume = "24",
number = "5",
pages = "1650--1677",
month = sep,
year = "2003",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/S1064827501397949",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed Aug 20 06:34:28 MDT 2003",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/24/5;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/39794",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Chien:2003:ALA,
author = "C.-S. Chien and S.-L. Chang",
title = "Application of the {Lanczos} algorithm for solving the
linear systems that occur in continuation problems",
journal = j-NUM-LIN-ALG-APPL,
volume = "10",
number = "4",
pages = "335--355",
month = jun,
year = "2003",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.306",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.interscience.wiley.com/journalfinder.html",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "30 Oct 2002",
}
@Article{Dolan:2003:EDS,
author = "P. Dolan and A. Gerber",
title = "Exterior differential systems, {Janet--Riquier} theory
and the {Riemann--Lanczos} problems in two, three, and
four dimensions",
journal = j-J-MATH-PHYS,
volume = "44",
number = "7",
pages = "3013--3034",
month = jul,
year = "2003",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1566095",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Tue Dec 16 11:36:04 MST 2003",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Dolan:2003:WLE,
author = "P. Dolan and A. Gerber",
title = "The {Weyl--Lanczos} equations and the {Lanczos} wave
equation in four dimensions as systems in involution",
journal = j-J-MATH-PHYS,
volume = "44",
number = "7",
pages = "3035--3045",
month = jul,
year = "2003",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1566096",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Tue Dec 16 11:36:04 MST 2003",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Edgar:2003:ECR,
author = "S. Brian Edgar",
title = "On effective constraints for the {Riemann--Lanczos}
system of equations",
journal = j-J-MATH-PHYS,
volume = "44",
number = "11",
pages = "5375--5385",
month = nov,
year = "2003",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1619203",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Tue Dec 16 11:36:07 MST 2003",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Gerber:2003:PMC,
author = "A. Gerber",
title = "Prolongation methods and {Cartan} characters for the
three-dimensional {Riemann--Lanczos} problem",
journal = j-J-MATH-PHYS,
volume = "44",
number = "7",
pages = "3059--3070",
month = jul,
year = "2003",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1578181",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Tue Dec 16 11:36:04 MST 2003",
bibsource = "http://www.aip.org/ojs/jmp.html;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Jia:2003:IRR,
author = "Zhongxiao Jia and Datian Niu",
title = "An Implicitly Restarted Refined Bidiagonalization
{Lanczos} Method for Computing a Partial Singular Value
Decomposition",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "25",
number = "1",
pages = "246--265",
year = "2003",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479802404192",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Fri Aug 15 05:16:22 MDT 2003",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/25/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/40419",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Kim:2003:DAS,
author = "Byoung-Wan Kim and Hyung-Jo Jung and Woon-Hak Kim and
In-Won Lee",
title = "Dynamic analysis of structures using modified
{Lanczos} co-ordinates",
journal = j-EARTHQUAKE-ENG-STRUCT-DYN,
volume = "32",
number = "9",
pages = "1469--1474",
day = "25",
month = jul,
year = "2003",
CODEN = "IJEEBG",
DOI = "https://doi.org/10.1002/eqe.284",
ISSN = "0098-8847 (print), 1096-9845 (electronic)",
ISSN-L = "0098-8847",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Earthquake engineering \& structural dynamics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1096-9845",
onlinedate = "9 May 2003",
}
@Book{Komzsik:2003:LME,
author = "Louis Komzsik",
title = "The {Lanczos} method: evolution and application",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xii + 87",
year = "2003",
ISBN = "0-89871-537-7 (paperback)",
ISBN-13 = "978-0-89871-537-8 (paperback)",
LCCN = "QA76.9.M35 .K66 2003",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
melvyl.cdlib.org:210/CDL90;
z3950.loc.gov:7090/Voyager",
series = "Software, environments, tools",
URL = "http://www.loc.gov/catdir/enhancements/fy0708/2002044643-d.html;
http://www.loc.gov/catdir/enhancements/fy0708/2002044643-t.html",
acknowledgement = ack-nhfb,
subject = "Computer science; Mathematics; Numerical analysis;
Computer algorithms; Eigenvalues",
tableofcontents = "Preface \\
Part I: Evolution \\
Chapter 1: The classical Lanczos method \\
Chapter 2: The Lanczos method in exact arithmetic \\
Chapter 3: The Lanczos method in finite precision \\
Chapter 4: Block real symmetric Lanczos method \\
Chapter 5: Block unsymmetric Lanczos method \\
Part II: Applications \\
Chapter 6: Industrial implementation of the Lanczos
method \\
Chapter 7: Free undamped vibrations \\
Chapter 8: Free damped vibrations \\
Chapter 9: Forced vibration analysis \\
Chapter 10: Linear systems and the Lanczos method \\
Closing Remarks \\
A Brief Biography of Cornelius Lanczos \\
Bibliography \\
Index",
}
@Article{Malyshev:2003:CNL,
author = "A. Malyshev and M. Sadkane",
title = "Condition numbers for {Lanczos} bidiagonalization with
complete reorthogonalization",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "371",
number = "1",
pages = "315--331",
day = "15",
month = sep,
year = "2003",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Tue Sep 16 08:20:04 MDT 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Book{McCartney:2003:PIP,
editor = "Mark McCartney and Andrew Whitaker",
title = "Physicists of {Ireland}: passion and precision",
publisher = "Institute of Physics Publishers",
address = "Bristol and Philadelphia",
pages = "xiv + 298",
year = "2003",
ISBN = "0-7503-0866-4 (hardback)",
ISBN-13 = "978-0-7503-0866-3 (hardback)",
LCCN = "QC15 .P47 2003",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/notes-rec-r-soc-lond.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0806/2007298520-d.html;
http://www.loc.gov/catdir/toc/fy0802/2007298520.html",
acknowledgement = ack-nhfb,
remark = "William Petty 1623--1687 / by Norman D. McMillan \\
Robert Boyle 1627--1691 / by D. Thorburn Burns \\
William Molyneux 1656--1698 / by Patrick Wayman and
Norman D. McMillan \\
Nicholas Callan 1799--1864 / by Niall E. McKeith \\
William Parsons, Earl of Rosse 1800--1867 / by Bob
Strunz \\
Humphrey Lloyd 1800--1881 / by James G. O'Hara \\
Thomas Grubb 1800--1878 and Howard Grubb 1844--1931 /
by Andrew Whitaker \\
William Rowan Hamilton 1805--1865 / by John J. O'Connor
and Edmund F. Robertson \\
James MacCullagh 1809--1847 / by James G. O'Hara \\
Thomas Andrews 1813--1885 / by D. Thorburn Burns \\
George Gabriel Stokes 1819--1903 / by Alastair Wood \\
John Tyndall 1820--1893 / by Norman D. McMillan \\
Samuel Haughton 1821--1897 / by Norman D. McMillan \\
William Thomson, Lord Kelvin 1824--1907 / by Mark
McCartney \\
George Johnstone Stoney 1826--1911 / by James G. O'Hara
\\
George Francis FitzGerald 1851--1901 / by John J.
O'Connor and Edmund F. Robertson \\
John Joly 1857--1933 / by Denis Weaire and Stephen
Coonan \\
Joseph Larmor 1857--1942 / by Raymond Flood \\
Frederick Thomas Trouton 1863--1922 / by James G.
O'Hara \\
John Sealy Edward Townsend 1868--1957 / by Mark
McCartney \\
John A. McClelland 1870--1920 / by Thomas C. O'Connor
\\
Erwin Schr{\"o}dinger 1887--1961 / by Andrew Whitaker
\\
Cornelius Lanczos 1893--1974 / by Barbara Gellai \\
John Synge 1897--1995 / by Petros S. Florides \\
John Desmond Bernal 1901--1971 / by Roy Johnston \\
Ernest Walton 1903--1995 / by Brian Cathcart \\
Walter Heitler 1904--1981 / by David Glass \\
Sir William McCrea 1904--1999 / by Iwan Williams \\
Cormac {\'O}Ceallaigh 1912--1996 / by Mark McCartney
\\
David Bates 1916--1994 / by Ray Flannery \\
John Stewart Bell 1928--1990 / by Andrew Whitaker \\
Lochlainn {\'O}Raifeartaigh 1933--2000 / by Siddhartha
Sen \\
Index of names",
subject = "Physicists; Ireland; Biography; Physiciens; Irlande;
Biographies; Natuurkundigen",
}
@Article{Odekunle:2003:PEE,
author = "M. R. Odekunle and M. A. Ibiejugba and P. Onumanyi",
title = "A posteriori error estimator for {Lanczos--Chebyshev}
reduction method",
journal = j-APPL-MATH-COMP,
volume = "137",
number = "2--3",
pages = "245--252",
day = "25",
month = may,
year = "2003",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Fri Jan 9 08:40:55 MST 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Odekunle:2003:SLC,
author = "M. R. Odekunle",
title = "Segmented {Lanczos--Chebyshev} reduction method for
convection dominated flows",
journal = j-APPL-MATH-LETT,
volume = "16",
number = "5",
pages = "777--784",
year = "2003",
CODEN = "AMLEEL",
DOI = "https://doi.org/10.1016/S0893-9659(03)00082-X",
ISSN = "0893-9659 (print), 1873-5452 (electronic)",
ISSN-L = "0893-9659",
bibdate = "Fri Jun 10 12:27:16 2011",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/appml/appml16.html#Odekunle03;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/08939659",
}
@Article{Simoncini:2003:AFS,
author = "V. Simoncini",
title = "Algebraic formulations for the solution of the
nullspace-free eigenvalue problem using the inexact
{Shift-and-Invert Lanczos} method",
journal = j-NUM-LIN-ALG-APPL,
volume = "10",
number = "4",
pages = "357--375",
month = jun,
year = "2003",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.307",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.interscience.wiley.com/journalfinder.html",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "30 Oct 2002",
}
@Article{Borchers:2004:BRL,
author = "Brian Borchers",
title = "Book Review: {{\em The Lanczos Method: Evolution and
Application}, by Louis Komzsik}",
journal = j-SCI-PROG,
volume = "12",
number = "3",
pages = "197--198",
month = "????",
year = "2004",
CODEN = "SCIPEV",
ISSN = "1058-9244 (print), 1875-919X (electronic)",
ISSN-L = "1058-9244",
bibdate = "Wed Sep 1 14:50:28 MDT 2010",
bibsource = "http://www.iospress.nl/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Scientific Programming",
journal-URL = "http://iospress.metapress.com/content/1058-9244",
}
@Article{Dolan:2004:WLR,
author = "P. Dolan and A. Gerber",
title = "The {Weyl--Lanczos} relations and the four-dimensional
{Lanczos} tensor wave equation and some symmetry
generators",
journal = j-J-MATH-PHYS,
volume = "45",
number = "1",
pages = "310--326",
month = jan,
year = "2004",
CODEN = "JMAPAQ",
DOI = "https://doi.org/10.1063/1.1625076",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Jun 10 07:45:40 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Guennouni:2004:BLM,
author = "A. El Guennouni and K. Jbilou and H. Sadok",
title = "The block {Lanczos} method for linear systems with
multiple right-hand sides",
journal = j-APPL-NUM-MATH,
volume = "51",
number = "2--3",
pages = "243--256",
month = nov,
year = "2004",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Sat May 14 10:50:47 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.sciencedirect.com/science/journal/01689274",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Kokiopoulou:2004:CSS,
author = "E. Kokiopoulou and C. Bekas and E. Gallopoulos",
title = "Computing smallest singular triplets with implicitly
restarted {Lanczos} bidiagonalization",
journal = j-APPL-NUM-MATH,
volume = "49",
number = "1",
pages = "39--61",
month = apr,
year = "2004",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Sat May 14 10:50:46 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.sciencedirect.com/science/journal/01689274",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Maslen:2004:CIP,
author = "David K. Maslen and Michael E. Orrison and Daniel N.
Rockmore",
title = "Computing Isotypic Projections with the {Lanczos}
Iteration",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "25",
number = "3",
pages = "784--803",
year = "2004",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/S0895479801399778",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
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/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/39977",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@PhdThesis{Pugh:2004:ALG,
author = "Glendon Ralpha Pugh",
title = "An Analysis of the {Lanczos} Gamma Approximation",
type = "{Ph.D.} thesis",
school = "Department of Mathematics, University of British
Columbia",
address = "Vancouver, BC, Canada",
pages = "viii + 154",
month = "????",
year = "2004",
ISBN = "0-612-99536-4",
ISBN-13 = "978-0-612-99536-9",
LCCN = "AW5 .B7 2005-995364",
bibdate = "Mon Nov 24 20:55:30 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Wang:2004:USC,
author = "Xiao-Gang Wang and Tucker {Carrington, Jr.}",
title = "Using simply contracted basis functions with the
{Lanczos} algorithm to calculate vibrational spectra",
journal = j-IJQC,
volume = "99",
number = "4",
pages = "556--566",
day = "15",
month = sep,
year = "2004",
CODEN = "IJQCB2",
DOI = "https://doi.org/10.1002/qua.10847",
ISSN = "0020-7608 (print), 1097-461X (electronic)",
ISSN-L = "0020-7608",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal of Quantum Chemistry",
journal-URL = "http://www.interscience.wiley.com/jpages/0020-7608/",
onlinedate = "29 Dec 2003",
}
@Article{Watkins:2004:HSL,
author = "David S. Watkins",
title = "On {Hamiltonian} and symplectic {Lanczos} processes",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "385",
number = "1",
pages = "23--45",
day = "1",
month = jul,
year = "2004",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Tue Nov 9 07:02:35 MST 2004",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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{Baglama:2005:AIR,
author = "James Baglama and Lothar Reichel",
title = "Augmented Implicitly Restarted {Lanczos}
Bidiagonalization Methods",
journal = j-SIAM-J-SCI-COMP,
volume = "27",
number = "1",
pages = "19--42",
month = jan,
year = "2005",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/04060593X",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Mon Nov 21 14:52:50 MST 2005",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/27/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/sam-bin/dbq/article/60593",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Borisov:2005:LPM,
author = "Andrei G. Borisov and Sergei V. Shabanov",
title = "{Lanczos} pseudospectral method for initial-value
problems in electrodynamics and its applications to
ionic crystal gratings",
journal = j-J-COMPUT-PHYS,
volume = "209",
number = "2",
pages = "643--664",
day = "1",
month = nov,
year = "2005",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2005.03.034",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:12:55 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999105001920",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Chang:2005:CBL,
author = "Shu-Ming Chang and Yuen-Cheng Kuo and Wen-Wei Lin and
Shih-Feng Shieh",
title = "A continuation {BSOR--Lanczos--Galerkin} method for
positive bound states of a multi-component
{Bose--Einstein} condensate",
journal = j-J-COMPUT-PHYS,
volume = "210",
number = "2",
pages = "439--458",
day = "10",
month = dec,
year = "2005",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2005.04.019",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:13:15 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999105002287",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Druskin:2005:SLR,
author = "Vladimir Druskin and Liliana Borcea and Leonid
Knizhnerman",
title = "On the sensitivity of {Lanczos} recursions to the
spectrum",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "396",
number = "1",
pages = "103--125",
day = "1",
month = feb,
year = "2005",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Sat May 14 07:59:08 MDT 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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{Fierro:2005:LRS,
author = "Ricardo D. Fierro and Eric P. Jiang",
title = "{Lanczos} and the {Riemannian SVD} in information
retrieval applications",
journal = j-NUM-LIN-ALG-APPL,
volume = "12",
number = "4",
pages = "355--372",
month = may,
year = "2005",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.394",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.interscience.wiley.com/journalfinder.html",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "17 Jun 2004",
}
@InProceedings{Hovinen:2005:RBL,
author = "Bradford Hovinen and Wayne Eberly",
title = "A reliable block {Lanczos} algorithm over small finite
fields",
crossref = "Kauers:2005:IJB",
pages = "177--184",
year = "2005",
bibdate = "Fri Oct 21 06:53:01 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Illge:2005:SGA,
author = "Reinhard Illge",
title = "Some general ans{\"a}tze for the {Lanczos} potential
spinor",
journal = j-MATH-NACHR,
volume = "278",
number = "14",
pages = "1681--1688",
month = nov,
year = "2005",
CODEN = "MTMNAQ",
DOI = "https://doi.org/10.1002/mana.200310333",
ISSN = "0025-584X",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematische Nachrichten",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
onlinedate = "29 Sep 2005",
}
@Article{Meerbergen:2005:BRL,
author = "Karl Meerbergen",
title = "Book review: {{\em The Lanczos method: evolution and
application}}",
journal = j-MATH-COMPUT,
volume = "74",
number = "250",
pages = "??--??",
month = apr,
year = "2005",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Aug 2 10:37:16 MDT 2005",
bibsource = "http://www.ams.org/mcom/2005-74-250;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.ams.org/mcom/2005-74-250/S0025-5718-04-01757-0/home.html;
http://www.ams.org/mcom/2005-74-250/S0025-5718-04-01757-0/S0025-5718-04-01757-0.dvi;
http://www.ams.org/mcom/2005-74-250/S0025-5718-04-01757-0/S0025-5718-04-01757-0.pdf;
http://www.ams.org/mcom/2005-74-250/S0025-5718-04-01757-0/S0025-5718-04-01757-0.ps;
http://www.ams.org/mcom/2005-74-250/S0025-5718-04-01757-0/S0025-5718-04-01757-0.tex",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{vandenEshof:2005:PLA,
author = "Jasper van den Eshof and Marlis Hochbruck",
title = "Preconditioning {Lanczos} Approximations to the Matrix
Exponential",
journal = j-SIAM-J-SCI-COMP,
volume = "27",
number = "4",
pages = "1438--1457",
month = jul,
year = "2005",
CODEN = "SJOCE3",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Tue Jun 27 09:24:24 MDT 2006",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/27/4;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://epubs.siam.org/volume-27/art_60546.html",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Wulling:2005:SCC,
author = "Wolfgang W{\"u}lling",
title = "On Stabilization and Convergence of Clustered {Ritz}
Values in the {Lanczos} Method",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "27",
number = "3",
pages = "891--908",
month = jan,
year = "2005",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/040608908",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue May 18 22:32:04 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Wulling:2005:SWL,
author = "Wolfgang W{\"u}lling",
title = "The Stabilization of Weights in the {Lanczos} and
Conjugate Gradient Method",
journal = j-BIT-NUM-MATH,
volume = "45",
number = "2",
pages = "395--414",
month = jun,
year = "2005",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/s10543-005-0017-0",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 15:06:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=45&issue=2;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bit.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=45&issue=2&spage=395",
acknowledgement = ack-nhfb,
journal-URL = "http://link.springer.com/journal/10543",
}
@Article{Baglama:2006:RBL,
author = "James Baglama and Lothar Reichel",
title = "Restarted block {Lanczos} bidiagonalization methods",
journal = j-NUMER-ALGORITHMS,
volume = "43",
number = "3",
pages = "251--272",
month = nov,
year = "2006",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-006-9057-z",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "subject classification (2000); 65F15; 15A18",
bibdate = "Tue Jul 8 19:14:29 MDT 2008",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=43&issue=3;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=43&issue=3&spage=251",
acknowledgement = ack-nhfb,
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "augmentation; implicit shifts; partial singular value
decomposition; restarted iterative method",
}
@Article{Bisseling:2006:MSM,
author = "Rob H. Bisseling and Ildik{\'o} Flesch",
title = "{Mondriaan} sparse matrix partitioning for attacking
cryptosystems by a parallel block {Lanczos} algorithm
--- a case study",
journal = j-PARALLEL-COMPUTING,
volume = "32",
number = "7--8",
pages = "551--567",
month = sep,
year = "2006",
CODEN = "PACOEJ",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Thu Sep 2 17:51:05 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.sciencedirect.com/science/journal/01678191",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@TechReport{Denisenko:2006:LMO,
author = "P. N. Denisenko",
title = "{Lanczos} $ \tau $-method optimal algorithm in {APS}
for approximating the mathematical functions",
institution = "????",
address = "????",
pages = "10",
year = "2006",
bibdate = "Fri Jun 10 12:30:05 2011",
bibsource = "DBLP;
http://dblp.uni-trier.de/db/journals/corr/corr0603.html#abs-math-0603606;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Based on a talk given at the Workshop on Symbolic
Calculations and Exact Methods in Mathematical Physics,
Kiev, June 20-26, 2005",
URL = "http://arxiv.org/abs/math/0603606",
abstract = "A new procedure is constructed by means of APS in
APLAN language. The procedure solves the initial-value
problem for linear differential equations of order $k$
with polynomial coefficients and regular singularity in
the initialization point in the interval $ [a, b] $ and
computes the algebraic polynomial $ y_n $ of given
order $n$. A new algorithm of Lanczos $ \tau $-method
is built for this procedure, the solution existence $
y_n $ of the initial-value problem proved on this
algorithm and also is proved the optimality by
precision of order $k$ derivative of the initial-value
problem solution.",
acknowledgement = ack-nhfb,
}
@Article{Garcia:2006:EAW,
author = "V. M. Garc{\'\i}a and A. Vidal and V. E. Boria and A.
M. Vidal",
title = "Efficient and accurate waveguide mode computation
using {BI-RME} and {Lanczos} methods",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "65",
number = "11",
pages = "1773--1788",
day = "12",
month = mar,
year = "2006",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1520",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "6 Oct 2005",
}
@Article{Hetmaniuk:2006:UAE,
author = "U. L. Hetmaniuk and R. B. Lehoucq",
title = "Uniform accuracy of eigenpairs from a shift-invert
{Lanczos} method",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "28",
number = "4",
pages = "927--948",
month = jan,
year = "2006",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/050629288",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue May 18 22:32:14 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Hnetynkova:2006:LTG,
author = "Iveta Hn{\v{e}}tynkov{\'a} and Martin Ple{\v{s}}inger
and Zden{\v{e}}k Strako{\v{s}}",
title = "{Lanczos} tridiagonalization, {Golub--Kahan}
bidiagonalization and coreproblem",
journal = j-PAMM,
volume = "6",
number = "1",
pages = "717--718",
month = dec,
year = "2006",
DOI = "https://doi.org/10.1002/pamm.200610339",
ISSN = "1617-7061",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings in Applied Mathematics and Mechanics",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1617-7061",
onlinedate = "23 Jan 2007",
}
@InCollection{Householder:2006:PVV,
author = "Alston Scott Householder",
title = "Proper values and vectors: normalization and reduction
of the matrix (methods of {Krylov, Webber-Voetter,
Danilevskii, Hessenberg, Lanczos, Samuelson and Bryan,
Leverrier}, etc.)",
crossref = "Householder:2006:TMN",
chapter = "6",
pages = "??--??",
year = "2006",
bibdate = "Tue Jun 19 06:30:20 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Meurant:2006:LCGa,
author = "G{\'e}rard Meurant and Zden{\v{e}}k Strako{\v{s}}",
title = "The {Lanczos} and conjugate gradient algorithms in
finite precision arithmetic",
journal = j-ACTA-NUMERICA,
volume = "15",
pages = "471--542",
year = "2006",
CODEN = "ANUMFU",
DOI = "https://doi.org/10.1017/S096249290626001X",
ISBN = "0-521-86815-7",
ISBN-13 = "978-0-521-86815-0",
ISSN = "0962-4929 (print), 1474-0508 (electronic)",
ISSN-L = "0962-4929",
MRclass = "65F15 (65F10 65G50)",
MRnumber = "2269746 (2007m:65031)",
MRreviewer = "A. Bultheel",
bibdate = "Sat Sep 24 10:35:17 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/actanumerica.bib",
abstract = "The Lanczos and conjugate gradient algorithms were
introduced more than five decades ago as tools for
numerical computation of dominant eigenvalues of
symmetric matrices and for solving linear algebraic
systems with symmetric positive definite matrices,
respectively. Because of their fundamental relationship
with the theory of orthogonal polynomials and Gauss
quadrature of the Riemann--Stieltjes integral, the
Lanczos and conjugate gradient algorithms represent
very interesting general mathematical objects, with
highly nonlinear properties which can be conveniently
translated from algebraic language into the language of
mathematical analysis, and vice versa. The algorithms
are also very interesting numerically, since their
numerical behaviour can be explained by an elegant
mathematical theory, and the interplay between analysis
and algebra is useful there too.\par
Motivated by this view, the present contribution wishes
to pay a tribute to those who have made an
understanding of the Lanczos and conjugate gradient
algorithms possible through their pioneering work, and
to review recent solutions of several open problems
that have also contributed to knowledge of the
subject.",
acknowledgement = ack-nhfb,
ajournal = "Acta Numer.",
fjournal = "Acta Numerica",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU",
onlinedate = "16 May 2006",
}
@Book{Meurant:2006:LCGb,
author = "G{\'e}rard A. Meurant",
title = "The {Lanczos} and conjugate gradient algorithms: from
theory to finite precision computations",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xv + 365",
year = "2006",
ISBN = "0-89871-616-0",
ISBN-13 = "978-0-89871-616-0",
LCCN = "QA218 .M48 2006",
bibdate = "Thu Jun 9 11:53:47 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
z3950.loc.gov:7090/Voyager",
series = "Software, environments, tools",
URL = "http://www.loc.gov/catdir/enhancements/fy0710/2006044391-d.html;
http://www.loc.gov/catdir/enhancements/fy0733/2006044391-b.html;
http://www.loc.gov/catdir/toc/fy0707/2006044391.html",
acknowledgement = ack-nhfb,
subject = "conjugate gradient methods; algorithms; methodology",
}
@Article{Perjes:2006:WKL,
author = "Zolt{\'a}n Perj{\'e}s",
title = "The works of {Korn{\'e}l L{\'a}nczos} on the theory of
relativity",
journal = "Bolyai Society mathematical studies",
volume = "??",
number = "??",
pages = "415--425",
month = "????",
year = "2006",
ISBN = "963-9453-04-8, 3-540-28945-3",
ISBN-13 = "978-963-9453-04-3, 978-3-540-28945-6",
ISSN = "1217-4696",
LCCN = "QA27.H9 P36 2006",
bibdate = "Tue Jun 14 15:10:29 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Vandebril:2006:NSC,
author = "Raf Vandebril and Marc {Van Barel}",
title = "Necessary and sufficient conditions for orthogonal
similarity transformations to obtain the
{Arnoldi(Lanczos)--Ritz} values",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "414",
number = "2--3",
pages = "435--444",
day = "15",
month = apr,
year = "2006",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Mar 13 16:56:13 MST 2006",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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{Ahsan:2007:LPG,
author = "Z. Ahsan and J. H. Caltenco and J. L{\'o}pez-Bonilla",
title = "{Lanczos} potential for the {G{\"o}del} spacetime",
journal = j-ANN-PHYS-1900,
volume = "16",
number = "4",
pages = "311--313",
month = apr,
year = "2007",
DOI = "https://doi.org/10.1002/andp.200610234",
ISSN = "1521-3889",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Annalen der Physik (1900)",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-3889",
onlinedate = "21 Dec 2006",
}
@Article{Bernabeu:2007:RPI,
author = "Miguel O. Bernabeu and M{\'a}riam Taroncher and
V{\'\i}ctor M. Garc{\'\i}a and Ana Vidal",
title = "Robust Parallel Implementation of a {Lanczos}-based
Algorithm for an Structured Electromagnetic Eigenvalue
Problem",
journal = j-SCPE,
volume = "8",
number = "3",
pages = "263--270",
month = sep,
year = "2007",
CODEN = "????",
ISSN = "1895-1767",
bibdate = "Thu Sep 2 11:55:11 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.scpe.org/content/8/3.toc",
URL = "http://www.scpe.org/vols/vol08/no3/SCPE_8_3_04.pdf;
http://www.scpe.org/vols/vol08/no3/SCPE_8_3_04.zip",
acknowledgement = ack-nhfb,
journal-URL = "http://www.scpe.org/",
}
@InBook{Brezinski:2007:LTM,
author = "Claude Brezinski",
title = "{Lanczos}-type methods",
crossref = "Brezinski:1997:PMS",
chapter = "4",
pages = "141--182",
year = "2007",
DOI = "https://doi.org/10.1016/S1570-579X(97)80020-1",
bibdate = "Fri Jun 10 17:37:25 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Chung:2007:WGM,
author = "Julianne Chung and James G. Nagy and Dianne P.
O'Leary",
title = "A weighted-{GCV} method for {Lanczos-hybrid}
regularization",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "28",
pages = "149--167",
year = "2007\slash 2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:30 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Special volume for Gene Golub.",
URL = "http://etna.mcs.kent.edu/vol.28.2007-2008/pp149-167.dir/pp149-167.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@InProceedings{Gokhberg:2007:MPC,
author = "K. Gokhberg and V. Averbukh and V. Vysotskiy and L. S.
Cederbaum",
title = "Molecular Photoionization Cross-Sections by
Application of {Stieltjes} Imaging to {Lanczos}
Pseudospectra",
crossref = "Simos:2007:CMS",
volume = "2A",
pages = "151--154",
year = "2007",
bibdate = "Thu Feb 21 14:34:40 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://proceedings.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&
id=APCPCS000963000002000151000001& idtype=cvips",
acknowledgement = ack-nhfb,
}
@Article{Hnetynkova:2007:LTC,
author = "Iveta Hn{\v{e}}tynkov{\'a} and Zden{\v{e}}k
Strako{\v{s}}",
title = "{Lanczos} tridiagonalization and core problems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "421",
number = "2--3",
pages = "243--251",
day = "1",
month = mar,
year = "2007",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2006.05.006",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Mar 30 14:19:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.sciencedirect.com/science/journal/00243795",
note = "Special Issue in honor of Miroslav Fiedler.",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Koteras:2007:ECT,
author = "J. R. Koteras and R. B. Lehoucq",
title = "Estimating the critical time-step in explicit dynamics
using the {Lanczos} method",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "69",
number = "13",
pages = "2780--2788",
day = "26",
month = mar,
year = "2007",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.1865",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "31 Aug 2006",
}
@Article{Najafi:2007:NRM,
author = "H. Saberi Najafi and A. Refahi",
title = "A new restarting method in the {Lanczos} algorithm for
generalized eigenvalue problem",
journal = j-APPL-MATH-COMP,
volume = "184",
number = "2",
pages = "421--428",
day = "15",
month = jan,
year = "2007",
CODEN = "AMHCBQ",
DOI = "https://doi.org/10.1016/j.amc.2006.06.079",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:01 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.sciencedirect.com/science/journal/00963003",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Tremblay:2007:RUL,
author = "Jean Christophe Tremblay and Tucker {Carrington Jr.}",
title = "A refined unsymmetric {Lanczos} eigensolver for
computing accurate eigentriplets of a real unsymmetric
matrix",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "28",
pages = "95--113",
year = "2007\slash 2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:30 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Special volume for Gene Golub.",
URL = "http://etna.mcs.kent.edu/vol.28.2007-2008/pp95-113.dir/pp95-113.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Vidal:2007:PCA,
author = "A. M. Vidal and A. Vidal and V. E. Boria and V. M.
Garc{\'\i}a",
title = "Parallel computation of arbitrarily shaped waveguide
modes using {BI-RME} and {Lanczos} methods",
journal = j-COMM-NUMER-METHODS-ENGRG,
volume = "23",
number = "4",
pages = "273--284",
month = apr,
year = "2007",
DOI = "https://doi.org/10.1002/cnm.901",
ISSN = "1069-8299 (print), 1099-0887 (electronic)",
ISSN-L = "1069-8299",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications in Numerical Methods in Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-0887",
onlinedate = "14 Aug 2006",
}
@Article{Zhang:2007:EMR,
author = "H. Zhang and C. H. Thurber",
title = "Estimating the model resolution matrix for large
seismic tomography problems based on {Lanczos}
bidiagonalization with partial reorthogonalization",
journal = j-GEOPHYS-J-INT,
volume = "170",
number = "1",
pages = "337--345",
month = jul,
year = "2007",
CODEN = "GJINEA",
DOI = "https://doi.org/10.1111/j.1365-246X.2007.03418.x",
ISSN = "0956-540x (print), 1365-246x (electronic)",
ISSN-L = "0956-540X",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Geophysical journal international",
journal-URL = "http://gji.oxfordjournals.org/content/by/year",
onlinedate = "21 May 2007",
}
@Article{Zhou:2007:CDA,
author = "Yunkai Zhou and Yousef Saad",
title = "A {Chebyshev--Davidson} Algorithm for Large Symmetric
Eigenproblems",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "29",
number = "3",
pages = "954--971",
month = "????",
year = "2007",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/050630404",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (15A18 65F50)",
MRnumber = "2365900 (2008k:65081)",
MRreviewer = "Ilse C. F. Ipsen",
bibdate = "Sun Sep 5 09:21:22 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Bekas:2008:AWI,
author = "C. Bekas and A. Curioni and W. Andreoni",
title = "Atomic wavefunction initialization in ab initio
molecular dynamics using distributed {Lanczos}",
journal = j-PARALLEL-COMPUTING,
volume = "34",
number = "6--8",
pages = "441--450",
month = jul,
year = "2008",
CODEN = "PACOEJ",
DOI = "https://doi.org/10.1016/j.parco.2008.01.005",
ISSN = "0167-8191 (print), 1872-7336 (electronic)",
ISSN-L = "0167-8191",
bibdate = "Thu Sep 2 17:51:09 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.sciencedirect.com/science/journal/01678191",
acknowledgement = ack-nhfb,
fjournal = "Parallel Computing",
journal-URL = "http://www.sciencedirect.com/science/journal/01678191",
}
@Article{Bekas:2008:CLI,
author = "C. Bekas and E. Kokiopoulou and Yousef Saad",
title = "Computation of Large Invariant Subspaces Using
Polynomial Filtered {Lanczos} Iterations with
Applications in Density Functional Theory",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "30",
number = "1",
pages = "397--418",
month = "????",
year = "2008",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/060675435",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (65F50)",
MRnumber = "2399587 (2009b:65095)",
MRreviewer = "Valeria Simoncini",
bibdate = "Sun Sep 5 09:21:22 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Dolan:2008:RLE,
author = "P. Dolan and A. Gerber",
title = "The {Riemann--Lanczos} equations in general relativity
and their integrability",
journal = j-J-MATH-PHYS,
volume = "49",
number = "6",
pages = "062501:1--062501:13",
month = jul,
year = "2008",
CODEN = "JMAPAQ",
ISSN = "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
ISSN-L = "0022-2488",
bibdate = "Fri Jun 10 07:43:06 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of Mathematical Physics",
journal-URL = "http://jmp.aip.org/",
}
@Article{Druskin:2008:MLA,
author = "Vladimir Druskin",
title = "On monotonicity of the {Lanczos} approximation to the
matrix exponential",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "429",
number = "7",
pages = "1679--1683",
day = "1",
month = oct,
year = "2008",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Mar 30 14:20:15 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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{Heller:2008:IDM,
author = "Eric J. Heller and Lev Kaplan and Frank Pollmann",
title = "Inflationary dynamics for matrix eigenvalue problems",
journal = j-PROC-NATL-ACAD-SCI-USA,
volume = "105",
number = "22",
pages = "7631--7635",
month = "????",
year = "2008",
CODEN = "PNASA6",
DOI = "https://doi.org/10.1073/pnas.0801047105",
ISSN = "0027-8424 (print), 1091-6490 (electronic)",
ISSN-L = "0027-8424",
bibdate = "Fri Jun 10 15:21:21 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Many fields of science and engineering require finding
eigenvalues and eigenvectors of large matrices. The
solutions can represent oscillatory modes of a bridge,
a violin, the disposition of electrons around an atom
or molecule, the acoustic modes of a concert hall, or
hundreds of other physical quantities. Often only the
few eigenpairs with the lowest or highest frequency
(extremal solutions) are needed. Methods that have been
developed over the past 60 years to solve such problems
include the Lanczos algorithm, Jacobi Davidson
techniques, and the conjugate gradient method. Here, we
present a way to solve the extremal eigenvalue\slash
eigenvector problem, turning it into a nonlinear
classical mechanical system with a modified Lagrangian
constraint. The constraint induces exponential
inflationary growth of the desired extremal
solutions.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the National Academy of Sciences of the
United States of America",
journal-URL = "http://www.pnas.org/search",
onlinedate = "29 May 2008",
}
@Article{Hernandez:2008:REP,
author = "Vicente Hern{\'a}ndez and Jos{\'e} E. Rom{\'a}n and
Andr{\'e}s Tom{\'a}s",
title = "A robust and efficient parallel {SVD} solver based on
restarted {Lanczos} bidiagonalization",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "31",
pages = "68--85",
year = "2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:30 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://etna.mcs.kent.edu/vol.31.2008/pp68-85.dir/pp68-85.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Jia:2008:ASI,
author = "Chunxia Jia and Detong Zhu",
title = "An affine scaling interior algorithm via {Lanczos}
path for solving bound-constrained nonlinear systems",
journal = j-APPL-MATH-COMP,
volume = "195",
number = "2",
pages = "558--575",
day = "1",
month = feb,
year = "2008",
CODEN = "AMHCBQ",
ISSN = "0096-3003 (print), 1873-5649 (electronic)",
ISSN-L = "0096-3003",
bibdate = "Sat Jul 12 09:03:10 MDT 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.sciencedirect.com/science/journal/00963003",
acknowledgement = ack-nhfb,
fjournal = "Applied Mathematics and Computation",
journal-URL = "http://www.sciencedirect.com/science/journal/00963003",
}
@Article{Lambers:2008:EKS,
author = "James V. Lambers",
title = "Enhancement of {Krylov} subspace spectral methods by
block {Lanczos} iteration",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "31",
pages = "86--109",
year = "2008",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:30 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://etna.mcs.kent.edu/vol.31.2008/pp86-109.dir/pp86-109.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Peterson:2008:LR,
author = "Michael Peterson and Chris Monico",
title = "{$ \mathbb {F}_2 $} {Lanczos} revisited",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "428",
number = "4",
pages = "1135--1150",
day = "1",
month = feb,
year = "2008",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2007.09.016",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Mar 30 14:19:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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{Schnack:2008:EIL,
author = "J{\"u}rgen Schnack and Peter Hage and Heinz-J{\"u}rgen
Schmidt",
title = "Efficient implementation of the {Lanczos} method for
magnetic systems",
journal = j-J-COMPUT-PHYS,
volume = "227",
number = "9",
pages = "4512--4517",
day = "20",
month = apr,
year = "2008",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2008.01.027",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:13:52 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999108000338",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Tuck-Lee:2008:AFW,
author = "James P. Tuck-Lee and Peter M. Pinsky",
title = "Adaptive frequency windowing for multifrequency
solutions in structural acoustics based on the matrix
{Pad{\'e}-via-Lanczos} algorithm",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "73",
number = "5",
pages = "728--746",
day = "29",
month = jan,
year = "2008",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.2102",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "30 May 2007",
}
@Article{Browne:2009:LBA,
author = "Kevin Browne and Sanzheng Qiao and Yimin Wei",
title = "A {Lanczos} bidiagonalization algorithm for {Hankel}
matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "430",
number = "5--6",
pages = "1531--1543",
day = "1",
month = mar,
year = "2009",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Mar 30 14:20:34 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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{Chen:2009:FAG,
author = "Jie Chen and Haw-ren Fang and Yousef Saad",
title = "Fast approximate {$k$NN} graph construction for high
dimensional data via recursive {Lanczos} bisection",
journal = "J. Mach. Learn. Res.",
volume = "10",
pages = "1989--2012",
year = "2009",
ISSN = "1532-4435",
MRclass = "05C85 (62-07 68T05)",
MRnumber = "2550098",
bibdate = "Sun Sep 5 09:21:22 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
MathSciNet database",
acknowledgement = ack-nhfb,
fjournal = "Journal of Machine Learning Research (JMLR)",
}
@Article{Chen:2009:LVV,
author = "Jie Chen and Yousef Saad",
title = "{Lanczos} vectors versus singular vectors for
effective dimension reduction",
journal = j-IEEE-TRANS-KNOWL-DATA-ENG,
volume = "21",
number = "8",
pages = "1091--1103",
month = "????",
year = "2009",
CODEN = "ITKEEH",
DOI = "https://doi.org/10.1109/TKDE.2008.228",
ISSN = "1041-4347 (print), 1558-2191 (electronic)",
ISSN-L = "1041-4347",
bibdate = "Fri Jun 10 22:32:15 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Knowledge and Data Engineering",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=69",
}
@Article{Frommer:2009:MCL,
author = "Andreas Frommer",
title = "Monotone convergence of the {Lanczos} approximations
to matrix functions of {Hermitian} matrices",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "35",
pages = "118--128",
year = "2009",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Sep 6 12:28:30 MDT 2010",
bibsource = "http://etna.mcs.kent.edu/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://etna.mcs.kent.edu/vol.35.2009/pp118-128.dir/pp118-128.pdf",
acknowledgement = ack-nhfb,
fjournal = "Electronic Transactions on Numerical Analysis",
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Jing:2009:LTV,
author = "Yan-Fei Jing and Ting-Zhu Huang and Yong Zhang and
Liang Li and Guang-Hui Cheng and Zhi-Gang Ren and Yong
Duan and Tomohiro Sogabe and Bruno Carpentieri",
title = "{Lanczos-type} variants of the {COCR} method for
complex nonsymmetric linear systems",
journal = j-J-COMPUT-PHYS,
volume = "228",
number = "17",
pages = "6376--6394",
day = "20",
month = sep,
year = "2009",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/j.jcp.2009.05.022",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Mon Jan 2 22:14:15 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0021999109002800",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
}
@Article{Moret:2009:RLA,
author = "Igor Moret",
title = "Rational {Lanczos} approximations to the matrix square
root and related functions",
journal = j-NUM-LIN-ALG-APPL,
volume = "16",
number = "6",
pages = "431--445",
month = jun,
year = "2009",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.625",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.interscience.wiley.com/journalfinder.html",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "19 Nov 2008",
}
@Article{Neymeyr:2009:PEI,
author = "Klaus Neymeyr",
title = "On preconditioned eigensolvers and {Invert--Lanczos}
processes",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "430",
number = "4",
pages = "1039--1056",
day = "1",
month = feb,
year = "2009",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Mar 30 14:20:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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{Rindler:2009:GEMa,
author = "Wolfgang Rindler",
title = "{G{\"o}del}, {Einstein}, {Mach}, {Gamow}, and
{Lanczos}: {G{\"o}del}'s remarkable excursion into
cosmology",
journal = j-AMER-J-PHYSICS,
volume = "77",
number = "6",
pages = "498--510",
month = jun,
year = "2009",
CODEN = "AJPIAS",
DOI = "https://doi.org/10.1119/1.3086933",
ISSN = "0002-9505 (print), 1943-2909 (electronic)",
ISSN-L = "0002-9505",
bibdate = "Wed May 30 05:50:23 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gamow-george.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib",
note = "Reprinted in \cite[Chapter 9]{Baaz:2011:KGF}.",
URL = "http://adsabs.harvard.edu/abs/2009AmJPh..77..498R;
http://ajp.aapt.org/resource/1/ajpias/v77/i6/p498_s1",
acknowledgement = ack-nhfb,
fjournal = "American Journal of Physics",
journal-URL = "http://scitation.aip.org/content/aapt/journal/ajp",
keywords = "General relativity and gravitation",
}
@Article{Yun:2009:CLT,
author = "Beong In Yun and Kyung Soo Rim",
title = "Construction of {Lanczos} type filters for the
{Fourier} series approximation",
journal = j-APPL-NUM-MATH,
volume = "59",
number = "2",
pages = "280--300",
month = feb,
year = "2009",
CODEN = "ANMAEL",
ISSN = "0168-9274 (print), 1873-5460 (electronic)",
ISSN-L = "0168-9274",
bibdate = "Tue Aug 24 11:17:22 MDT 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.sciencedirect.com/science/journal/01689274",
acknowledgement = ack-nhfb,
fjournal = "Applied Numerical Mathematics: Transactions of IMACS",
journal-URL = "http://www.sciencedirect.com/science/journal/01689274",
}
@Article{Abdel-Rehim:2010:DRS,
author = "Abdou M. Abdel-Rehim and Ronald B. Morgan and Dywayne
A. Nicely and Walter Wilcox",
title = "Deflated and Restarted Symmetric {Lanczos} Methods for
Eigenvalues and Linear Equations with Multiple
Right-Hand Sides",
journal = j-SIAM-J-SCI-COMP,
volume = "32",
number = "1",
pages = "129--149",
month = "????",
year = "2010",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/080727361",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:44:24 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/32/1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Book{Gellai:2010:INT,
author = "Barbara Gellai",
title = "The intrinsic nature of things: the life and science
of {Cornelius Lanczos}",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "xv + 168",
year = "2010",
ISBN = "0-8218-5166-7",
ISBN-13 = "978-0-8218-5166-1",
LCCN = "QA29.L285 G45 2010",
bibdate = "Wed Jun 8 14:42:43 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
subject = "Lanczos, Cornelius; Mathematicians; Hungary;
Biography; Physicists",
subject-dates = "1893--1974",
}
@Article{Ilic:2010:RLA,
author = "M. Ili{\'c} and I. W. Turner and D. P. Simpson",
title = "A restarted {Lanczos} approximation to functions of a
symmetric matrix",
journal = j-IMA-J-NUMER-ANAL,
volume = "30",
number = "4",
pages = "1044--1061",
month = oct,
year = "2010",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/drp003",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
bibdate = "Wed Oct 13 18:32:48 MDT 2010",
bibsource = "http://imanum.oxfordjournals.org/content/30/4.toc;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://imajna.oxfordjournals.org/content/30/4/1044.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "IMA Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
onlinedate = "June 17, 2009",
}
@Article{Jia:2010:RHL,
author = "Zhongxiao Jia and Datian Niu",
title = "A Refined Harmonic {Lanczos} Bidiagonalization Method
and an Implicitly Restarted Algorithm for Computing the
Smallest Singular Triplets of Large Matrices",
journal = j-SIAM-J-SCI-COMP,
volume = "32",
number = "2",
pages = "714--744",
month = "????",
year = "2010",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/080733383",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
bibdate = "Wed May 19 10:44:27 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/32/2;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
}
@Article{Knizhnerman:2010:SLR,
author = "Leonid Knizhnerman",
title = "Sensitivity of the {Lanczos} recurrence to {Gaussian}
quadrature data: How malignant can small weights be?",
journal = j-J-COMPUT-APPL-MATH,
volume = "233",
number = "5",
pages = "1238--1244",
day = "1",
month = jan,
year = "2010",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/j.cam.2007.12.028",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65F18",
bibdate = "Fri Jun 10 16:32:10 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Special Issue Dedicated to William B. Gragg on the
Occasion of His 70th Birthday.",
abstract = "Stability of passing from Gaussian quadrature data to
the Lanczos recurrence coefficients is considered.
Special attention is paid to estimates explicitly
expressed in terms of quadrature data and not having
weights in denominators. It has been shown that the
recent approach, exploiting integral representation of
Hankel determinants, implies quantitative improvement
of D. Laurie's constructive estimate.\par
It has also been demonstrated that a particular
implementation on the Hankel determinant approach gives
an estimate being unimprovable up to a coefficient; the
corresponding example involves quadrature data with a
small but not too small weight. It follows that
polynomial increase of a general case upper bound in
terms of the dimension is unavoidable.",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "Gaussian quadrature formula; Jacobi inverse eigenvalue
problem; Lanczos recurrence; Orthogonal polynomials;
Small weights; Stability estimates",
}
@Article{Li:2010:SRC,
author = "Ren-Cang Li",
title = "Sharpness in rates of convergence for the symmetric
{Lanczos} method",
journal = j-MATH-COMPUT,
volume = "79",
number = "269",
pages = "419--435",
month = jan,
year = "2010",
CODEN = "MCMPAF",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Fri May 14 06:21:04 MDT 2010",
bibsource = "http://www.ams.org/mcom/2010-79-269;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.ams.org/journals/mcom/2010-79-269/S0025-5718-09-02258-3/home.html;
http://www.ams.org/journals/mcom/2010-79-269/S0025-5718-09-02258-3/S0025-5718-09-02258-3.pdf",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Liew:2010:MPL,
author = "Haw-Ling Liew and Peter M. Pinsky",
title = "Matrix-{Pad{\'e}} via {Lanczos} solutions for
vibrations of fluid-structure interaction",
journal = j-INT-J-NUMER-METHODS-ENG,
volume = "84",
number = "10",
pages = "1183--1204",
day = "3",
month = dec,
year = "2010",
CODEN = "IJNMBH",
DOI = "https://doi.org/10.1002/nme.2936",
ISSN = "0029-5981 (print), 1097-0207 (electronic)",
ISSN-L = "0029-5981",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "International Journal for Numerical Methods in
Engineering",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207",
onlinedate = "11 Nov 2010",
}
@Article{Meerbergen:2010:LMP,
author = "Karl Meerbergen and Zhaojun Bai",
title = "The {Lanczos} Method for Parameterized Symmetric
Linear Systems with Multiple Right-Hand Sides",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "4",
pages = "1642--1662",
month = "????",
year = "2010",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/08073144X",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Tue May 18 22:32:39 MDT 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toclist/SIMAX/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Paige:2010:ASR,
author = "Christopher C. Paige",
title = "An Augmented Stability Result for the {Lanczos}
{Hermitian} Matrix Tridiagonalization Process",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "31",
number = "5",
pages = "2347--2359",
month = "????",
year = "2010",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Sun Nov 28 22:55:40 MST 2010",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/31/5;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
onlinedate = "July 13, 2010",
}
@Article{Rezghi:2010:LBP,
author = "Mansoor Rezghi and S. M. Hosseini",
title = "{Lanczos} based preconditioner for discrete ill-posed
problems",
journal = j-COMPUTING,
volume = "88",
number = "1--2",
pages = "79--96",
month = jun,
year = "2010",
CODEN = "CMPTA2",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
bibdate = "Sun Oct 31 11:10:10 MDT 2010",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=88&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=88&issue=1&spage=79",
acknowledgement = ack-nhfb,
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
}
@InCollection{Temme:2010:LTS,
author = "N. M. Temme",
title = "{Lanczos} Tridiagonalization of a Symmetric Matrix",
crossref = "Olver:2010:NHM",
pages = "75--75",
year = "2010",
bibdate = "Sun Jun 12 09:55:34 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@Article{Yamazaki:2010:APS,
author = "Ichitaro Yamazaki and Zhaojun Bai and Horst Simon and
Lin-Wang Wang and Kesheng Wu",
title = "Adaptive Projection Subspace Dimension for the
Thick-Restart {Lanczos} Method",
journal = j-TOMS,
volume = "37",
number = "3",
pages = "27:1--27:18",
year = "2010",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/1824801.1824805",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Sep 27 10:15:50 MDT 2010",
bibsource = "http://www.acm.org/pubs/contents/journals/toms/;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "The Thick-Restart Lanczos (TRLan) method is an
effective method for solving large-scale Hermitian
eigenvalue problems. The performance of the method
strongly depends on the dimension of the projection
subspace used at each restart. In this article, we
propose an objective function to quantify the
effectiveness of the selection of subspace dimension,
and then introduce an adaptive scheme to dynamically
select the dimension to optimize the performance. We
have developed an open-source software package
$a$-TRLan to include this adaptive scheme in the TRLan
method. When applied to calculate the electronic
structure of quantum dots, $a$-TRLan runs up to 2.3x
faster than a state-of-the-art preconditioned conjugate
gradient eigensolver.",
acknowledgement = ack-nhfb,
articleno = "27",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "Adaptive subspace dimension; electronic structure
calculation; Lanczos; thick-restart",
}
@Article{Baris:2011:TCS,
author = "Osman Bari{\c{s} and } Malc{\i}o{\u{g}}lu and Ralph
Gebauer and Dario Roccad and Stefano Baronia",
title = "{turboTDDFT} --- {A} code for the simulation of
molecular spectra using the {Liouville--Lanczos}
approach to time-dependent density-functional
perturbation theory",
journal = j-COMP-PHYS-COMM,
volume = "182",
number = "8",
pages = "1744--1754",
month = aug,
year = "2011",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2011.04.020",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Fri Jun 10 16:29:27 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Gruning:2011:ITL,
author = "Myrta Gr{\"u}ning and Andrea Marini and Xavier
Gonzee",
title = "Implementation and testing of {Lanczos}-based
algorithms for {Random-Phase Approximation}
eigenproblems",
journal = j-COMPUT-MATER-SCI,
volume = "50",
number = "7",
pages = "2148--2156",
month = may,
year = "2011",
CODEN = "CMMSEM",
DOI = "https://doi.org/10.1016/j.commatsci.2011.02.021",
ISSN = "0927-0256 (print), 1879-0801 (electronic)",
ISSN-L = "0927-0256",
bibdate = "Fri Jun 10 17:01:56 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
fjournal = "Computational Materials Science",
journal-URL = "http://www.sciencedirect.com/science/journal/09270256",
}
@Article{Pang:2011:SIL,
author = "Hong-Kui Pang and Hai-Wei Sun",
title = "Shift-invert {Lanczos} method for the symmetric
positive semidefinite {Toeplitz} matrix exponential",
journal = j-NUM-LIN-ALG-APPL,
volume = "18",
number = "3",
pages = "603--614",
month = may,
year = "2011",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.747",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Fri Jun 10 10:27:45 MDT 2011",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www3.interscience.wiley.com/journalfinder.html",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "26 Sep 2010",
}
@InCollection{Rindler:2011:GEMb,
author = "Wolfgang Rindler",
title = "{G{\"o}del}, {Einstein}, {Mach}, {Gamow}, and
{Lanczos}: {G{\"o}del}'s Remarkable Excursion into
Cosmology",
crossref = "Baaz:2011:KGF",
pages = "185--212",
year = "2011",
bibdate = "Tue Sep 20 17:56:03 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/gamow-george.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
}
@InBook{Saad:2011:KSM,
author = "Youcef Saad",
title = "{Krylov} Subspace Methods",
crossref = "Saad:2011:NML",
chapter = "6",
pages = "125--162",
year = "2011",
bibdate = "Fri Jun 10 21:40:13 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
keywords = "Arnoldi; block Krylov; convergence of Arnold process;
convergence of Lanczos process; Davidson; Hermitian
Lanczos; Jacobi--Davidson; Non-Hermitian Lanczos",
}
@Book{Golub:2013:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
edition = "Fourth",
pages = "xxi + 756",
year = "2013",
ISBN = "1-4214-0794-9 (hardcover), 1-4214-0859-7 (e-book)",
ISBN-13 = "978-1-4214-0794-4 (hardcover), 978-1-4214-0859-0
(e-book)",
LCCN = "QA188 .G65 2013",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
series = "Johns Hopkins Studies in the Mathematical Sciences",
URL = "https://jhupbooks.press.jhu.edu/title/matrix-computations",
abstract = "This revised edition provides the mathematical
background and algorithmic skills required for the
production of numerical software. It includes rewritten
and clarified proofs and derivations, as well as new
topics such as Arnoldi iteration, and domain
decomposition methods.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
shorttableofcontents = "1: Matrix multiplication \\
2: Matrix analysis \\
3: General linear systems \\
4: Special linear systems \\
5: Orthogonalization and least squares \\
6: Modified least squares problems and methods \\
7: Unsymmetric eigenvalue problems \\
8: Symmetric eigenvalue problems \\
9: Functions of matrices \\
10: Large sparse eigenvalue problems \\
11: Large sparse linear system problems \\
12: Special topics",
subject = "Matrices; Data processing; Data processing.; Matrix.;
Matrizenrechnung.; Matrizentheorie.; Numerische
Mathematik.",
tableofcontents = "Preface \\
Global References \\
Other Books \\
Useful URLs \\
Common Notation \\
1: Matrix Multiplication \\
1.1 Basic Algorithms and Notation \\
1.2 Structure and Efficiency \\
1.3 Block Matrices and Algorithms \\
1.4 Fast Matrix--Vector Products \\
1.5 Vectorization and Locality \\
1.6 Parallel Matrix Multiplication \\
2: Matrix Analysis \\
2.1 Basic Ideas from Linear Algebra \\
2.2 Vector Norms \\
2.3 Matrix Norms \\
2.4 The Singular Value Decomposition \\
2.5 Subspace Metrics \\
2.6 The Sensitivity of Square Systems \\
2.7 Finite Precision Matrix Computations \\
3: General Linear Systems \\
3.1 Triangular Systems \\
3.2 The $L U$ Factorization \\
3.3 Roundoff Error in Gaussian Elimination \\
3.4 Pivoting \\
3.5 Improving and Estimating Accuracy \\
3.6 Parallel $L U$ \\
4: Special Linear Systems \\
4.1 Diagonal Dominance and Symmetry \\
4.2 Positive Definite Systems \\
4.3 Banded Systems \\
4.4 Symmetric Indefinite Systems \\
4.5 Block Tridiagonal Systems \\
4.6 Vandermonde Systems \\
4.7 Classical Methods for Toeplitz Systems \\
4.8 Circulant and Discrete Poisson Systems \\
5: Orthogonalization and Least Squares \\
5.1 Householder and Givens Transformations \\
5.2 The $Q R$ Factorization \\
5.3 The Full-Rank Least Squares Problem \\
5.4 Other Orthogonal Factorizations \\
5.5 The Rank-Deficient Least Squares Problem \\
5.6 Square and Underdetermined Systems \\
6: Modified Least Squares Problems and Methods \\
6.1 Weighting and Regularization \\
6.2 Constrained Least Squares \\
6.3 Total Least Squares \\
6.4 Subspace Computations with the SVD \\
6.5 Updating Matrix Factorizations \\
7: Unsymmetric Eigenvalue Problems \\
7.1 Properties and Decompositions \\
7.2 Perturbation Theory \\
7.3 Power Iterations \\
7.4 The Hessenberg and Real Schur Forms \\
7.5 The Practical $Q R$ Algorithm \\
7.6 Invariant Subspace Computations \\
7.7 The Generalized Eigenvalue Problem \\
7.8 Hamiltonian and Product Eigenvalue Problems \\
7.9 Pseudospectra \\
8: Symmetric Eigenvalue Problems \\
8.1 Properties and Decompositions \\
8.2 Power Iterations \\
8.3 The Symmetric $Q R$ Algorithm \\
8.4 More Methods for Tridiagonal Problems \\
8.5 Jacobi Methods \\
8.6 Computing the SVD \\
8.7 Generalized Eigenvalue Problems with Symmetry \\
9: Functions of Matrices \\
9.1 Eigenvalue Methods \\
9.2 Approximation Methods \\
9.3 The Matrix Exponential \\
9.4 The Sign, Square Root, and Log of a Matrix \\
10: Large Sparse Eigenvalue Problems \\
10.1 The Symmetric Lanczos Process \\
10.2 Lanczos, Quadrature, and Approximation \\
10.3 Practical Lanczos Procedures \\
10.4 Large Sparse SVD Frameworks \\
10.5 Krylov Methods for Unsymmetric Problems \\
10.6 Jacobi--Davidson and Related Methods \\
11: Large Sparse Linear System Problems \\
11.1 Direct Methods \\
11.2 The Classical Iterations \\
11.3 The Conjugate Gradient Method \\
11.4 Other Krylov Methods \\
11.5 Preconditioning \\
11.6 The Multigrid Framework \\
12: Special Topics \\
12.1 Linear Systems with Displacement Structure \\
12.2 Structured-Rank Problems \\
12.3 Kronecker Product Computations \\
12.4 Tensor Unfoldings and Contractions \\
12.5 Tensor Decompositions and Iterations \\
Index",
}
@Article{Boyd:2014:RBC,
author = "John P. Boyd and Rolfe Petschek",
title = "The Relationships Between {Chebyshev}, {Legendre} and
{Jacobi} Polynomials: The Generic Superiority of
{Chebyshev} Polynomials and Three Important
Exceptions",
journal = j-J-SCI-COMPUT,
volume = "59",
number = "1",
pages = "1--27",
month = apr,
year = "2014",
CODEN = "JSCOEB",
DOI = "https://doi.org/10.1007/s10915-013-9751-7",
ISSN = "0885-7474 (print), 1573-7691 (electronic)",
ISSN-L = "0885-7474",
bibdate = "Sat Mar 8 11:16:37 MST 2014",
bibsource = "http://link.springer.com/journal/10915;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=59&issue=1;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/jscicomput.bib",
note = "See \cite{Lanczos:1952:F}.",
URL = "http://link.springer.com/article/10.1007/s10915-013-9751-7;
http://link.springer.com/content/pdf/10.1007/s10915-013-9751-7.pdf",
acknowledgement = ack-nhfb,
fjournal = "Journal of Scientific Computing",
journal-URL = "http://link.springer.com/journal/10915",
keywords = "Cornelius Lanczos",
}
@Book{Arbenz:2016:LNS,
author = "Peter Arbenz",
title = "Lecture Notes on Solving Large Scale Eigenvalue
Problems",
publisher = "Computer Science Department, ETH Z{\"u}rich",
address = "Z{\"u}rich, Switzerland",
pages = "vi + 259",
year = "2016",
bibdate = "Mon Sep 04 10:05:42 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/pagerank.bib",
URL = "https://people.inf.ethz.ch/arbenz/ewp/Lnotes/lsevp.pdf",
acknowledgement = ack-nhfb,
tableofcontents = "1 Introduction / 1 \\
1.1 What makes eigenvalues interesting? / 1 \\
1.2 Example 1: The vibrating string / 2 \\
1.2.1 Problem setting / 2 \\
1.2.2 The method of separation of variables / 5 \\
1.3 Numerical methods for solving 1-dimensional
problems / 6 \\
1.3.1 Finite differences / 6 \\
1.3.2 The finite element method / 7 \\
1.3.3 Global functions / 8 \\
1.3.4 A numerical comparison / 9 \\
1.4 Example 2: The heat equation / 9 \\
1.5 Example 3: The wave equation / 12 \\
1.6 The 2D Laplace eigenvalue problem / 13 \\
1.6.1 The finite difference method / 13 \\
1.6.2 The finite element method (FEM) / 16 \\
1.6.3 A numerical example / 20 \\
1.7 Cavity resonances in particle accelerators / 21 \\
1.8 Spectral clustering / 23 \\
1.8.1 The graph Laplacian / 24 \\
1.8.2 Spectral clustering / 25 \\
1.8.3 Normalized graph Laplacians / 27 \\
1.9 Google's PageRank / 28 \\
1.10 Other sources of eigenvalue problems / 30 \\
Bibliography / 31 \\
2 Basics / 33 \\
2.1 Notation / 33 \\
2.2 Statement of the problem / 34 \\
2.3 Similarity transformations / 37 \\
2.4 Schur decomposition / 38 \\
2.5 The real Schur decomposition / 39 \\
2.6 Normal matrices / 40 \\
2.7 Hermitian matrices / 41 \\
2.8 The Jordan normal form / 43 \\
2.9 Projections / 45 \\
2.10 The Rayleigh quotient / 47 \\
2.11 Cholesky factorization / 49 \\
2.12 The singular value decomposition (SVD) / 50 \\
Bibliography / 52 \\
3 Newton methods / 53 \\
3.1 Linear and nonlinear eigenvalue problems / 53 \\
3.2 Zeros of the determinant / 54 \\
3.2.1 Algorithmic differentiation / 55 \\
3.2.2 Hyman's algorithm / 55 \\
3.2.3 Computing multiple zeros / 58 \\
3.3 Newton methods for the constrained matrix problem /
58 \\
3.4 Successive linear approximations / 60 \\
Bibliography / 61 \\
4 The $ Q R $ Algorithm / 63 \\
4.1 The basic $ Q R $ algorithm / 63 \\
4.1.1 Numerical experiments / 64 \\
4.2 The Hessenberg $ Q R $ algorithm / 67 \\
4.2.1 A numerical experiment / 69 \\
4.2.2 Complexity / 70 \\
4.3 The Householder reduction to Hessenberg form / 71
\\
4.3.1 Householder reflectors / 71 \\
4.3.2 Reduction to Hessenberg form / 71 \\
4.4 Improving the convergence of the $ Q R $ algorithm
/ 73 \\
4.4.1 A numerical example / 74 \\
4.4.2 $ Q R $ algorithm with shifts / 75 \\
4.4.3 A numerical example / 76 \\
4.5 The double shift $ Q R $ algorithm / 77 \\
4.5.1 A numerical example / 81 \\
4.5.2 The complexity / 83 \\
4.6 The symmetric tridiagonal $ Q R $ algorithm / 84
\\
4.6.1 Reduction to tridiagonal form / 84 \\
4.6.2 The tridiagonal $ Q R $ algorithm / 85 \\
4.7 Research / 87 \\
4.8 Summary / 87 \\
Bibliography / 88 \\
5 Cuppen's Divide and Conquer Algorithm / 91 \\
5.1 The divide and conquer idea / 91 \\
5.2 Partitioning the tridiagonal matrix / 92 \\
5.3 Solving the small systems / 92 \\
5.4 Deflation / 93 \\
5.4.1 Numerical examples / 94 \\
5.5 The eigenvalue problem for $D + \rho v v^T$ / 95
\\
5.6 Solving the secular equation / 98 \\
5.7 A first algorithm / 99 \\
5.7.1 A numerical example / 100 \\
5.8 The algorithm of Gu and Eisenstat / 103 \\
5.8.1 A numerical example [continued] / 104 \\
Bibliography / 107 \\
6 LAPACK and the BLAS / 109 \\
6.1 LAPACK / 109 \\
6.2 BLAS / 110 \\
6.2.1 Typical performance numbers for the BLAS / 111
\\
6.3 Blocking / 113 \\
6.4 LAPACK solvers for the symmetric eigenproblems /
114 \\
6.5 Generalized Symmetric Definite Eigenproblems (GSEP)
/ 116 \\
6.6 An example of a LAPACK routines / 116 \\
Bibliography / 122 \\
7 Vector iteration (power method) / 125 \\
7.1 Simple vector iteration / 125 \\
7.2 Angles between vectors / 126 \\
7.3 Convergence analysis / 127 \\
7.4 A numerical example / 130 \\
7.5 The symmetric case / 131 \\
7.6 Inverse vector iteration / 135 \\
7.7 The generalized eigenvalue problem / 139 \\
7.8 Computing higher eigenvalues / 139 \\
7.9 Rayleigh quotient iteration / 140 \\
7.9.1 A numerical example / 143 \\
Bibliography / 144 \\
8 Simultaneous vector or subspace iterations / 145 \\
8.1 Basic subspace iteration / 145 \\
8.2 Angles between subspaces / 146 \\
8.3 Convergence of basic subspace iteration / 148 \\
8.4 Accelerating subspace iteration / 153 \\
8.5 Relation between subspace iteration and $ Q R $
algorithm / 158 \\
8.6 Addendum / 161 \\
Bibliography / 161 \\
9 Krylov subspaces / 163 \\
9.1 Introduction / 163 \\
9.2 Definition and basic properties / 164 \\
9.3 Polynomial representation of Krylov subspaces / 165
\\
9.4 Error bounds of Saad / 168 \\
Bibliography / 171 \\
10 Arnoldi and Lanczos algorithms / 173 \\
10.1 An orthonormal basis for the Krylov space Kj (x) /
173 \\
10.2 Arnoldi algorithm with explicit restarts / 175 \\
10.3 The Lanczos basis / 176 \\
10.4 The Lanczos process as an iterative method / 178
\\
10.5 An error analysis of the unmodified Lanczos
algorithm / 185 \\
10.6 Partial reorthogonalization / 187 \\
10.7 Block Lanczos / 190 \\
10.8 External selective reorthogonalization / 193 \\
Bibliography / 194 \\
11 Restarting Arnoldi and Lanczos algorithms / 195 \\
11.1 The $m$-step Arnoldi iteration / 195 \\
11.2 Implicit restart / 196 \\
11.3 Convergence criterion / 198 \\
11.4 The generalized eigenvalue problem / 199 \\
11.5 A numerical example / 201 \\
11.6 Another numerical example / 206 \\
11.7 The Lanczos algorithm with thick restarts / 210
\\
11.8 Krylov--Schur algorithm / 213 \\
11.9 The rational Krylov space method / 214 \\
Bibliography / 215 \\
12 The Jacobi--Davidson Method / 217 \\
12.1 The Davidson algorithm / 217 \\
12.2 The Jacobi orthogonal component correction / 218
\\
12.2.1 Restarts / 221 \\
12.2.2 The computation of several eigenvalues / 221 \\
12.2.3 Spectral shifts / 222 \\
12.3 The generalized Hermitian eigenvalue problem / 224
\\
12.4 A numerical example / 224 \\
12.5 The Jacobi--Davidson algorithm for interior
eigenvalues / 228 \\
12.6 Harmonic Ritz values and vectors / 229 \\
12.7 Refined Ritz vectors / 231 \\
12.8 The generalized Schur decomposition / 233 \\
12.9 JDQZ: Computing a partial $ Q Z $ decomposition /
233 \\
12.9.1 Restart / 235 \\
12.9.2 Deflation / 235 \\
12.9.3 Algorithm / 236 \\
12.10 Jacobi--Davidson for nonlinear eigenvalue
problems / 236 \\
Bibliography / 239 \\
13 Rayleigh quotient and trace minimization / 241 \\
13.1 Introduction / 241 \\
13.2 The method of steepest descent / 242 \\
13.3 The conjugate gradient algorithm / 243 \\
13.4 Locally optimal PCG (LOPCG) / 247 \\
13.5 The block Rayleigh quotient minimization algorithm
(BRQMIN) / 250 \\
13.6 The locally-optimal block preconditioned conjugate
gradient method (LOBPCG) / 250 \\
13.7 A numerical example / 251 \\
13.8 Trace minimization / 253 \\
Bibliography / 258",
}
@Article{Gazzola:2016:LGK,
author = "Silvia Gazzola and Enyinda Onunwor and Lothar Reichel
and Giuseppe Rodriguez",
title = "On the {Lanczos} and {Golub--Kahan} reduction methods
applied to discrete ill-posed problems",
journal = j-NUM-LIN-ALG-APPL,
volume = "23",
number = "1",
pages = "187--204",
month = jan,
year = "2016",
CODEN = "NLAAEM",
DOI = "https://doi.org/10.1002/nla.2020",
ISSN = "1070-5325 (print), 1099-1506 (electronic)",
ISSN-L = "1070-5325",
bibdate = "Tue Feb 9 06:31:34 MST 2016",
bibsource = "http://www.interscience.wiley.com/jpages/1070-5325;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/numlinaa.bib;
http://www3.interscience.wiley.com/journalfinder.html",
acknowledgement = ack-nhfb,
fjournal = "Numerical Linear Algebra with Applications",
journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
onlinedate = "12 Oct 2015",
}
@Article{Bentbib:2018:EGL,
author = "A. H. Bentbib and M. {El Ghomari} and C. Jagels and K.
Jbilou and L. Reichel",
title = "The extended global {Lanczos} method for matrix
function approximation",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "50",
pages = "144--163",
year = "2018",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Mar 18 13:30:42 MDT 2019",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/etna.bib",
URL = "http://etna.mcs.kent.edu/vol.50.2018/pp144-163.dir/pp144-163.pdf;
http://etna.mcs.kent.edu/volumes/2011-2020/vol50/abstract.php?vol=50&pages=144-163",
acknowledgement = ack-nhfb,
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Pozza:2018:LAC,
author = "Stefano Pozza and Miroslav S. Prani{\'c} and
Zden{\v{e}}k Strako{\v{s}}",
title = "The {Lanczos} algorithm and complex {Gauss}
quadrature",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "50",
pages = "1--19",
year = "2018",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Wed Nov 7 07:27:24 MST 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/etna.bib",
URL = "http://etna.mcs.kent.edu/vol.50.2018/pp1-19.dir/pp1-19.pdf;
http://etna.mcs.kent.edu/volumes/2011-2020/vol50/abstract.php?vol=50&pages=1-19",
acknowledgement = ack-nhfb,
journal-URL = "http://etna.mcs.kent.edu/",
remark = "Special volume dedicated to Walter Gautschi on the
occasion of his 90th birthday.",
abstract = "Gauss quadrature can be naturally generalized in order
to approximate quasi-definite linear functionals, where
the interconnections with (formal) orthogonal
polynomials, (complex) Jacobi matrices, and the Lanczos
algorithm are analogous to those in the positive
definite case. In this survey we review these
relationships with giving references to the literature
that presents them in several related contexts. In
particular, the existence of the $n$-weight (complex)
Gauss quadrature corresponds to successfully performing
the first $n$ steps of the Lanczos algorithm for
generating biorthogonal bases of the two associated
Krylov subspaces. The Jordan decomposition of the
(complex) Jacobi matrix can be explicitly expressed in
terms of the Gauss quadrature nodes and weights and the
associated orthogonal polynomials. Since the output of
the Lanczos algorithm can be made real whenever the
input is real, the value of the Gauss quadrature is a
real number whenever all relevant moments of the
quasi-definite linear functional are real.",
}
@Article{Paige:2019:ALP,
author = "Christopher C. Paige",
title = "Accuracy of the {Lanczos} Process for the Eigenproblem
and Solution of Equations",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "40",
number = "4",
pages = "1371--1398",
month = "????",
year = "2019",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/17M1133725",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu May 28 10:55:46 MDT 2020",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/40/4;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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 2019",
}
@Article{Garza-Vargas:2020:LAU,
author = "Jorge Garza-Vargas and Archit Kulkarni",
title = "The {Lanczos} Algorithm Under Few Iterations:
Concentration and Location of the Output",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "41",
number = "3",
pages = "1312--1346",
month = "????",
year = "2020",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/19M1275231",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
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/l/lanczos-cornelius.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{Simonova:2022:WDL,
author = "Dorota {\v{S}}imonov{\'a} and Petr Tich{\'y}",
title = "When does the {Lanczos} algorithm compute exactly?",
journal = j-ELECTRON-TRANS-NUMER-ANAL,
volume = "55",
pages = "547--567",
year = "2022",
CODEN = "????",
ISSN = "1068-9613 (print), 1097-4067 (electronic)",
ISSN-L = "1068-9613",
bibdate = "Mon Jun 3 08:23:56 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/etna.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "https://etna.math.kent.edu/vol.55.2022/pp547-567.dir/pp547-567.pdf;
https://etna.math.kent.edu/volumes/2021-2030/vol55/abstract.php?vol=55&pages=547-567",
abstract = "In theory, the Lanczos algorithm generates an
orthogonal basis of the corresponding Krylov subspace.
However, in finite precision arithmetic the
orthogonality and linear independence of the computed
Lanczos vectors is usually lost quickly. In this paper
we study a class of matrices and starting vectors
having a special nonzero structure that guarantees
exact computations of the Lanczos algorithm whenever
floating point arithmetic satisfying the IEEE 754
standard is used. Analogous results are formulated also
for an implementation of the conjugate gradient method
called cgLanczos. This implementation then computes
approximations that agree with their exact counterparts
to a relative accuracy given by the machine precision
and the condition number of the system matrix. The
results are extended to the Arnoldi algorithm, the
nonsymmetric Lanczos algorithm, the Golub-Kahan
bidiagonalization, the block-Lanczos algorithm, and
their counterparts for solving linear systems.",
acknowledgement = ack-nhfb,
journal-URL = "http://etna.mcs.kent.edu/",
}
@Article{Cipolla:2023:LTP,
author = "Stefano Cipolla and Stefano Pozza and Michela
Redivo-Zaglia and Niel {Van Buggenhout}",
title = "A {Lanczos}-type procedure for tensors",
journal = j-NUMER-ALGORITHMS,
volume = "92",
number = "1",
pages = "377--406",
month = jan,
year = "2023",
CODEN = "NUALEG",
DOI = "https://doi.org/10.1007/s11075-022-01351-6",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
bibdate = "Mon Jan 30 12:22:09 MST 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
URL = "https://link.springer.com/article/10.1007/s11075-022-01351-6",
acknowledgement = ack-nhfb,
ajournal = "Numer. Algorithms",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
}
@Article{Zbikowski:2023:BBL,
author = "Ryan M. Zbikowski and Calvin W. Johnson",
title = "Bootstrapped block {Lanczos} for large-dimension
eigenvalue problems",
journal = j-COMP-PHYS-COMM,
volume = "291",
number = "??",
pages = "Article 108835",
month = oct,
year = "2023",
CODEN = "CPHCBZ",
DOI = "https://doi.org/10.1016/j.cpc.2023.108835",
ISSN = "0010-4655 (print), 1879-2944 (electronic)",
ISSN-L = "0010-4655",
bibdate = "Thu Aug 10 07:51:47 MDT 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0010465523001807",
abstract = "The Lanczos algorithm has proven itself to be a
valuable matrix eigensolver for problems with large
dimensions, up to hundreds of millions or even tens of
billions. The computational cost of using any Lanczos
algorithm is dominated by the number of sparse
matrix-vector multiplications required to reach
suitable convergence. Block Lanczos replaces sparse
matrix-vector multiplication with sparse matrix-matrix
multiplication; sparse matrix-matrix multiplication is
more efficient, due to improved data locality and
amortizing the cost of fetching or constructing a
matrix element, but for a randomly chosen starting
block (or pivot), block Lanczos requires more
multiplications to reach convergence. We find that a
bootstrapped pivot block, that is, an initial block
constructed from approximate eigenvectors computed in a
truncated space, leads to a dramatically reduced number
of multiplications, significantly outperforming both
standard vector Lanczos and block Lanczos with a random
pivot. A key condition for speed-up is that the pivot
block has a non-trivial overlap with the final
converged vector. We implement this approach in a
configuration-interaction code for nuclear structure,
and find a reduction in time-to-solution by a factor of
two or more, up to a factor of ten.",
acknowledgement = ack-nhfb,
fjournal = "Computer Physics Communications",
journal-URL = "http://www.sciencedirect.com/science/journal/00104655",
}
@Article{Carson:2024:TUC,
author = "Erin Carson and J{\"o}rg Liesen and Zden{\v{e}}k
Strako{\v{s}}",
title = "Towards understanding {CG} and {GMRES} through
examples",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "692",
number = "??",
pages = "241--291",
day = "1",
month = jul,
year = "2024",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/j.laa.2024.04.003",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Wed Apr 24 13:20:32 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/tex/bib/linala2020.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S0024379524001381",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
%%% ====================================================================
%%% Cross-referenced entries must come last:
@Proceedings{Griffith:1957:DPA,
editor = "R. M. Griffith and J. A. Ovenstone and G. E. Barlow
and J. H. Stapleton and L. A. J. Malone",
booktitle = "Data Processing and Automatic Computing Machines:
Proceedings of Conference Held at {Weapons Research
Establishment, Salisbury, SA, June 3rd--8th, 1957}",
title = "Data Processing and Automatic Computing Machines:
Proceedings of Conference Held at {Weapons Research
Establishment, Salisbury, SA, June 3rd--8th, 1957}",
publisher = pub-WRE,
address = pub-WRE:adr,
pages = "vi + 298 (variously numbered)",
year = "1957",
bibdate = "Tue Sep 10 09:17:04 2024",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/givens-wallace.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "https://www.massey.ac.nz/~rmclachl/DPACM/",
acknowledgement = ack-nhfb,
tableofcontents = "Preface \\
Organising committee \\
H. J. Brown, Introduction \\
Table of contents \\
Proceedings \\
B. G. Gates, Opening address \\
R. W. McG. Boswell, Introductory remarks to the
Conference on Data Processing and Automatic Computing
Machines \\
W. C. J. White, Introduction to the WRE data processing
system \\
J. A. Ovenstone, The WREDAC system \\
T. M. Cherry and F. Hirst, The Machine CSIRAC \\
J. M. Bennett and B. E. Swire, The SILLIAC \\
R. G. Smart, The UTECOM digital computer \\
T. Pearcey, Data reduction in pure scientific research
\\
A. D. Booth, Machine translation of languages \\
F. W. Harwood, Linguistic applications of computing
machinery \\
M. V. Wilkes, Some remarks on the numerical solution of
ordinary differential equations \\
J. W. Carr III, Generalised functional round-off error
analysis [abstract only] \\
R. H. Merson, An operational method for the study of
integration processes \\
J. M. Bennett, Continuant matrices in numerical
analysis \\
J. H. Wilkinson, The calculation of the eigenvectors of
codiagonal matrices produced by the Givens and Lanczos
processes \\
A. Jones, Eigenvalues and vectors of a symmetric matrix
using Jacobi's method \\
A. S. Douglas, On the solution of parabolic partial
differential equations by difference methods \\
T. M. Cherry, Numerical solution of a problem in forced
convection \\
B. A. Chartres, Monte Carlo calculation of the multiple
scattering of muons \\
J. C. Butcher, On the numerical inversion of Laplace
and Mellin transforms \\
P. J. Claringbold, The automatic design and analysis of
biological experiments \\
A. S. Douglas, Computers and Crystallography \\
H. C. Freeman, `SILLIAC' computer programs for X-ray
crystal structure analysis \\
C. L. Hamblin, An addressless coding scheme based on
mathematical notation \\
G. W. Hill and J. G. Sanderson, Automatic computing \\
R. G. Smart, The DEUCE matrix interpretive scheme \\
I. M. Bassett, Interpretive programming \\
J. M. Bennett, J. C. Butcher, M. Chapple, A new
diagnostic routine block \\
Appendices \\
Abstract cards \\
Volume I complete",
}
@Book{Householder:1964:TMN,
author = "Alston Scott Householder",
booktitle = "The Theory of Matrices in Numerical Analysis",
title = "The Theory of Matrices in Numerical Analysis",
publisher = pub-BLAISDELL,
address = pub-BLAISDELL:adr,
pages = "viii + 257",
year = "1964",
LCCN = "QA188 .H67 1964",
bibdate = "Tue Jun 19 06:23:59 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
series = "Introductions to higher mathematics; A Blaisdell book
in the pure and applied sciences",
acknowledgement = ack-nhfb,
author-dates = "1904--",
subject = "Matrices; Numerical analysis",
tableofcontents = "1. Some basic identities and inequalities \\
2. Norms, bounds, and convergence \\
3. Localization theorems and other inequalities
(exclusion theorems; inclusion and separation theorems;
minimax theorems: inequalities of Wielandt and
Kantorovich) \\
4. The solution of linear systems: methods of
successive approximation \\
5. Direct methods of inversion \\
6. Proper values and vectors: normalization and
reduction of the matrix (methods of Krylov,
Webber-Voetter, Danilevskii, Hessenberg, Lanczos,
Samuelson and Bryan, Leverrier, etc.) \\
7. Proper values and vectors: successive approximation
(methods of Jacobi, Collar and Jahn; power method; $LR$
and $QR$ transformations)",
}
@Book{Wilkinson:1965:AEP,
author = "J. H. Wilkinson",
booktitle = "The Algebraic Eigenvalue Problem",
title = "The Algebraic Eigenvalue Problem",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xviii + 662",
year = "1965",
ISBN = "0-19-853403-5",
ISBN-13 = "978-0-19-853403-7",
LCCN = "QA218 .W686 1965",
MRclass = "65.40",
MRnumber = "MR0184422 (32 \#1894)",
MRreviewer = "A. S. Householder",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
shorttableofcontents = "1. Theoretical Background \\
2. Perturbation Theory \\
3. Error Analysis \\
4. Solution of Linear Algebraic Equations \\
5. Hermitian Matrices \\
6. Reduction of a General Matrix to Condensed Form \\
7. Eigenvalues of Matrices of Condensed Forms \\
8. The $ L R $ and $ Q R $ Algorithms \\
9. Iterative Methods \\
Bibliography / 649 \\
Index / 657",
tableofcontents = "1. Theoretical Background \\
Introduction / 1 \\
Definitions / 2 \\
Eigenvalues and eigenvectors of the transposed matrix /
3 \\
Distinct eigenvalues / 4 \\
Similarity transformations / 6 \\
Multiple eigenvalues and canonical forms for general
matrices / 7 \\
Defective system of eigenvectors / 9 \\
The Jordan (classical) canonical form / 10 \\
The elementary divisors / 12 \\
Companion matrix of the characteristic polynomial of
$A$ / 12 \\
Non-derogatory matrices / 13 \\
The Frobenius (rational) canonical form / 15 \\
Relationship between the Jordan and Frobenius canonical
forms / 16 \\
Equivalence transformations / 17 \\
Lambda matrices / 18 \\
Elementary operations / 19 \\
Smith's canonical form / 19 \\
The highest common factor of $k$-rowed minors of a
$A$-matrix / 22 \\
Invariant factors of $ (A - \lambda M) $ / 22 \\
The triangular canonical form / 24 \\
Hermitian and symmetric matrices / 24 \\
Elementary properties of Hermitian matrices / 25 \\
Complex symmetric matrices / 26 \\
Reduction to triangular form by unitary transformations
/ 27 \\
Quadratic forms / 27 \\
Necessary and sufficient conditions for positive
definiteness / 28 \\
Differential equations with constant coefficients / 30
\\
Solutions corresponding to non-linear elementary
divisors / 31 \\
Differential equations of higher order / 32 \\
Second-order equations of special form / 34 \\
Explicit solution of $ B \ddot{y} = -A y$ / 35 \\
Equations of the form $(AB - \lambda I) x = 0$ / 35 \\
The minimum polynomial of a vector / 36 \\
The minimum polynomial of a matrix / 37 \\
Cayley--Hamilton theorem / 38 \\
Relation between minimum polynomial and canonical forms
/ 39 \\
Principal vectors / 42 \\
Elementary similarity transformations / 43 \\
Properties of elementary matrices / 45 \\
Reduction to triangular canonical form by elementary
similarity transformations / 46 \\
Elementary unitary transformations / 47 \\
Elementary unitary Hermitian matrices / 48 \\
Reduction to triangular form by elementary unitary
transformations / 50 \\
Normal matrices / 51 \\
Commuting matrices / 52 \\
Eigenvalues of $A B$ / 54 \\
Vector and matrix norms / 55 \\
Subordinate matrix norms / 56 \\
The Euclidean and spectral norms / 57 \\
Norms and limits / 58 \\
Avoiding use of infinite matrix series / 60 \\
2. Perturbation Theory \\
Introduction / 62 \\
Ostrowski's theorem on continuity of the eigenvalues /
63 \\
Algebraic functions / 64 \\
Numerical examples / 65 \\
Perturbation theory for simple eigenvalues / 66 \\
Perturbation of corresponding eigenvectors / 67 \\
Matrix with linear elementary divisors / 68 \\
First-order perturbations of eigenvalues / 68 \\
First-order perturbations of eigenvectors / 69 \\
Higher-order perturbations / 70 \\
Multiple eigenvalues / 70 \\
Gerschgorin's theorems / 71 \\
Perturbation theory based on Gerschgorin's theorems /
72 \\
Case 1. Perturbation of a simple eigenvalue $\lambda_1$
of a matrix having linear elementary divisors / 72 \\
Case 2. Perturbation of a multiple eigenvalue
$\lambda_1$ of a matrix having linear elementary
divisors / 75 \\
Case 3. Perturbation of a simple eigenvalue of a matrix
having one or more non-linear elementary divisors / 77
\\
Case 4. Perturbations of the eigenvalues corresponding
to a non-linear elementary divisor of a non-derogatory
matrix / 79 \\
Case 5. Perturbations of eigenvalues $\lambda_i$ when
there is more than one divisor involving $(\lambda_i -
\lambda_)$ and at least one of them is non-linear / 80
\\
Perturbations corresponding to the general distribution
of non-linear divisors / 81 \\
Perturbation theory for the eigenvectors from Jordan
canonical form / 81 \\
Perturbations of eigenvectors corresponding to a
multiple eigenvalue (linear elementary divisors) / 83
\\
Limitations of perturbation theory / 84 \\
Relationships between the $s_i$ / 85 \\
The condition of a computing problem / 86 \\
Condition numbers / 86 \\
Spectral condition number of A with respect to its
eigenproblem / 87 \\
Properties of spectral condition number / 88 \\
Invariant properties of condition numbers / 89 \\
Very ill-conditioned matrices / 90 \\
Perturbation theory for real symmetric matrices / 93
\\
Unsymmetric perturbations / 93 \\
Symmetric perturbations / 94 \\
Classical techniques / 94 \\
Symmetric matrix of rank unity / 97 \\
Extremal properties of eigenvalues / 98 \\
Minimax characterization of eigenvalues / 99 \\
Eigenvalues of the sum of two symmetric matrices / 101
\\
Practical applications / 102 \\
Further applications of minimax principle / 103 \\
Separation theorem / 103 \\
The Wielandt--Hoffman theorem / 104 \\
3. Error Analysis \\
Introduction / 110 \\
Fixed-point operations / 110 \\
Accumulation of inner-products / 111 \\
Floating-point operations / 112 \\
Simplified expressions for error bounds / 113 \\
Error bounds for some basic floating-point computations
/ 114 \\
Bounds for norms of the error matrices / 115 \\
Accumulation of inner-products in floating-point
arithmetic / 116 \\
Error bounds for some basic $\fl_2( )$ computations /
117 \\
Computation of square roots / 118 \\
Block-floating vectors and matrices / 119 \\
Fundamental limitations oft-digit computation / 120 \\
Eigenvalue techniques based on reduction by similarity
transformations / 123 \\
Error analysis of methods based on elementary
non-unitary transformations / 124 \\
Error analysis of methods based on elementary unitary
transformations / 126 \\
Superiority of the unitary transformation / 128 \\
Real symmetric matrices / 129 \\
Limitations of unitary transformations / 129 \\
Error analysis of floating-point computation of plane
rotations / 131 \\
Multiplication by a plane rotation / 133 \\
Multiplication by a sequence of plane rotations / 134
\\
Error in product of approximate plane rotations / 139
\\
Errors in similarity transforms / 140 \\
Symmetric matrices / 141 \\
Plane rotations in fixed-point arithmetic / 143 \\
Alternative computation of $\sin \theta$ and $\cos
\theta$ / 145 \\
Pre-multiplication by an approximate fixed-point
rotation / 145 \\
Multiplication by a sequence of plane rotations
(fixed-point) / 147 \\
The computed product of an approximate set of plane
rotations / 148 \\
Errors in similarity transformations / 148 \\
General comments on the error bounds / 151 \\
Elementary Hermitian matrices in floating-point / 152
\\
Error analysis of the computation of an elementary
Hermitian matrix / 153 \\
Numerical example / 156 \\
Pre-multiplication by an approximate elementary
Hermitian matrix / 157 \\
Multiplication by a sequence of approximate elementary
Hermitians / 160 \\
Non-unitary elementary matrices analogous to plane
rotations / 162 \\
Non-unitary elementary matrices analogous to elementary
Hermitian matrices / 163 \\
Pre-multiplication by a sequence of non-unitary
matrices / 165 \\
A priori error bounds / 166 \\
Departure from normality / 167 \\
Simple examples / 169 \\
A posteriori bounds / 170 \\
A posteriori bounds for normal matrices / 170 \\
Rayleigh quotient / 172 \\
Error in Rayleigh quotient / 173 \\
Hermitian matrices / 174 \\
Pathologically close eigenvalues / 176 \\
Non-normal matrices / 178 \\
Error analysis for a complete eigensystem / 180 \\
Numerical example / 181 \\
Conditions limiting attainable accuracy / 181 \\
Non-linear elementary, divisors / 182 \\
Approximate invariant subspaces / 184 \\
Almost normal matrices / 187 \\
4. Solution of Linear Algebraic Equations \\
Introduction / 189 \\
Perturbation theory / 189 \\
Condition numbers / 191 \\
Equilibrated matrices / 192 \\
Simple practical examples / 193 \\
Condition of matrix of eigenvectors / 193 \\
Explicit solution / 194 \\
General comments on condition of matrices / 195 \\
Relation of ill-conditioning to near-singularity / 196
\\
Limitations imposed by t-digit arithmetic / 197 \\
Algorithms for solving linear equations / 198 \\
Gaussian elimination / 200 \\
Triangular decomposition / 201 \\
Structure of triangular decomposition matrices / 201
\\
Explicit expressions for elements of the triangles /
202 \\
Breakdown of Gaussian elimination / 204 \\
Numerical stability / 205 \\
Significance of the interchanges / 206 \\
Numerical example / 207 \\
Error analysis of Gaussian elimination / 209 \\
Upper bounds for the perturbation matrices using
fixed-point arithmetic / 211 \\
Upper bound for elements of reduced matrices / 212 \\
Complete pivoting / 212 \\
Practical procedure with partial pivoting / 214 \\
Floating-point error analysis / 214 \\
Floating-point decomposition without pivoting / 215 \\
Loss of significant figures / 217 \\
A popular fallacy / 217 \\
Matrices of special form / 218 \\
Gaussian elimination on a high-speed computer / 220 \\
Solutions corresponding to different right-hand sides /
221 \\
Direct triangular decomposition / 221 \\
Relations between Gaussian elimination and direct
triangular decomposition / 223 \\
Examples of failure and non-uniqueness of decomposition
/ 224 \\
Triangular decomposition with row interchanges / 225
\\
Error analysis of triangular decomposition / 227 \\
Evaluation of determinants / 228 \\
Cholesky decomposition / 229 \\
Symmetric matrices which are not positive definite /
230 \\
Error analysis of Cholesky decomposition in fixed-point
arithmetic / 231 \\
An ill-conditioned matrix / 233 \\
Triangularization using elementary Hermitian matrices /
233 \\
Error analysis of Householder triangularization / 236
\\
Triangularization by elementary stabilized matrices of
the type M1, / 236 \\
Evaluation of determinants of leading principal minors
/ 237 \\
Triangularization by plane rotations / 239 \\
Error analysis of Givens reduction / 240 \\
Uniqueness of orthogonal triangularization / 241 \\
Schmidt orthogonalization / 242 \\
Comparison of the methods of triangularization / 244
\\
Back-substitution / 247 \\
High accuracy of computed solutions of triangular sets
of equations / 249 \\
Solution of a general set of equations / 251 \\
Computation of the inverse of a general matrix / 252
\\
Accuracy of computed solutions / 253 \\
Ill-conditioned matrices which give no small pivots /
254 \\
Iterative improvements of approximate solution / 255
\\
Effect of rounding errors on the iterative process /
256 \\
The iterative procedure in fixed-point computation /
257 \\
Simple example of iterative procedure / 258 \\
General comments on the iterative procedure / 260 \\
Related iterative procedures / 261 \\
Limitations of the iterative procedure / 261 \\
Rigorous justification of the iterative method / 262
\\
5. Hermitian Matrices \\
Introduction / 265 \\
The classical Jacobi method for real symmetric matrices
/ 266 \\
Rate of convergence / 267 \\
Convergence to fixed diagonal matrix / 268 \\
Serial Jacobi method / 269 \\
The Gerschgorin discs / 269 \\
Ultimate quadratic convergence of Jacobi methods / 270
\\
Close and multiple eigenvalues / 271 \\
Numerical examples / 273 \\
Calculation of cos 8 and sin B / 274 \\
Simpler determination of the angles of rotation / 276
\\
The threshold Jacobi method / 277 \\
Calculation of the eigenvectors / 278 \\
Numerical example / 279 \\
Error analysis of the Jacobi method / 279 \\
Accuracy of the computed eigenvectors / 280 \\
Error bounds for fixed-point computation / 281 \\
Organizational problems / 282 \\
Givens' method / 282 \\
Givens' process on a computer with a two-level store /
284 \\
Floating-point error analysis of Givens' process / 286
\\
Fixed-point error analysis / 287 \\
Numerical example / 288 \\
Householder's method / 290 \\
Taking advantage of symmetry / 292 \\
Storage considerations / 293 \\
Householder's process on a computer with a two-level
store / 294 \\
Householder's method in fixed-point arithmetic / 294
\\
Numerical example / 296 \\
Error analyses of Householder's method / 297 \\
Eigenvalues of a symmetric tri-diagonal matrix / 299
\\
Sturm sequence property / 300 \\
Method of bisection / 302 \\
Numerical stability of the bisection method / 302 \\
Numerical example / 305 \\
General comments on the bisection method / 306 \\
Small eigenvalues / 307 \\
Close eigenvalues and small $\beta_i$ / 308 \\
Fixed-point computation of the eigenvalues / 312 \\
Computation of the eigenvectors of a tri-diagonal form
/ 315 \\
Instability of the explicit expression for the
eigenvector / 316 \\
Numerical examples / 319 \\
Inverse iteration / 321 \\
Choice of initial vector $b$ / 322 \\
Error analysis / 323 \\
Numerical example / 325 \\
Close eigenvalues and small $\beta_i$ / 327 \\
Independent vectors corresponding to coincident
eigenvalues / 328 \\
Alternative method for computing the eigenvectors / 330
\\
Numerical example / 331 \\
Comments on the eigenproblem for tri-diagonal matrices
/ 332 \\
Completion of the Givens and Householder methods / 333
\\
Comparison of methods / 334 \\
Quasi-symmetric tri-diagonal matrices / 335 \\
Calculation of the eigenvectors / 336 \\
Equations of the form $A x = \lambda B x$ and $A B x =
\lambda X $ / 337 \\
Numerical example / 339 \\
Simultaneous reduction of $A$ and $B$ to diagonal form
/ 340 \\
Tri-diagonal $A$ and $B$ / 340 \\
Complex Hermitian matrices / 342 \\
6. Reduction of a General Matrix to Condensed Form \\
Introduction / 345 \\
Givens' method / 345 \\
Householder's method / 347 \\
Storage considerations / 350 \\
Error analysis / 350 \\
Relationship between the Givens and Householder methods
/ 351 \\
Elementary stabilized transformations / 353 \\
Significance of the permutations / 355 \\
Direct reduction to Hessenberg form / 357 \\
Incorporation of interchanges / 359 \\
Numerical example / 360 \\
Error analysis / 363 \\
Related error analyses / 365 \\
Poor determination of the Hessenberg matrix / 368 \\
Reduction to Hessenberg form using stabilized matrices
of the type $ M^'_{ji} $ / 368 \\
The method of Krylov / 369 \\
Gaussian elimination by columns / 370 \\
Practical difficulties / 371 \\
Condition of O for some standard distributions of
eigenvalues / 372 \\
Initial vectors of grade less than n / 374 \\
Practical experience / 376 \\
Generalized Hessenberg processes / 377 \\
Failure of the generalized Hessenberg process / 378 \\
The Hessenberg method / 379 \\
Practical procedure / 380 \\
Relation between the Hessenberg method and earlier
methods / 381 \\
The method of Arnoldi / 382 \\
Practical considerations / 383 \\
Significance of re-orthogonalization / 385 \\
The method of Lanczos / 388 \\
Failure of procedure / 389 \\
Numerical example / 390 \\
The practical Lanczos process / 391 \\
Numerical example / 392 \\
General comments on the unsymmetric Lanczos process /
394 \\
The symmetric Lanczos process / 394 \\
Reduction of a Hessenberg matrix to a more compact form
/ 395 \\
Reduction of a lower Hessenberg matrix to tri-diagonal
form / 396 \\
The use of interchanges / 397 \\
Effect of a small pivotal element / 398 \\
Error analysis / 399 \\
The Hessenberg process applied to a lower Hessenberg
matrix / 402 \\
Relationship between the Hessenberg process and the
Lanczos process / 402 \\
Reduction of a general matrix to tri-diagonal form /
403 \\
Comparison with Lanczos method / 404 \\
Re-examination of reduction to tri-diagonal form / 404
\\
Reduction from upper Hessenberg form to Frobenius form
/ 405 \\
Effect of small pivot / 407 \\
Numerical example / 408 \\
General comments on the stability / 408 \\
Specialized upper Hessenberg form / 409 \\
Direct determination of the characteristic polynomial /
410 \\
7. Eigenvalues of Matrices of Condensed Forms \\
Introduction / 413 \\
Explicit polynomial form / 413 \\
Condition numbers of explicit polynomials / 416 \\
Some typical distributions of zeros / 417 \\
Final assessment of Krylov's method / 421 \\
General comments on explicit polynomials / 421 \\
Tri-diagonal matrices / 423 \\
Determinants of Hessenberg matrices / 426 \\
Effect of rounding errors / 427 \\
Floating-point accumulation / 428 \\
Evaluation by orthogonal transformations / 429 \\
Evaluation of determinants of general matrices / 431
\\
The generalized eigenvalue problem / 432 \\
Indirect determinations of the characteristic
polynomial / 432 \\
Le Verrier's method / 434 \\
Iterative methods based on interpolation / 435 \\
Asymptotic rate of convergence / 436 \\
Multiple zeros / 437 \\
Inversion of the functional relationship / 439 \\
The method of bisection / 440 \\
Newton's method / 441 \\
Comparison of Newton's method with interpolation / 442
\\
Methods giving cubic convergence / 443 \\
Laguerre's method / 443 \\
Complex zeros / 446 \\
Complex conjugate zeros / 447 \\
Bairstow's method / 449 \\
The generalized Bairstow method / 450 \\
Practical considerations / 452 \\
Effect of rounding errors on asymptotic convergence /
453 \\
The method of bisection / 453 \\
Successive linear interpolation / 455 \\
Multiple and pathologically close eigenvalues / 457 \\
Other interpolation methods / 458 \\
Methods involving the use of a derivative / 459 \\
Criterion for acceptance of a zero / 461 \\
Effect of rounding errors / 462 \\
Suppression of computed zeros / 464 \\
Deflation for Hessenberg matrices / 465 \\
Deflation of tri-diagonal matrices / 468 \\
Deflation by rotations or stabilized elementary
transformations / 469 \\
Stability of the deflation / 472 \\
General comments on deflation / 474 \\
Suppression of computed zeros / 474 \\
Suppression of computed quadratic factors / 475 \\
General comments on the methods of suppression / 476
\\
Asymptotic rates of convergence / 478 \\
Convergence in the large / 478 \\
Complex zeros / 481 \\
Recommendations / 482 \\
Complex matrices / 483 \\
Matrices containing an independent parameter / 483 \\
8. The $ L R $ and $ Q R $ Algorithms \\
Introduction / 485 \\
Real matrices with complex eigenvalues / 486 \\
The $ L R $ algorithm / 487 \\
Proof of the convergence of the $A_s$ / 489 \\
Positive definite Hermitian matrices / 493 \\
Complex conjugate eigenvalues / 494 \\
Introduction of interchanges / 498 \\
Numerical example / 499 \\
Convergence of the modified process / 501 \\
Preliminary reduction of original matrix / 501 \\
Invariance of upper Hessenberg form / 502 \\
Simultaneous row and column operations / 504 \\
Acceleration of convergence / 505 \\
Incorporation of shifts of origin / 506 \\
Choice of shift of origin / 507 \\
Deflation of the matrix / 509 \\
Practical experience of convergence / 510 \\
Improved shift strategy / 511 \\
Complex conjugate eigenvalues / 512 \\
Criticisms of the modified $ L R $ algorithm. / 515 \\
The $ Q R $ algorithm / 515 \\
Convergence of the $ Q R $ algorithm / 516 \\
Formal proof of convergence / 517 \\
Disorder of the eigenvalues / 519 \\
Eigenvalues of equal modulus / 520 \\
Alternative proof for the $ L R $ technique / 521 \\
Practical application of the $ Q R $ algorithm / 523
\\
Shifts of origin / 524 \\
Decomposition of A8 / 525 \\
Numerical example / 527 \\
Practical procedure / 527 \\
Avoiding complex conjugate shifts / 528 \\
Double $ Q R $ step using elementary Hermitians / 532
\\
Computational details / 534 \\
Decomposition of A8 / 535 \\
Double-shift technique for $ L R $ / 537 \\
Assessment of $ L R $ and $ Q R $ algorithms / 538 \\
Multiple eigenvalues / 540 \\
Special use of the deflation process / 543 \\
Symmetric matrices / 544 \\
Relationship between $ L R $ and $ Q R $ algorithms /
545 \\
Convergence of the Cholesky $ L R $ algorithm / 546 \\
Cubic convergence of the $ Q R $ algorithm / 548 \\
Shift of origin in Cholesky $ L R $ / 549 \\
Failure of the Cholesky decomposition / 550 \\
Cubically convergent $ L R $ process / 551 \\
Band matrices / 553 \\
$ Q R $ decomposition of a band matrix / 557 \\
Error analysis / 561 \\
Unsymmetric band matrices / 562 \\
Simultaneous decomposition and recombination in $ Q R $
algorithm / 565 \\
Reduction of band width / 567 \\
9. ITERATIVE METHODS \\
Introduction / 570 \\
The power method / 570 \\
Direct iteration with a single vector / 571 \\
Shift of origin / 572 \\
Effect of rounding errors / 573 \\
Variation of $p$ / 576 \\
{\em Ad hoc\/} choice of $p$ / 577 \\
Aitken's acceleration technique / 578 \\
Complex conjugate eigenvalues / 579 \\
Calculation of the complex eigenvector / 581 \\
Shift of origin / 582 \\
Non-linear divisors / 582 \\
Simultaneous determination of several eigenvalues / 583
\\
Complex matrices / 584 \\
Deflation / 584 \\
Deflation based on similarity transformations / 585 \\
Deflation using invariant subspaces / 587 \\
Deflation using stabilized elementary transformations /
587 \\
Deflation using unitary transformations / 589 \\
Numerical stability / 590 \\
Numerical example / 592 \\
Stability of unitary transformations / 594 \\
Deflation by non-similarity transformations / 596 \\
General reduction using invariant subspaces / 599 \\
Practical application / 601 \\
Treppen-iteration / 602 \\
Accurate determination of complex conjugate eigenvalues
/ 604 \\
Very close eigenvalues / 606 \\
Orthogonalization techniques / 606 \\
Analogue of treppen-iteration using orthogonalization /
607 \\
Bi-iteration / 609 \\
Numerical example / 610 \\
Richardson's purification process / 614 \\
Matrix squaring / 615 \\
Numerical stability / 616 \\
Use of Chebyshev polynomials / 617 \\
General assessment of methods based on direct iteration
/ 618 \\
Inverse iteration / 619 \\
Error analysis of inverse iteration / 620 \\
General comments on the analysis / 621 \\
Further refinement of eigenvectors / 622 \\
Non-linear elementary divisors / 626 \\
Inverse iteration with Hessenberg matrices / 626 \\
Degenerate cases / 627 \\
Inverse iteration with band matrices / 628 \\
Complex conjugate eigenvectors / 629 \\
Error analysis / 631 \\
Numerical example / 633 \\
The generalized eigenvalue problem / 633 \\
Variation of approximate eigenvalues / 635 \\
Refinement of eigensystems / 637 \\
Numerical example / 639 \\
Refinement of the eigenvectors / 641 \\
Complex conjugate eigenvalues / 643 \\
Coincident and pathologically close eigenvalues / 644
\\
Comments on the ACE programmes / 646 \\
Bibliography / 649 \\
Index / 657",
}
@Book{Householder:1975:TMN,
author = "Alston Scott Householder",
booktitle = "The Theory of Matrices in Numerical Analysis",
title = "The Theory of Matrices in Numerical Analysis",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xi + 257",
year = "1975c1964",
ISBN = "0-486-61781-5",
ISBN-13 = "978-0-486-61781-7",
LCCN = "QA188 .H67 1975",
bibdate = "Tue Jun 19 06:23:59 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
price = "US\$4.00",
acknowledgement = ack-nhfb,
author-dates = "1904--",
remark = "Originally published in
\cite{Householder:1964:TMN}.",
subject = "Matrices; Numerical analysis",
tableofcontents = "1. Some basic identities and inequalities \\
2. Norms, bounds, and convergence \\
3. Localization theorems and other inequalities
(exclusion theorems; inclusion and separation theorems;
minimax theorems: inequalities of Wielandt and
Kantorovich) \\
4. The solution of linear systems: methods of
successive approximation \\
5. Direct methods of inversion \\
6. Proper values and vectors: normalization and
reduction of the matrix (methods of Krylov,
Webber-Voetter, Danilevskii, Hessenberg, Lanczos,
Samuelson and Bryan, Leverrier, etc.) \\
7. Proper values and vectors: successive approximation
(methods of Jacobi, Collar and Jahn; power method; $LR$
and $QR$ transformations)",
}
@Book{Householder:2006:TMN,
author = "Alston Scott Householder",
booktitle = "The Theory of Matrices in Numerical Analysis",
title = "The Theory of Matrices in Numerical Analysis",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "xi + 257",
year = "2006",
ISBN = "0-486-44972-6 (paperback)",
ISBN-13 = "978-0-486-44972-2 (paperback)",
LCCN = "QA188 .H67 2006",
bibdate = "Tue Jun 19 06:23:59 MDT 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://www.loc.gov/catdir/enhancements/fy0634/2005054775-d.html",
acknowledgement = ack-nhfb,
author-dates = "1904--",
remark = "Originally published in
\cite{Householder:1964:TMN}.",
subject = "Matrices; Numerical analysis",
tableofcontents = "1. Some basic identities and inequalities \\
2. Norms, bounds, and convergence \\
3. Localization theorems and other inequalities
(exclusion theorems; inclusion and separation theorems;
minimax theorems: inequalities of Wielandt and
Kantorovich) \\
4. The solution of linear systems: methods of
successive approximation \\
5. Direct methods of inversion \\
6. Proper values and vectors: normalization and
reduction of the matrix (methods of Krylov,
Webber-Voetter, Danilevskii, Hessenberg, Lanczos,
Samuelson and Bryan, Leverrier, etc.) \\
7. Proper values and vectors: successive approximation
(methods of Jacobi, Collar and Jahn; power method; $LR$
and $QR$ transformations)",
}
@Book{Anonymous:1962:RDG,
editor = "Anonymous",
booktitle = "Recent Developments in General Relativity",
title = "Recent Developments in General Relativity",
publisher = "Pergamon Press",
address = "London, UK",
pages = "472",
year = "1962",
LCCN = "QC 6 .R295",
bibdate = "Mon May 29 07:39:23 2017",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/i/infeld-leopold.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/einstein.bib",
note = "This book is dedicated to Leopold Infeld in connection
with his 60th birthday.",
acknowledgement = ack-nhfb,
author-dates = "Paul Adrian Maurice Dirac (1902--1984); Cornelius
Lanczos (1893--1974); John Lighton Synge (1897--1995);
Alfred Schild (1921--1977); Andrzej Mariusz Trautman
(1933--)",
tableofcontents = "Part I \\
B{\'a}za{\'n}ski, S. / The problem of motion / 13 \\
Bergmann, P. G. and Komar, A. B. / Status report on the
quantization of the gravitational field / 31 \\
Bondi, H. / Relativity and cosmology / 47 \\
Ginzburg, V. L. / Experimental verifications of the
general theory of relativity / 57 \\
Lichnerowicz, A. et Four{\`e}s-Bruhat, Y. /
Probl{\`e}mes math{\'e}matiques en relativit{\'e} / 73
\\
Pirani, F. A. E. / Survey of gravitational radiation
theory / 89 \\
Tonneltat, M. A. / Les espoirs et les difficult{\'e}s
de la th{\'e}orie du champ unifi{\'e} d'Einstein / 107
\\
Part II \\
Anderson, J. L. / Absolute change in general relativity
/ 121 \\
Arnowitt, R. L., Deser, S. and Misner, C. W. /
Canonical analysis of general relativity / 127 \\
B{\'a}za{\'n}ski, S. / The equations of motion and the
action principle in general relativity / 137 \\
Belinfante, F. J. / Two kinds of Schr{\"o}dinger
equations in general relativity theory / 151 \\
Bonnor, W. B. / On Birkhoff's theorem / 167 \\
Costa de Beauregard, O. / Une exp{\'e}rience
macroscopique pour tester l'asmm{\'e}trie du tenseur
inertial des milieux dou{\'e}s de spin / 171 \\
Dewitt, B. S. / Invariant commutators for the quantized
gravitational field / 175 \\
Dirac, P. A. M. / Interacting gravitational and spinor
fields / 191 \\
Ehlers, J. / Relativistic hydrodynamics and its
relation to interior solutions of the gravitational
field equations / 201 \\
Fock, V. / Einsteinian statics in conformal space / 209
\\
Gold, T. / The arrow of time / 225 \\
Goldberg, I. / On the quantum theory of gravitation /
235 \\
Golderg, J. N. / Dynamical variables and surface
integrals / 241 \\
Gupta, S. N. / Quantum theory of gravitation / 251 \\
Havas, P. / General relativity and the special
relativistic equations of motion of paint particles /
259 \\
Hoffmann, B. / On the extension of Birkhoff's theorem
to the case in which an electromagnetic field is
present / 279 \\
Jordan, P. / Empirical confirmation of Dirac's
hypothesis of diminishing gravitation / 283 \\
Jordan, P. / Remarks about the Ambarzumian's conception
of prestellar matter / 289 \\
Klein, O. / Mach's principle and cosmology in their
relation to general relativity / 293 \\
Kundt, W. and Hoffmann, B. / Determination of
gravitational standard time / 303 \\
Kundt, W. / Note on the equivalence problem / 307 \\
Lanczos, C. / Some properties of the
Riemann--Christoffel curvature tensor / 313 \\
Laurent, B. E. / On a generally covariant quantum
theory / 323 \\
Marder, L. / Locally isometric space-times / 333 \\
0zsv{\'a}th, I. and Sch{\"u}cking, E. / An
anti-Mach-metric / 339 \\
Papapetrou, A. and Treder, H. / Shock waves in general
relativity / 351 \\
Peres, A. / Motion and radiation of pole particles /
361 \\
Peres, A. and Rosen, N. / Boundary conditions in
general relativity theory / 367 \\
Petrov, A. Z. / Invariant classification of
gravitational fields / 371 \\
Petrov, A. Z. / Gravitational field geometry as the
geometry of automorphisms / 379 \\
Rosen, G. / Interpretation of Rainich geometry / 387
\\
Sachs, R. / Distance and the asymptotic behavior of
waves in general relativity / 395 \\
Schild, A. / Conservative gravitational theories of
Whitehead's type / 409 \\
Sciama, D. W. / On the analogy between charge and spin
in general relativity / 415 \\
Synge, J. L. / Relativity based on chronometry / 441
\\
Taub, A. H. / On spherically symmetric distributions of
incompressible fluids / 449 \\
Trautman, A. / On the propagation of information by
waves / 459 \\
Tulczyjew, B. and Tulczyjew, W. / On multipole
formalism in general relativity / 465--472",
}
@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",
}
@Book{Kardos:1978:SFF,
editor = "Istv{\'a}n Kardos",
title = "Scientists face to face",
publisher = "Corvina",
address = "Budapest, Hungary",
pages = "400",
year = "1978",
ISBN = "963-13-0373-X",
ISBN-13 = "978-963-13-0373-5",
ISSN = "0139-3014",
LCCN = "Q141 .S3714",
bibdate = "Tue Jun 14 15:34:33 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Translated from Hungarian to English by Inez Kemenes
and others.",
acknowledgement = ack-nhfb,
tableofcontents = "{\'A}brah{\'a}m Ambrus (1893--1989) \\
Alexits Gy{\"o}rgy (1899--1978) \\
Breuer Marcel (1902--1981) \\
Freund Mih{\'a}ly (1889--1984) \\
G{\'a}bor D{\'e}nes (1900--1979) \\
Gegesi Kiss P{\'a}l (1900--1993) \\
Gerevich L{\'a}szl{\'o} (1911--1997) \\
Germanus Gyula (1884--1979) \\
Korach M{\'o}r (1888--1975) \\
L{\'a}nczos Korn{\'e}l (1893--1974)",
}
@Book{Kardos:1978:WIS,
editor = "Istv{\'a}n Kardos",
title = "{Wissenschaftler im Scheinwerferlicht}. ({German})
[{Scientists} in the spotlight]",
publisher = "Corvina",
address = "Budapest, Hungary",
pages = "443",
year = "1978",
ISBN = "963-13-0374-8",
ISBN-13 = "978-963-13-0374-2",
ISSN = "0139-3022",
LCCN = "????",
bibdate = "Tue Jun 14 15:34:33 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Translated from Hungarian to German by Tam{\'a}s
Sz{\'a}nt{\'o} und Hannelore Weichenhain.",
acknowledgement = ack-nhfb,
language = "German",
tableofcontents = "{\'A}brah{\'a}m Ambrus (1893--1989) \\
Alexits Gy{\"o}rgy (1899--1978) \\
Breuer Marcel (1902--1981) \\
Freund Mih{\'a}ly (1889--1984) \\
G{\'a}bor D{\'e}nes (1900--1979) \\
Gegesi Kiss P{\'a}l (1900--1993) \\
Gerevich L{\'a}szl{\'o} (1911--1997) \\
Germanus Gyula (1884--1979) \\
Korach M{\'o}r (1888--1975) \\
L{\'a}nczos Korn{\'e}l (1893--1974)",
}
@Book{Banizs:2002:LKS,
author = "{Banizs K{\'a}roly}",
title = "{A ``L{\'a}nczos Korn{\'e}l --- Szekf{\"u} Gyula
{\"O}szt{\"o}nd{\'\i}j'' Alap{\'\i}tv{\'a}ny 10
{\'e}ve, 1993-2002: jubileumi kiadv{\'a}ny: L{\'a}nczos
Korn{\'e}l {\'e}s Szekf Gyula {\'e}lete {\'e}s
munk{\'a}ss{\'a}ga}. ({Hungarian}) [{The} {L{\'a}nczos
Kornel Gyula Szekf{\"u} Scholarship Foundation} 10
years anniversary 1993--2002: jubilee publication:
{Kornel L{\'a}nczos} and {Gyula Szekf{\"u}} life and
work]",
publisher = "Sz{\'e}kesfeh{\'e}rv{\'a}r Megyei-jog{\'u} V{\'a}ros
{\"O}nkorm{\'a}nyzata",
address = "Sz{\'e}kesfeh{\'e}rv{\'a}r, Hungary",
pages = "134",
year = "2002",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Tue Jun 14 15:22:52 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
language = "Hungarian",
}
@Book{Anonymous:1952:TCP,
editor = "Anonymous",
booktitle = "Tables of {Chebyshev} polynomials, {$ S_n(x) $} and {$
C_n(x) $}",
title = "Tables of {Chebyshev} polynomials, {$ S_n(x) $} and {$
C_n(x) $}",
volume = "9",
publisher = pub-USGPO,
address = pub-USGPO:adr,
pages = "xxx + 161",
year = "1952",
LCCN = "????",
MRclass = "65.0X",
MRnumber = "68893",
MRreviewer = "L. Fox",
bibdate = "Wed Jun 08 18:57:59 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "Foreword by J. C. P. Miller. Introduction by Cornelius
Lanczos.",
series = "National Bureau of Standards Applied Mathematics
Series",
acknowledgement = ack-nhfb,
reviewer-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}
@Proceedings{Anonymous:1955:PSS,
editor = "Anonymous",
booktitle = "{Proceedings of the [1951] symposium on spectral
theory and differential problems}",
title = "{Proceedings of the [1951] symposium on spectral
theory and differential problems}",
publisher = "Mathematics Department, Oklahoma Agricultural and
Mechanical College",
address = "Stillwater, OK, USA",
pages = "454",
year = "1955",
LCCN = "QA3 .O5 1951",
bibdate = "Wed Jun 8 19:25:45 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
melvyl.cdlib.org:210/CDL90",
acknowledgement = ack-nhfb,
remark = "Jointly sponsored by the American Mathematical
Society, the Office of Naval Research, and the Oklahoma
Agricultural and Mechanical College.",
subject = "Mathematics",
}
@Book{Szego:1962:SMA,
editor = "G{\'a}bor Szeg{\H{o}} and others",
booktitle = "Studies in mathematical analysis and related topics;
essays in honor of {George P{\'o}lya}",
title = "Studies in mathematical analysis and related topics;
essays in honor of {George P{\'o}lya}",
volume = "4",
publisher = pub-STANFORD,
address = pub-STANFORD:adr,
pages = "xxi + 447",
year = "1962",
LCCN = "QA3 .S8525",
bibdate = "Fri Jun 10 06:25:16 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
series = "Stanford studies in mathematics and statistics",
acknowledgement = ack-nhfb,
remark = "English, German, or French.",
subject = "P\'olya, George; Mathematics",
subject-dates = "1887--1985",
}
@Proceedings{Treder:1966:ESE,
editor = "Hans-J{\"u}rgen Treder",
booktitle = "{Einstein-Symposium ``Entstehung, Entwicklung und
Perspektiven der Einsteinschen Gravitationstheorie'':
vom 2.--5. November 1965 in Berlin aus Anla{\ss} des
50. Jahrestages der Entdeckung der allgemeinen
relativistischen Gravitationsgleichungen und ihrer
Vorlage in der Gesamtsitzung der Berliner Akademie am
4. November 1915 durch Albert Einstein: Vortr{\"a}ge
und Diskussionen}",
title = "{Einstein-Symposium ``Entstehung, Entwicklung und
Perspektiven der Einsteinschen Gravitationstheorie'':
vom 2.--5. November 1965 in Berlin aus Anla{\ss} des
50. Jahrestages der Entdeckung der allgemeinen
relativistischen Gravitationsgleichungen und ihrer
Vorlage in der Gesamtsitzung der Berliner Akademie am
4. November 1915 durch Albert Einstein: Vortr{\"a}ge
und Diskussionen}",
publisher = pub-AKADEMIE-VERLAG,
address = pub-AKADEMIE-VERLAG:adr,
pages = "314",
year = "1966",
LCCN = "????",
bibdate = "Fri Jun 10 06:39:31 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.gbv.de:20011/gvk",
acknowledgement = ack-nhfb,
}
@Proceedings{Cohen:1967:PBC,
editor = "Robert Sonn{\'e} Cohen and Marx W. Wartofsky",
booktitle = "Proceedings of the {Boston} colloquium for the
philosophy of science 1964\slash 1966, in memory of
{Norwood Russell Hanson}",
title = "Proceedings of the {Boston} colloquium for the
philosophy of science 1964\slash 1966, in memory of
{Norwood Russell Hanson}",
volume = "3",
publisher = pub-REIDEL,
address = pub-REIDEL:adr,
bookpages = "xlix + 489",
pages = "xlix + 489",
year = "1967",
DOI = "https://doi.org/10.1007/978-94-010-3508-8",
ISBN = "90-277-0013-3, 94-010-3508-3",
ISBN-13 = "978-90-277-0013-1, 978-94-010-3508-8",
ISSN = "0068-0346",
ISSN-L = "0068-0346",
LCCN = "Q175 .B731 v.3",
bibdate = "Sat Nov 10 09:55:12 MST 2018",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/bsphs.bib",
series = ser-BOSTON-STUD-PHILOS-SCI,
URL = "https://link.springer.com/book/10.1007/978-94-010-3508-8",
acknowledgement = ack-nhfb,
editor-dates = "Marx W. Wartofsky (1928--1997)",
series-URL = "https://link.springer.com/bookseries/5710",
subject-dates = "Norwood Russell Hanson (1924--1967)",
tableofcontents = "Front Matter / / i--xlix \\
The Early Modern Revolution in Science and Philosophy
\\
The Early Modern Revolution in Science and Philosophy /
Benjamin Nelson / 1--40 \\
Taxonomy and Information \\
Taxonomy and Information / David Hawkins / 41--55 \\
On the Elementarity of Measurement in General
Relativity: Toward a General Theory / Mendel Sachs /
56--80 \\
Symposium on Innate Ideas \\
Recent Contributions to the Theory of Innate Ideas /
Noam Chomsky / 81--90 \\
The `Innateness Hypothesis' and Explanatory Models in
Linguistics / Hilary Putnam / 91--101 \\
The Epistemological Argument / Nelson Goodman /
102--107 \\
Natural Kinds / G. Schlesinger / 108--122 \\
Metaphysics as Heuristic for Science / Marx Wartofsky /
123--172 \\
Comments / Ruth Anna Putnam / 173--180 \\
Rationalism and the Physical World / C. Lanczos /
181--198 \\
On the Foundations of Probability Theory / Hilda
Geiringer / 199--227 \\
Comments / Laszlo Tisza / 228--235 \\
Elementarity and Reality in Particle Physics / William
A. Wallace / 236--263 \\
Comments / Mary B. Miller / 264--271 \\
Semantic Sources of the Concept of Law / Gerd Buchdahl
/ 272--292 \\
Science in Flux / Joseph Agassi / 293--323 \\
Comments / Judith Jarvis Thomson / 324--330 \\
Conceptual Revolutions in Science / Stephen Toulmin /
331--347 \\
Comment on Stephen Toulmin's `Conceptual Revolutions in
Science' / Louis O. Mink / 348--355 \\
The Center of the World / Asher Moore / 356--375 \\
Comments: Analytic Premises and Existential Conclusions
/ Michael Martin / 376--386 \\
On the Improvement of the Sciences and the Arts, and
the Possible Identity of the Two / Paul K. Feyerabend /
387--415 \\
Comments: Acute Proliferitis / Peter Achinstein /
416--424 \\
An Answer / Norman Rudich / 425--432 \\
Comments: Illustration vs. Experimental Test / Marx W.
Wartofsky / 433--439 \\
Logic as Calculus and Logic as Language / Jean Van
Heijenoort / 440--446 \\
Three Studies in the Philosophy of Space and Time /
Zdzis{\l}aw Augustynek / 447--466 \\
What I Don't Believe / Norwood Russell Hanson /
467--489",
}
@Proceedings{Clark:1969:MMS,
editor = "R. C. (Roger Cortham) Clark and G. H. (Graham
Holbrook) Derrick",
title = "Mathematical methods in solid state and superfluid
theory",
publisher = "Oliver and Boyd",
address = "Edinburgh, UK",
bookpages = "400",
pages = "400",
year = "1969",
LCCN = "QC176.A1 S36 1967",
bibdate = "Mon Jun 20 15:09:42 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
meetingname = "Scottish Universities' Summer School in Physics (8th :
1967 : St. Andrews, Scotland)",
subject = "Solids; Superfluidity",
}
@Book{Salam:1972:AQT,
editor = "Abdus Salam and Eugene Paul Wigner",
booktitle = "Aspects of quantum theory",
title = "Aspects of quantum theory",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xvi + 268",
year = "1972",
ISBN = "0-521-08600-0",
ISBN-13 = "978-0-521-08600-4",
LCCN = "QC174.1 .A85 1972",
bibdate = "Mon May 16 14:00:57 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/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
URL = "http://hooke.lib.cam.ac.uk/cgi-bin/bib_seek.cgi?cat=ul&bib=1733506;
http://www.loc.gov/catdir/enhancements/fy1001/72075298-d.html;
http://www.loc.gov/catdir/enhancements/fy1001/72075298-t.html",
acknowledgement = ack-nhfb,
subject = "Quantum theory; Dirac, P. A. M; (Paul Adrien
Maurice)",
subject-dates = "1902--1984",
tableofcontents = "Prepared to commemorate the 70th birthday of P. A.
M. Dirac \\
Bibliography of P. A. M. Dirac (p. xiii--xvi) \\
Eden, R. J. and Polkinghorne, J. C. / Dirac in
Cambridge \\
Van Vleck, J. H. / Travels with Dirac in the Rockies
\\
Mehra, J. / The golden age of theoretical physics: P.
A. M. Dirac's scientific work from 1924 to 1933 \\
Jost, R. / Foundation of quantum field theory \\
Pais, A. / The early history of the theory of the
electron: 1897--1947 \\
Wightman, A. S. / The Dirac equation \\
Peierls, R. / Fermi--Dirac statistics \\
Heisenberg, W. / Indefinite metric in state space \\
Jauch, J. M. / On bras and kets \\
Lanczos, C. / The Poisson bracket \\
Schwartz, L. / La fonction $\delta$ et les noyaux \\
Amaldi, E. and Cabibbo, N. / On the Dirac magnetic
poles \\
Dyson, F. J. / The fundamental constants and their time
variation \\
Wigner, E. P. / On the time-energy uncertainty relation
\\
Salam, A. and Strathdee, J. / The path-integral
quantization of gravity",
}
@Proceedings{Miller:1973:TNA,
editor = "John J. H. Miller",
booktitle = "{Topics in numerical analysis: Proceedings of the
Royal Irish Academy Conference on Numerical Analysis,
Dublin, 14--18 August, 1972}",
title = "{Topics in numerical analysis: Proceedings of the
Royal Irish Academy Conference on Numerical Analysis,
Dublin, 14--18 August, 1972}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xviii + 348",
year = "1973",
ISBN = "0-12-496950-X",
ISBN-13 = "978-0-12-496950-6",
LCCN = "QA297 .R691 1972",
bibdate = "Mon Jun 20 15:17:47 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
}
@Proceedings{Glockner:1974:SSG,
editor = "P. G. Glockner and M. C. Singh",
booktitle = "{Symmetry, similarity and group theoretic methods in
mechanics. Proceedings of symposium held at the
University of Calgary, August 19--21, 1974}",
title = "{Symmetry, similarity and group theoretic methods in
mechanics. Proceedings of symposium held at the
University of Calgary, August 19--21, 1974}",
publisher = "University of Calgary",
address = "Calgary, AB, Canada",
pages = "633",
year = "1974",
LCCN = "QA805.C65x 1974",
bibdate = "Mon Jun 20 15:23:12 MDT 2011",
bibsource = "fsz3950.oclc.org:210/WorldCat;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
subject = "Mechanics, Analytic; Congresses",
}
@Book{Scaife:1974:SNA,
editor = "B. K. P. (Brendan Kevin Patrick) Scaife",
booktitle = "Studies in numerical analysis: papers in honour of
{Cornelius Lanczos}",
title = "Studies in numerical analysis: papers in honour of
{Cornelius Lanczos}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xxii + 333",
year = "1974",
ISBN = "0-12-621150-7",
ISBN-13 = "978-0-12-621150-4",
LCCN = "QA297 .S86",
bibdate = "Wed Jun 8 14:07:51 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
z3950.loc.gov:7090/Voyager",
note = "Published for the Royal Irish Academy.",
URL = "http://catalog.hathitrust.org/Record/000575557",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Lanczos, Cornelius; Bibliography",
subject-dates = "1893--1974",
tableofcontents = "Contributors / v \\
Editor's Foreword / vii \\
Cornelius Lanczos --- A Biographical Note / ix \\
List of Publications by Cornelius Lanczos / xii \\
\\
Table-making at the National Bureau of Standards /
Gertrude Blanch and Ida Rhodes / 1 \\
\\
Vignette of a Cultural Episode / Wilhelm Magnus / 7 \\
\\
The Physicist as Poet / Janice Bireline / 15 \\
\\
Conservation Laws in Einstein's General Theory of
Relativity / William R. Davis / 29 \\
\\
I Introduction / 29 \\
II Historical Comments --- Field Conservation Laws
proposed for General Relativity 1916--1959 / 31 \\
III Properties of General Covariant Field Theories / 34
\\
IV Remarks on Symmetry Properties and Invariance
Principles in Physical Theories / 37 \\
V Conservation Laws of Particle Mechanics in Riemannian
Spacetime / 40 \\
VI Particle Conservation Laws for Symmetry Properties
not representable by Point Deformations / 41 \\
VII Field Conservation Law Generators in General
Relativity / 43 \\
VIII Comments on Application of Conservation Laws for
Physically Closed Systems / 45 \\
IX Tensorial Tetrad Conservation Law Generators / 47
\\
X Conservation Laws for Curve Congruences with Special
Kinematical and Symmetry Properties / 50 \\
XI Other Integral Conservation Expressions / 52 \\
XII Conclusions / 54 \\
\\
An elementary procedure for the evaluation of electric
networks / L. Janossy / 65 \\
\\
Canonical Polynomials in the Lanczos Tau Method ---
Eduardo L. Ortiz / 73 \\
\\
I Introduction / 73 \\
II Mathematical Tables and Machine Tables / 74 \\
III The Tau Method / 76 \\
IV The Canonical Polynomials / 77 \\
V The Recursive Form of the Tau Method / 78 \\
VI Algebraic Formulation / 81 \\
VII Integrated Forms of the Tau Method / 82 \\
VIII Expansion of the Approximate Solution in More
General Bases / 86 \\
IX Eigenvalue Problems / 90 \\
\\
Rational Approximations from Chebyshev Series --- C. W.
Clenshaw and K. Lord / 95 \\
\\
I Introduction / 95 \\
II The Generalized Pad{\'e} Approximation / 98 \\
III The Chebyshev--Pad{\'e} Table / 98 \\
IV The Calculation of $S_{m,n}(x)$ / 101 \\
V An Example / 102 \\
VI Case of Slow Convergence / 104 \\
VII Computational Aspects / 105 \\
VIII Numerical Results / 107 \\
\\
Accuracy of Computed Eigensystems and Invariant
Subspaces / G. Peters and J. H. Wilkinson / 115 \\
\\
I Introduction / 115 \\
II Summary of Perturbation Theory for Normal Matrices /
115 \\
III Perturbation Theory for Non-Normal Matrices / 119
\\
IV Eigenvector Perturbations / 123 \\
V Computation of Orthogonal Bases for an Invariant
Subspace / 124 \\
VI Numerical Example / 127 \\
VII Attainable Accuracy / 129 \\
VIII Low Relative Errors in Small Eigenvalues / 132 \\
\\
Buckling of a Beam under Axial Compression with Elastic
Support / A. P. Gallagher / 137 \\
\\
I Introduction / 137 \\
II Formulation of the Integro--Differential Equation /
139 \\
III Analysis of the Even Modes of Buckling / 140 \\
IV Analysis of the Odd Modes of Buckling / 142 \\
V Numerical Results / 143 \\
\\
The Frequency Approach to Numerical Analysis / R. W.
Hamming / 151 \\
\\
I Introduction / 151 \\
II The effects of Sampling-Aliasing / 152 \\
III The Finite Fourier Series / 154 \\
IV The Nyquist Interval and the Sampling Theorem / 158
\\
V The Difference Table and Noise / 160 \\
VI A Quick Look at Integration / 162 \\
VII Smoothing / 163 \\
VIII The Gibbs Phenomenon / 166 \\
IX Elementary Filter Theory / 169 \\
X More Advanced Filter Theory / 172 \\
\\
Detouring around Computational Roadblocks --- A Tale of
Two Integrals / Forman S. Acton / 177 \\
\\
The Hypercircle Method / J. L. Synge / 201 \\
\\
I Simplification / 201 \\
II An Example: The Dirichlet Problem / 203 \\
III The Pay-Off in the Dirichlet Problem / 207 \\
IV More General View. The Hypercircle / 209 \\
V Historical Note / 212 \\
VI The Significance of a Small Hypersphere / 213 \\
VII Vertices / 215 \\
\\
Lower Bounds for the Dirichlet Integral / J. J. McMahon
/ 219 \\
\\
I The Problem / 219 \\
II Essential Inequality / 220 \\
III Method of Constructing Normally-Continuous
Divergent-Free Vector-Fields / 221 \\
IV A Class of Functions and Vector-Fields / 223 \\
V Properties of $P''_{\rho \sigma}$ / ??? \\
VI Formulae for the Three Fundamental Vector-Fields /
225 \\
VII Integrals of Vector-Fields / 228 \\
VIII Use of Symmetry / 230 \\
IX A Calculation with Lattice Edge $a = 1$ / 231 \\
\\
The Koenig--Hadamard Theorem again / Alston S.
Householder / 235 \\
\\
Significance Arithmetic --- On the Algebra of Binary
Strings / N. Metropolis and Gian-Carlo Rota / 241 \\
\\
I Introduction / 241 \\
II The Arithmetic of Binary Strings / 243 \\
III Multiplication / 247 \\
IV Binary Functions / 250 \\
\\
Practical Algorithms for Finding the Type of a
Polynomial / John J. H. Miller / / 253 \\
\\
I Introduction / 253 \\
II The Type of a Polynomial Relative to the Unit Circle
/ 254 \\
III The Type of a Polynomial Relative to the Imaginary
Axis / 256 \\
IV Examples / 260 \\
\\
The Edge-Function Method in Elastostatics / P. M.
Quinlan / 265 \\
\\
Introduction / 265 \\
I The Elastostatic Problem / 266 \\
II Edge-Functions for a Polygonal Region / 267 \\
III Derived Edge-Functions / 269 \\
IV Some Particular Integrals / 271 \\
V Polygonal Beam: The Boundary Identity Problem / 272
\\
VI Trapezoidal Beam --- Illustration Examples / 276 \\
VII Polar Elasto-Functions / 278 \\
VIII Singular Loadings / 282 \\
IX Singular Loadings on Boundary / 284 \\
X Symmetrical Functions / 286 \\
XI Symmetrical Singular Loadings / 287 \\
XII Applications / 288 \\
\\
Generalised Lobatto Quadrature Formulas for Contour
Integrals / S. J. Maskell and R. A. Sack / 295 \\
\\
I Introduction / 295 \\
II General Formulas for the Coefficients / 298 \\
I II Generalized Lobatto- Mehler Quadrature / 300 \\
IV Numerical Tests / 303 \\
V Conclusions / 308 \\
\\
Spline Functions and Differential Equations --- First
Order Equations / I. J. Schoenberg / 311 \\
\\
I A Remark Due to C. Lanczos / 311 \\
II The Spline Approximations of Higher Degree / 313 \\
III The Construction of the Spline Approximation $S(x)$
/ 314 \\
IV The Unique Existence of $S_n(x)$ and on Error
Estimate / 316 \\
V All Derivatives of $S(x)$ Approximate those of $y(x)$
/ 320 \\
VI Examples / 321",
}
@Proceedings{Rice:1977:MSI,
editor = "John R. Rice",
booktitle = "{Mathematical software III: Proceedings of a symposium
conducted by the Mathematics Research Center, the
University of Wisconsin--Madison, March 28--30, 1977}",
title = "{Mathematical software III: Proceedings of a symposium
conducted by the Mathematics Research Center, the
University of Wisconsin--Madison, March 28--30, 1977}",
number = "39",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 388",
year = "1977",
DOI = "https://doi.org/10.1016/C2013-0-11364-5",
ISBN = "0-12-587260-7",
ISBN-13 = "978-0-12-587260-7",
LCCN = "QA3 .U45 no. 39; QA297 .M36 1977",
bibdate = "Fri Dec 08 08:24:52 1995",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/brandt-achi.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/Bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/unix.bib",
series = "Publication of the Mathematics Research Center, the
University of Wisconsin, Madison",
URL = "https://www.sciencedirect.com/book/9780125872607/mathematical-software",
acknowledgement = ack-nhfb,
shorttableofcontents = "Contributors / / vii \\
Preface / / ix \\
Research, Development, and UNPACK / G. W. Stewart / 1
\\
A Technique that Gains Speed and Accuracy in the
Minimax Solution of Overdetermined Linear Equations /
M. J. Hopper and M. J. D. Powell / 15 \\
Infallible Calculation of Polynomial Zeros to Specified
Precision / G. E. Collins / 35 \\
Representation and Approximation of Surfaces / Robert
E. Barnhill / 69 \\
Simulation: Conflicts between Real-Time and Software /
C. W. Gear / 121 \\
Mathematical Software and Exploratory Data Analysis /
David C. Hoaglin / 139 \\
Software for $C^1$ Surface Interpolation / C. L. Lawson
/ 161 \\
Mathematical Software Production / W. R. Cowell and L.
D. Fosdick / 195 \\
Computational Aspects of the Finite Element Method / I.
Babuska and W. Rheinboldt / 225 \\
The Art of Writing a Runge-Kutta Code, Part I / L. F.
Shampine and H. A. Watts / 257 \\
Multi-Level Adaptive Techniques (MLAT) for Partial
Differential Equations: Ideas and Software / Achi
Brandt / 277 \\
ELLPACK: A Research Tool for Elliptic Partial
Differential Equations Software / John R. Rice / 319
\\
A Realistic Model of Floating-Point Computation / W. S.
Brown / 343 \\
The Block Lanczos Method for Computing Eigenvalues / G.
H. Golub and R. Underwood / 361 \\
Index / / 379",
tableofcontents = "Contributors \\
Preface \\
\\
1: Research, Development, and Linpack \\
Abstract \\
1. Introduction \\
2. Estimation of Condition Numbers \\
3. Stability of Least Squares Solutions \\
4. Scaling and Column Elimination \\
5. Downdating \\
6. Timing the BLAS \\
References \\
\\
2: A Technique That Gains Speed and Accuracy in the
Minimax Solution of Overdetermined Linear Equations \\
Abstract \\
1. Introduction \\
2. Numerical Instability in the Exchange Algorithm \\
3. The New Technique \\
4. Theory \\
5. Discussion \\
References \\
\\
3: Infallible Calculation Of Polynomial Zeros To
Specified Precision \\
Abstract \\
1. Introduction \\
2. Preliminaries \\
3. Sturm Sequences For Real Zeros \\
4. Sturm Sequences For Complex Zeros \\
5. Rolle's Theorem For Real Zeros \\
6. Descartes' Theorem For Real Zeros \\
7. Application of Interval Arithmetic \\
8. Complex Zeros Without Sturm Sequences \\
References \\
\\
4: Representation and Approximation of Surfaces \\
Abstract \\
1. Introduction \\
2. Interpolation Methods Defined Over Rectangles \\
3. Interpolation Schemes Defined Over Triangles \\
4. Interpolation Methods For Arbitrarily Placed Data 5.
Conclusions \\
References \\
Acknowledgements \\
\\
5: Simulation: Conflicts Between Real-Time And Software
\\
Abstract \\
1. Introduction \\
2. Simulation \\
3. Real-Time Operation \\
4. Numerical Integration in Real-Time \\
5. Errors in Numerical Integration \\
6. Methods For Reducing Delay and Improving Stability
\\
7. Conclusions \\
References \\
\\
6: Mathematical Software and Exploratory Data Analysis
\\
Abstract \\
1. Introduction \\
2. Overview of Exploratory Data Analysis \\
3. An Example: Timing Data \\
4. Software Needs of Exploratory Data Analysis \\
5. Summary \\
References \\
\\
7: Software For $C^1$ Surface Interpolation \\
1. Introduction \\
2. Problem Statement \\
3. Expected Applications \\
4. Published Work On Surface Interpolation To
Irregularly Located Data \\
5. Outline of the Algorithmic Approach Selected \\
6. Constructing a Triangular Grid \\
7. Estimating Partial Derivatives At the Grid Nodes \\
8. Lookup in the Triangular Grid \\
9. Interpolation in a Triangle \\
10. Examples \\
11. Three Criteria For Triangulation of a Strictly
Convex Quadrilateral \\
12. Global Consequences of the Local Optimization
Procedure \\
13. Mclain's Triangulation Method \\
14. Limits On Grid Changes When Adding a New Point \\
15. Conclusions \\
References \\
\\
8: Mathematical Software Production \\
Abstract \\
I. Introduction \\
II. The Evolution of Mathematical Software Production
\\
III. Intellectual Challenges \\
IV. Projects To Produce Mathematical Software \\
V. Trends in Mathematical Software Production \\
References \\
\\
9: Computational Aspects of the Finite Element Method
\\
1. Introduction \\
2. Goals of the Computational Analysis \\
3. The Principal Stages of the Computational Analysis
\\
4. Some Software Aspects \\
5. Some Computational Results \\
References",
}
@Proceedings{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/l/lanczos-cornelius.bib;
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{Feilmeier:1984:PCP,
editor = "M. Feilmeier and G. Joubert and U. Schendel",
booktitle = "Parallel Computing 83: Proceedings of the
International Conference on Parallel Computing",
title = "Parallel Computing 83: Proceedings of the
International Conference on Parallel Computing",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
year = "1984",
bibdate = "Fri Jun 10 15:04:16 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
}
@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/d/duff-iain-s.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.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/l/lanczos-cornelius.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: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/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/2008749",
acknowledgement = ack-nhfb,
remark = "See review by J. H. B. in Mathematics of Computation,
Vol. 53, No. 188 (Oct., 1989), p. 775.",
}
@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,
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 = "Marinus A. Kaashoek and Jan H. van Schuppen and
Andr{\'e} C. M. Ran",
booktitle = "{Proceedings of the International Symposium MTNS-89.
Realization and modelling in system theory. Amsterdam,
The Netherlands, June 19--23, 1989}",
title = "{Proceedings of the International Symposium MTNS-89.
Realization and modelling in system theory. Amsterdam,
The Netherlands, June 19--23, 1989}",
volume = "3--5",
publisher = pub-BIRKHAUSER-BOSTON,
address = pub-BIRKHAUSER-BOSTON:adr,
pages = "xxii + 593",
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/l/lanczos-cornelius.bib;
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{Vaccaro:1991:SSP,
editor = "Richard J. Vaccaro",
booktitle = "SVD and Signal Processing, II. Algorithms, Analysis
and Applications",
title = "{SVD} and Signal Processing, {II}. Algorithms,
Analysis and Applications",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
pages = "xv + 512",
year = "1991",
ISBN = "0-444-88896-9",
ISBN-13 = "978-0-444-88896-9",
LCCN = "TK5102.5.S93 1991",
bibdate = "Fri Dec 20 18:20:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb,
confdate = "25--27 June 1990",
conflocation = "Kingston, RI, USA",
confsponsor = "Coll. Eng. URI; IEEE; EURASIP; SIAM",
pubcountry = "Netherlands",
}
@Book{Hussaini:1993:ATC,
editor = "M. Y. Hussaini and A. Kumar and M. D. Salas",
booktitle = "Algorithmic Trends in Computational Fluid Dynamics",
title = "Algorithmic Trends in Computational Fluid Dynamics",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xvi + 423",
year = "1993",
ISBN = "0-387-94014-6 (New York), 3-540-94014-6 (Berlin)",
ISBN-13 = "978-0-387-94014-4 (New York), 978-3-540-94014-2
(Berlin)",
LCCN = "QA911 .A555 1993",
bibdate = "Fri Jun 10 19:00:59 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "ICASE/NASA LaRC Series",
acknowledgement = ack-sf,
}
@Proceedings{Natori:1993:PPS,
editor = "Makoto Natori and T. Nodera",
booktitle = "{Parallel processing for scientific computing
(Yokohama, 1993)}",
title = "{Parallel processing for scientific computing
(Yokohama, 1993)}",
volume = "9",
publisher = "Keio University",
address = "Yokohama, Japan",
pages = "70",
year = "1993",
LCCN = "????",
bibdate = "Wed Jan 17 10:14:47 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib",
series = "Advances in numerical methods for large sparse sets of
linear equations",
acknowledgement = ack-nhfb,
xxISBN = "none",
}
@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/hartree-douglas-r.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{IEEE:1995:PEW,
editor = "{IEEE}",
booktitle = "Proceedings: Euromicro Workshop on Parallel and
Distributed Processing, San Remo, Italy, January
25--27, 1995",
title = "Proceedings: Euromicro Workshop on Parallel and
Distributed Processing, San Remo, Italy, January
25--27, 1995",
publisher = pub-IEEE,
address = pub-IEEE:adr,
pages = "xiii + 582",
year = "1995",
ISBN = "0-8186-7031-2, 0-8186-7032-0",
ISBN-13 = "978-0-8186-7031-2, 978-0-8186-7032-9",
LCCN = "QA76.58 .E97 1995",
bibdate = "Wed Aug 14 09:02:28 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "Euromicro Workshop on Parallel and Distributed
Processing 1995; 3rd",
acknowledgement = ack-nhfb,
xxeditor1 = "I. Martin and J. C. Fabero and F. Tirado and A.
Bautista",
xxeditor2 = "V. Gianuzzi and F. Merani",
}
@Proceedings{Moonen:1995:SSP,
editor = "Marc S. Moonen and Bart L. R. de Moor",
booktitle = "{SVD and signal processing III: algorithms,
architectures, and applications}",
title = "{SVD and signal processing III: algorithms,
architectures, and applications}",
publisher = pub-ELSEVIER,
address = pub-ELSEVIER:adr,
bookpages = "xi + 485",
pages = "xi + 485",
year = "1995",
ISBN = "0-444-82107-4",
ISBN-13 = "978-0-444-82107-2",
LCCN = "TK5102.9 .S83 1995",
bibdate = "Fri Jun 10 17:22:20 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
acknowledgement = ack-nhfb,
remark = "Papers based on contributions presented at the 3rd
International Workshop on SVD and Signal Processing,
held in Leuven, August 22--25, 1994.",
subject = "Signal processing; Digital techniques; Congresses;
Decomposition (Mathematics)",
}
@Proceedings{ACM:1996:FCP,
editor = "{ACM}",
booktitle = "FCRC '96: Conference proceedings of the 1996
International Conference on Supercomputing:
Philadelphia, Pennsylvania, {USA}, May 25--28, 1996",
title = "{FCRC} '96: Conference proceedings of the 1996
International Conference on Supercomputing:
Philadelphia, Pennsylvania, {USA}, May 25--28, 1996",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xii + 406",
year = "1996",
ISBN = "0-89791-803-7",
ISBN-13 = "978-0-89791-803-9",
LCCN = "QA76.5 I61 1996",
bibdate = "Wed Mar 18 12:33:29 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "ACM order number 415961.",
acknowledgement = ack-nhfb,
keywords = "Supercomputers --- Congresses.",
}
@Proceedings{Bode:1996:PVM,
editor = "Arndt Bode and J. Dongarra and T. Ludwig and V.
Sunderam",
booktitle = "Parallel virtual machine, {EuroPVM} '96: third
European {PVM} conference, Munich, Germany, October
7--9, 1996: proceedings",
title = "Parallel virtual machine, {EuroPVM} '96: third
European {PVM} conference, Munich, Germany, October
7--9, 1996: proceedings",
volume = "1156",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xiv + 362",
year = "1996",
ISBN = "3-540-61779-5",
ISBN-13 = "978-3-540-61779-2",
ISSN = "0302-9743 (print), 1611-3349 (electronic)",
LCCN = "QA76.58 .E975 1996 Bar",
bibdate = "Sat Dec 21 16:06:37 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = ser-LNCS,
acknowledgement = ack-nhfb,
keywords = "Parallel computers -- Congresses; Virtual computer
systems -- Congresses.",
}
@Proceedings{May:1996:CTA,
editor = "R. L. May and A. K. Easton",
booktitle = "{Computational techniques and applications, CTAC 95:
proceedings of the Seventh Biennial Conference,
Swinburne University of Technology, Melbourne,
Australia, 3-5 July, 1995}",
title = "{Computational techniques and applications, CTAC 95:
proceedings of the Seventh Biennial Conference,
Swinburne University of Technology, Melbourne,
Australia, 3-5 July, 1995}",
publisher = pub-WORLD-SCI,
address = pub-WORLD-SCI:adr,
pages = "xvii + 875",
year = "1996",
ISBN = "981-02-2820-1",
ISBN-13 = "978-981-02-2820-0",
LCCN = "QA299.6 .I56 1995",
bibdate = "Wed Mar 18 12:33:18 MST 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "COMPUTATIONAL TECHNIQUES AND APPLICATIONS 1995; 7th",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:1997:SHP,
editor = "{ACM}",
booktitle = "{SC'97: High Performance Networking and Computing:
Proceedings of the 1997 ACM\slash IEEE SC97 Conference:
November 15--21, 1997, San Jose, California, USA}",
title = "{SC'97: High Performance Networking and Computing:
Proceedings of the 1997 ACM\slash IEEE SC97 Conference:
November 15--21, 1997, San Jose, California, USA}",
publisher = pub-ACM # " and " # pub-IEEE,
address = pub-ACM:adr # " and " # pub-IEEE:adr,
pages = "vii + 159",
year = "1997",
ISBN = "0-89791-985-8",
ISBN-13 = "978-0-89791-985-2",
LCCN = "QA76.88 .S8571 1997",
bibdate = "Sat Mar 21 09:10:00 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "ACM SIGARCH order number 415972. IEEE Computer Society
Press order number RS00160.",
URL = "http://www.supercomp.org/sc97/proceedings/",
acknowledgement = ack-nhfb,
xxnote = "Check ISBN: UC/Melvyl has this one for ``Proceedings /
Second ACM Workshop on Role-Based Access Control,
Fairfax, Virginia, USA, November 6--7, 1997''.",
}
@Book{Brezinski:1997:PMS,
author = "Claude Brezinski",
booktitle = "Projection methods for systems of equations",
title = "Projection methods for systems of equations",
volume = "7",
publisher = "Elsevier Science",
address = "Amsterdam, The Netherlands",
pages = "vii + 400",
year = "1997",
ISBN = "0-444-82777-3",
ISBN-13 = "978-0-444-82777-7",
LCCN = "QA214 .B74 1997",
bibdate = "Fri Jun 10 17:39:08 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
series = "Studies in computational mathematics",
URL = "http://www.loc.gov/catdir/enhancements/fy0602/97043588-d.html;
http://www.loc.gov/catdir/enhancements/fy0602/97043588-t.html",
acknowledgement = ack-nhfb,
subject = "Equations, Simultaneous; Numerical solutions;
Iterative methods (Mathematics)",
}
@Proceedings{Kuchlin:1997:IJM,
editor = "Wolfgang W. K{\"u}chlin",
booktitle = "{ISSAC 97: July 21--23, 1997, Maui, Hawaii, USA:
proceedings of the 1997 International Symposium on
Symbolic and Algebraic Computation}",
title = "{ISSAC 97: July 21--23, 1997, Maui, Hawaii, USA:
proceedings of the 1997 International Symposium on
Symbolic and Algebraic Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xxii + 414",
year = "1997",
ISBN = "0-89791-875-4",
ISBN-13 = "978-0-89791-875-6",
LCCN = "QA76.95",
bibdate = "Sat Mar 23 12:41:32 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.acm.org/pubs/contents/proceedings/issac/258726/",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:1998:SHP,
editor = "{ACM}",
booktitle = "SC'98: High Performance Networking and Computing:
Proceedings of the 1998 ACM\slash IEEE SC98 Conference:
Orange County Convention Center, Orlando, Florida, USA,
November 7--13, 1998",
title = "{SC}'98: High Performance Networking and Computing:
Proceedings of the 1998 {ACM}\slash {IEEE} {SC98}
Conference: Orange County Convention Center, Orlando,
Florida, {USA}, November 7--13, 1998",
publisher = pub-ACM # " and " # pub-IEEE,
address = pub-ACM:adr # " and " # pub-IEEE:adr,
pages = "????",
year = "1998",
ISBN = "????",
ISBN-13 = "????",
LCCN = "????",
bibdate = "Wed Oct 07 08:51:34 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.supercomp.org/sc98/papers/",
acknowledgement = ack-nhfb,
}
@Book{Davis:1998:CLC,
author = "William R. (William Robert) Davis and others",
booktitle = "{Cornelius Lanczos}, collected published papers with
commentaries, {Volumes I--VI}",
title = "{Cornelius Lanczos}, collected published papers with
commentaries, {Volumes I--VI}",
publisher = "College of Physical and Mathematical Sciences, North
Carolina State University",
address = "Raleigh, NC, USA",
pages = "xlvi + 3117",
year = "1998",
ISBN = "0-929493-00-1, 0-929493-01-X",
ISBN-13 = "978-0-929493-00-8, 978-0-929493-01-5",
LCCN = "QC19.3 .L35 1998",
MRclass = "01A75 (00A05 00A79 01A70)",
MRnumber = "1707325 (2000j:01121)",
bibdate = "Thu Jun 9 12:34:46 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
note = "Six volumes. With a foreword by George Marx and a
biographical essay by Barbara Gellai, Translated by
J{\'o}zsef Illy, Laurent Choquet, Don Ridgeway and
Judith Konts{\'a}g Mesk{\'o}.",
URL = "http://catalog.hathitrust.org/Record/004015572",
acknowledgement = ack-nhfb,
author-dates = "1893--1974",
language = "English, German, French, and Hungarian",
remark = "This Collection has been published by North Carolina
State University in cooperation with the E{\"o}tv{\"o}s
Physical Society, Hungary.",
subject = "Mathematical physics; Physics; Mathematics; Lanczos,
Cornelius",
subject-dates = "1893--1974",
}
@Proceedings{Csendes:1999:DRC,
editor = "Tibor Csendes",
booktitle = "{Developments in Reliable Computing: Papers presented
at the International Symposium on Scientific Computing,
Computer Arithmetic, and Validated Numerics, SCAN-98,
in Szeged, Hungary}",
title = "{Developments in Reliable Computing: Papers presented
at the International Symposium on Scientific Computing,
Computer Arithmetic, and Validated Numerics, SCAN-98,
in Szeged, Hungary}",
volume = "5(3)",
publisher = pub-KLUWER,
address = pub-KLUWER:adr,
pages = "viii + 402",
year = "1999",
ISBN = "0-7923-6057-5",
ISBN-13 = "978-0-7923-6057-5",
LCCN = "QA76.9.E94 D48 1999",
bibdate = "Sat Nov 29 11:31:21 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = j-RELIABLE-COMPUTING,
acknowledgement = ack-nhfb,
tableofcontents = "Rigorous Global Search: Industrial Applications /
G. F. Corliss, R. B. Kearfott. \\
Influences of Rounding Errors in Solving Large Sparse
Linear Systems / A. Facius. \\
A Hardware Approach to Interval Arithmetic for Sine and
Cosine Functions / J. Hormigo, et al. \\
Towards an Optimal Control of the Wrapping Effect / W.
K{\"u}hn. \\
On Existence and Uniqueness of Solutions of Linear
Algebraic Equations in Kaucher's Interval Arithmetic /
A. V. Lakeyev. \\
A Comparison of Subdivision Strategies for Verified
Multi-Dimensional Gaussian Quadrature / B. Lang. \\
INTLAB - INTerval LABoratory / S. M. Rump. \\
Verified Calculation of the Solution of Algebraic
Riccati Equation / W. Luther, W. Otten. \\
Expression Concepts in Scientific Computing / M. Lerch.
\\
Performance Evaluation Technique STU and libavi Library
/ R. Sagula, et al. \\
Single-Number Interval I/O / M. Schulte, et al. \\
Interval Analysis for Embedded Systems / K. Musch, G.
Schumacher. \\
Prediction by Extrapolation for Interval Tightening
Methods / Y. Lebbah, O. Lhomme. \\
The Contribution of T. Sunaga to Interval Analysis and
Reliable Computing / S. Markov, K. Okumura. \\
Surface-to-Surface Intersection with Complete and
Guaranteed Results / E. Hubert, W. Barth. \\
An Algorithm that Computes a Lower Bound on the
Distance Between a Segment and Z2 / V. Lef{\`e}vre. \\
Verified Computation of Fast Decreasing Polynomials /
N. S. Dimitrova, S. M. Markov. \\
An Accurate Distance-Calculation Algorithm for Convex
Polyhedra / E. Dyllong, et al. \\
Verified Error Bounds for Linear Systems through the
Lanczos Process / A. Frommer, A. Weinberg. \\
A Representation of the Interval Hull of a Tolerance
Polyhedron Describing Inclusions of Function Values and
Slopes / G. Heindl. \\
A Few Results on Table-Based Methods / J.-M. Muller.
\\
An Interval Hermite-Obreschkoff Method for Computing
Rigorous Bounds on the Solution of an Initial Value
Problem for an Ordinary Differential Equation / N. S.
Nedialkov, K. R. Jackson. \\
The Interval-Enhanced GNU Fortran Compiler / M.
Schulte, et al. \\
Outer Estimation of Generalized Solution Sets to
Interval Linear Systems / S. P. Shary. \\
A Real Polynomial Decision Algorithm Using
Arbitrary-Precision Floating Point Arithmetic / A.
Strzebonski. \\
A Numerical Verification Method of Solutions for the
Navier--Stokes Equations / Y. Watanabe, et al. \\
Convex Sets of Full Rank Matrices / B. Kolodziejczak,
T. Szulc. \\
Multiaspect Interval Types / M. Lerch, J. W. von
Gudenberg. \\
MATLAB-Based Analysis of Roundoff Noise / R. Dunay, I.
Kollar. \\
SCAN-98 Collected Bibliography / G. F. Corliss",
}
@Proceedings{Frommer:2000:NCL,
editor = "Andreas Frommer and others",
booktitle = "{Numerical challenges in lattice quantum
chromodynamics: joint interdisciplinary workshop of
John von Neumann Institute for Computing, J{\"u}lich,
and Institute of Applied Computer Science, Wuppertal
University, August 1999}",
title = "{Numerical challenges in lattice quantum
chromodynamics: joint interdisciplinary workshop of
John von Neumann Institute for Computing, J{\"u}lich,
and Institute of Applied Computer Science, Wuppertal
University, August 1999}",
volume = "15",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 184",
year = "2000",
ISBN = "3-540-67732-1",
ISBN-13 = "978-3-540-67732-1",
ISSN = "1439-7358",
LCCN = "QC793.3.G38 N86 2000",
bibdate = "Tue Feb 05 09:39:44 2002",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib",
series = ser-LNCSE,
acknowledgement = ack-nhfb,
keywords = "Lattice gauge theories--Mathematical
models--Congresses; Quantum
chromodynamics--Mathematical models--Congresses",
}
@Book{Lide:2001:CEM,
editor = "D. R. Lide",
booktitle = "A Century of Excellence in Measurements, Standards,
and Technology: {A} Chronicle of Selected {NBS\slash
NIST} Publications, 1901--2000",
title = "A Century of Excellence in Measurements, Standards,
and Technology: {A} Chronicle of Selected {NBS\slash
NIST} Publications, 1901--2000",
volume = "958",
publisher = pub-NTIS,
address = pub-NTIS:adr,
pages = "ix + 386",
year = "2001",
bibdate = "Wed Oct 25 15:09:56 2023",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/h/hestenes-magnus-r.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
https://www.math.utah.edu/pub/bibnet/authors/t/taussky-todd-olga.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
note = "NIST Special Publication",
URL = "https://nvlpubs.nist.gov/nistpubs/sp958-lide/cntsp958old.htm",
acknowledgement = ack-nhfb,
subject-dates = "Magnus Rudolph Hestenes (13 February 1906--31 May
1991)",
tableofcontents = "Introduction / David R. Lide / 002 \\
The Absolute Measurement of Inductance / A-M. Jeffrey,
N. B. Belecki, and J. F. Mayo-Wells / 005 \\
Determination of the Constants of Total Radiation From
a Black Body / Albert C. Parr / 007 \\
The Testing of Thermal Insulators / Robert R. Zarr /
010 \\
Precipitation Hardening of Metal Alloys / Sam Coriell /
014 \\
Construction and Operation of a Simple Homemade Radio
Receiving Outfit / Brian Belanger / 016 \\
Methods for Standardizing and Testing Precision Gage
Blocks / Ted Doiron / 019 \\
Recommended Minimum Requirements for Small Dwelling
Construction / Joel P. Zingeser / 022 \\
Visibility of Radiant Energy / Jonathan E. Hardis / 025
\\
Test of the Severity of Building Fires / David Evans,
Daniel Gross, and Richard Wright / 028 \\
Calculation of Compounds in Portland Cements / Geoffrey
Frohnsdorff / 033 \\
Development of the Visual-Type Airway Radio-Beacon
System / Hans J. Oser / 038 \\
A Hydrogen Isotope of Mass 2 / Walter J. Hamer and H.
Steffen Peiser / 043 \\
Air Flow and Turbulence in Boundary Layers / Norman A.
Mease and James E. Potzick / 046 \\
Thermodynamic Properties of Water and Steam for Power
Generation / Allan H. Harvey and Johanna M. H. Levelt
Sengers / 049 \\
Absolute Pressure Calibrations of Microphones / Victor
Nedzelnitsky / 053 \\
Absolute Determination of the Ampere / E. R. Williams,
R. E. Elmquist, N. B. Belecki, and J. F. Mayo-Wells /
056 \\
Radio Proximity Fuzes / John W. Lyons, E. A. Brown, and
B. Fonoroff / 059 \\
Stability of Double-Walled Manganin Resistors / R.
Dziuba, N. B. Belecki, and J. F. Mayo-Wells / 063 \\
Manufacture of Paper for War Maps and Other
Applications / William K. Wilson / 066 \\
Transmission of Sound Waves in Gases at Low Pressures /
Thomas M. Proctor / 069 \\
Atomic Energy Levels and Other Spectroscopic Data /
Wolfgang L. Wiese / 073 \\
Iteration Method for the Solution of the Eigenvalue
Problem of Linear Differential and Integral Operators /
Dianne P. O'Leary / 077 \\
Methods of Conjugate Gradients for Solving Linear
Systems / Dianne P. O'Leary / 081 \\
Computer Development at the National Bureau of
Standards / Russell A. Kirsch / 086 \\
Thermal Converters as AC--DC Transfer Standards for
Current and Voltage Measurements at Audio Frequencies /
J. R. Kinard, Jr., N. B. Belecki, and J. F. Mayo-Wells
/ 090 \\
Selected Values of Chemical Thermodynamic Properties /
David R. Lide / 093 \\
Applied Inorganic Analysis / Charles M. Beck II / 097
\\
The Diamond Anvil Pressure Cell / Gasper Piermarini and
Stanley Block / 100 \\
Polymer Crystallization With Folded Chains / Freddy
Khoury, John Hoffman, and Tom Davis / 104 \\
Cryogenic Engineering / Richard H. Kropschot / 107 \\
Reversal of the Parity Conservation Law in Nuclear
Physics / Ralph P. Hudson / 111 \\
Effects of Configuration Interaction on Intensities and
Phase Shifts / Charles W. Clark / 116 \\
Electromagnetic Waves in Stratified Media / D. A. Hill
/ 120 \\
``Second Breakdown'' in Transistors / Harry A. Schafft
/ 123 \\
Stress Relaxation With Finite Strain / Elliot Kearsley
and Barry Bernstein / 126 \\
Realistic Evaluation of the Precision and Accuracy of
Instrument Calibration Systems / M. Carroll Croarkin /
129 \\
Experimental Statistics / M. Carroll Croarkin / 132 \\
Handbook of Mathematical Functions / Ronald F. Boisvert
and Daniel W. Lozier / 135 \\
Paths, Trees, and Flowers / Christoph Witzgall, Ronald
Boisvert, Geraldine Cheok, Saul Gass, Alan Goldman, and
James Lawrence / 140 \\
Concepts, Terminology, and Notation for Optical
Modulation / Calvin S. McCamy / 145 \\
Theory of Light Scattering in Fluids / Raymond D.
Mountain / 149 \\
Scaling Analysis of Thermodynamic Properties in the
Critical Region of Fluids / Raymond D. Mountain / 152
\\
Resonance Tunneling of Field Emitted Electrons Through
Adsorbates on Metal Surfaces / J. W. Gadzuk / 155 \\
Quantitative Electron Probe Microanalysis / Dale E.
Newbury / 160 \\
Limits for Qualitative Detection and Quantitative
Determination / Richard M. Lindstrom / 164 \\
Traceability: An Evolving Concept / Brian Belanger,
Stanley Rasberry, Ernest Garner, Carroll Brickencamp,
and Charles Ehrlich / 167 \\
Code for Information Interchange / Martha M. Gray / 172
\\
Consumer Information Series / Walter G. Leight and W.
Reeves Tilley / 174 \\
Theory of Isoperibol Calorimetry for Laser Power and
Energy Measurement / Thomas R. Scott / 178 \\
Influence of Water on Crack Growth in Glass / Edwin
Fuller, William Luecke, and Stephen Freiman / 181 \\
Phase Equilibria Diagrams / Ronald Munro, Howard
McMurdie, Helen Ondik, and Terrell Vanderah / 184 \\
Determination of Reduced Cells in Crystallography /
Alan D. Mighell, Vicky Lynn Karen, and Ronald Munro /
188 \\
Speed of Light From Direct Frequency and Wavelength
Measurements / Donald B. Sullivan / 191 \\
Connecting Visible Wavelength Standards With X Rays and
{gamma}Rays / Richard D. Deslattes / 194 \\
Laser Cooling of Atoms / D. B. Sullivan / 200 \\
Spin-Polarized Electrons / Daniel T. Pierce and Robert
J. Celotta / 203 \\
Needs for Radioactivity Standards and Measurements in
Different Fields / Bert Coursey / 209 \\
The Topografiner: An Instrument for Measuring Surface
Microtopography / J. S. Villarurubia, R. D. Young, F.
Scire, E. C. Teague, and J. W. Gadzuk / 214 \\
Electron-Stimulated Desorption / Ted Madey and John
Yates / 219 \\
Photochemistry of Small Molecules / James R. McNesby
and Ralph Klein / 224 \\
Role of Standard Reference Materials in Measurement
Systems / Thomas E. Gills / 227 \\
Metrology and Standardization to Assist Industrializing
Economies / Lewis M. Branscomb / 230 \\
Publications Taking Us Toward a Metric America / Ralph
A. Richter / 234 \\
A New Approach to Manipulator Control: The Cerebellar
Model Articulation Controller / James S. Albus / 237
\\
Three Dimensional Metrology / Ted Doiron / 241 \\
Initial Graphics Exchange Specifications / Sharon K.
Kemmerer / 246 \\
Data Encryption Standard / William E. Burr / 250 \\
OMNIDATA and the Computerization of Scientific Data /
John R. Rumble, Jr. / 254 \\
FORTRAN Test Programs / John Cugini / 258 \\
Design and Evaluation Criteria for Energy Conservation
in New Buildings / Jim L. Heldenbrand / 260 \\
Computer Program for Heating and Cooling Loads in
Buildings / George Walton / 266 \\
Methods for Testing and Rating the Performance of
Heating and Air Conditioning Systems / James E. Hill /
270 \\
System for Fire Safety Evaluation of Health Care
Facilities / Harold Nelson / 275 \\
Estimation of Rate of Heat Release by Means of Oxygen
Consumption Measurements / Kenneth D. Steckler / 280
\\
Probability-Based Load Criteria for Structural Design /
Bruce R. Ellingwood / 283 \\
Resistivity-Dopant Density Relationship for
Phosphorus-Doped Silicon / W. R. Thurber / 289 \\
Critical Data for Critical Needs / John R. Rumble, Jr.
/ 291 \\
Materials at Low Temperatures / Fred Fickett / 294 \\
Optical Fiber Characterization / D. L. Franzen / 297
\\
Quasicrystals / Ronald Munro, Frank Gale, and Carol
Handwerker / 300 \\
Protein Crystallography by Joint X-Ray and Neutron
Diffraction / Norman F. Berk / 303 \\
Strain Effects in Superconducting Compounds / J. W.
Ekin / 306 \\
Dental Research at the National Bureau of Standards /
John Tesk and Ronald Munro / 309 \\
Handbook for Standard Reference Materials Users /
Thomas E. Gills / 313 \\
A Practical Josephson Voltage Standard at One Volt / Y.
Tang, N. B. Belecki, and J. F. Mayo-Wells / 315 \\
Plane-Wave Scattering-Matrix Theory of Antennas and
Antenna-Antenna Interactions / A. G. Repjar and J. F.
Mayo-Wells / 319 \\
The Automated Manufacturing Research Facility / James
S. Albus / 322 \\
Submicrometer Linewidth Metrology / Michael T. Postek
and Robert D. Larrabee / 328 \\
Observation of Atoms Laser-Cooled Below the Doppler
Limit / Steven Rolston / 331 \\
Laser-Excited Hot-Electron Induced Desorption / J. W.
Gadzuk / 334 \\
Measurement of the Universal Gas Constant Using an
Acoustic Resonator / Michael R. Moldover / 339 \\
Thermal and Oxidative Degradation of Polymers / Takashi
Kashiwagi / 344 \\
HAZARD I: Software for Fire Hazard Assessment / Richard
Bukowski / 347 \\
Analysis of the Catastrophic Rupture of a Pressure
Vessel / Tom Siewert / 350 \\
Curing Those Uncontrollable Fits of Interaction / Don
Libes / 353 \\
Baldrige Criteria for Performance Excellence / Curt
Reimann and Debbie Smyth / 357 \\
The Advanced Technology Program / Robert Sienkiewicz
and Richard N. Spivack / 359 \\
NIST Manufacturing Extension Partnership / Anita
O'Brien / 363 \\
Questions and Answers on Quality / Maureen Breitenberg
/ 366 \\
Uniformity in Weights and Measures Laws and Regulations
/ Joan Koenig / 368 \\
Certification of 10 $\mu$m Diameter Polystyrene Spheres
(``Space Beads'') / Tom Lettieri / 371 \\
Bose--Einstein Condensation in a Dilute Atomic Vapor /
James Faller / 375 \\
Index / David R. Lide / 379",
}
@Book{Braun:2002:EV,
editor = "Simon (Simon G.) Braun and D. J. Ewins and S. S. Rao",
booktitle = "Encyclopedia of vibration",
title = "Encyclopedia of vibration",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xxviii + 1595",
year = "2002",
ISBN = "0-12-227085-1 (set), 0-12-227086-X (volume 1),
0-12-227087-8 (volume 2), 0-12-227088-6 (volume 3)",
ISBN-13 = "978-0-12-227085-7 (set), 978-0-12-227086-4 (volume 1),
978-0-12-227087-1 (volume 2), 978-0-12-227088-8 (volume
3)",
LCCN = "TA355 .E52 2002",
bibdate = "Fri Jun 10 17:31:07 MDT 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
z3950.loc.gov:7090/Voyager",
note = "Three volumes.",
URL = "(E-STREAMS);
http://www.e-streams.com/es0504/es0504\_1818.htm;
http://www.loc.gov/catdir/description/els031/2001092782.html;
http://www.loc.gov/catdir/toc/els051/2001092782.html",
acknowledgement = ack-nhfb,
subject = "Vibration; Encyclopedias",
}
@Proceedings{Kauers:2005:IJB,
editor = "Manuel Kauers",
booktitle = "{ISSAC '05: July 24--27, 2005, Beijing, China:
Proceedings of the 2005 International Symposium on
Symbolic and Algebraic Computation}",
title = "{ISSAC '05: July 24--27, 2005, Beijing, China:
Proceedings of the 2005 International Symposium on
Symbolic and Algebraic Computation}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiv + 374",
year = "2005",
ISBN = "1-59593-095-7",
ISBN-13 = "978-1-59593-095-8",
LCCN = "QA76.95 .I59 2005",
bibdate = "Fri Oct 21 07:01:24 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
note = "ACM Order Number 505050.",
acknowledgement = ack-nhfb,
}
@Book{Chan:2007:MMC,
editor = "Raymond H. Chan and Chen Greif and Dianne P. O'Leary",
booktitle = "Milestones in Matrix Computation: the Selected Works
of {Gene H. Golub} with Commentaries",
title = "Milestones in Matrix Computation: the Selected Works
of {Gene H. Golub} with Commentaries",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xi + 565 + 3",
year = "2007",
ISBN = "0-19-920681-3",
ISBN-13 = "978-0-19-920681-0",
LCCN = "QA188 .G67 2007",
MRclass = "65-06 (01A75 65Fxx)",
MRnumber = "MR2281939 (2008b:65004)",
MRreviewer = "David Scott Watkins",
bibdate = "Sat Apr 07 10:23:33 2007",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib;
https://www.math.utah.edu/pub/tex/bib/technometrics1970.bib",
URL = "http://www.loc.gov/catdir/enhancements/fy0737/2007276086-d.html",
abstract = "The text presents and discusses some of the most
influential papers in Matrix Computation authored by
Gene H. Golub, one of the founding fathers of the
field. The collection of 21 papers in divided into five
main areas: iterative methods for linear systems,
solution of least squares problems, matrix
factorizations and applications, orthogonal polynomials
and quadrature, and eigenvalue problems an commentaries
for each area are provided by leading experts: Anne
Greenbaum, {\AA}ke Bj{\"o}rck, Nicholas Higham, Walter
Gautschi, and G. W. (Pete) Stewart. Comments on each
paper are also provided by the original authors,
providing the reader with historical information on how
the paper came to be written and under what
circumstances the collaboration was undertaken.
Including a brief biography and facsimiles of the
original papers, this text will be of great interest to
students and researchers in numerical analysis and
scientific computation.",
acknowledgement = ack-nhfb,
tableofcontents = "List of Plates / x \\
I: Gene H. Golub \\
1 Gene H. Golub Biography, by Chen Greif / 3 \\
2 Publications of Gene H. Golub / 13 \\
3 Major Awards / 30 \\
4 Students of Gene H. Golub / 32 \\
II: Iterative Methods for Linear Systems \\
5 Commentary, by Anne Greenbaum / 35 \\
References / 43 \\
6 Chebyshev semi-iterative methods, successive
over-relaxation iterative methods, and second-order
Richardson iterative methods, Parts I and II (with R.
S. Varga) / 45 \\
7 A generalized conjugate gradient method for
non-symmetric systems of linear equations (with Paul
Concus) / 68 \\
8 A generalized conjugate gradient method for the
numerical solution of elliptic partial differential
equations (with Paul Concus and Dianne P. O'Leary) / 79
\\
9 Hermitian and Skew-Hermitian Splitting Methods for
Non-Hermitian Positive Definite Linear Systems (with
Zhong-Zhi Bai and Michael K. Ng) / 102 \\
III: Solution of Least Squares Problems \\
10 Commentary, by {\AA}ke Bj{\"o}rck / 129 \\
References / 141 \\
11 Numerical methods for solving linear least squares
problems / 148 \\
12 Singular value decomposition and least squares
solutions (with C. Reinsch) / 160 \\
13 The differentiation of pseudo-inverses and
non-linear least squares problems whose variables
separate (with V. Pereyra) / 181 \\
14 Generalized cross-validation as a method for
choosing a good ridge parameter (with M. Heath and G.
Wahba) / 202 \\
15 An analysis of the total least squares problem (with
C. Van Loan) / 213 \\
IV: Matrix Factorizations and Applications \\
16 Commentary, by Nicholas Higham / 227 \\
References / 233 \\
17 Calculating the singular values and pseudo-inverse
of a matrix (with W. Kahan) / 236 \\
18 The simplex method of linear programming using $ L U
$ decomposition (with R. H. Bartels) / 257 \\
19 On direct methods for solving Poisson's equation
(with B. L. Buzbee and C. W. Nielson) / 261 \\
20 Numerical methods for computing angles between
linear subspaces (with {\AA}. Bj{\"o}rck) / 292 \\
21 Methods for modifying matrix factorizations (with P.
E. Gill, W. Murray and M. A. Saunders) / 309 \\
V: Orthogonal Polynomials and Quadrature \\
22 Commentary, by Walter Gautschi / 345 \\
References / 354 \\
23 Calculation of Gauss quadrature rules (with J. H.
Welsch) / 359 \\
24 Matrices, moments, and quadrature (with G{\'e}rard
Meurant) / 380 \\
25 Computation of Gauss--Kronrod Quadrature Rules (with
D. Calvetti, W. B. Gragg and L. Reichel) / 434 \\
VI: Eigenvalue Problems \\
26 Commentary, by G. W. Stewart / 457 \\
References / 465 \\
27 Some modified matrix eigenvalue problems / 467 \\
28 Ill-conditioned eigensystems and the computation of
the Jordan canonical form (with J. H. Wilkinson) / 485
\\
29 The block Lanczos method for computing eigenvalues
(with R. Underwood) / 528 \\
30 The numerically stable reconstruction of a Jacobi
matrix from spectral data (with C. de Boor) / 546 Index
/ 563",
}
@Book{Hogben:2007:HLA,
editor = "Leslie Hogben",
booktitle = "Handbook of Linear Algebra",
title = "Handbook of Linear Algebra",
publisher = pub-CHAPMAN-HALL-CRC,
address = pub-CHAPMAN-HALL-CRC:adr,
pages = "xxx + 1370",
year = "2007",
ISBN = "1-58488-510-6 (hardcover), 1-4200-1057-3 (e-book)",
ISBN-13 = "978-1-58488-510-8 (hardcover), 978-1-4200-1057-2
(e-book)",
LCCN = "QA184.2 .H36 2007",
MRclass = "15-00 (00A20)",
MRnumber = "2279160 (2007j:15001)",
bibdate = "Fri Nov 21 06:49:56 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
z3950.loc.gov:7090/Voyager",
note = "Associate editors: Richard Brualdi, Anne Greenbaum and
Roy Mathias.",
series = "Discrete Mathematics and its Applications (Boca
Raton)",
URL = "http://www.crcnetbase.com/isbn/9781420010572;
http://www.crcnetbase.com/isbn/9781584885108;
http://www.loc.gov/catdir/enhancements/fy0647/2006045491-d.html",
abstract = "\booktitle{Handbook of Linear Algebra} covers all
aspects of linear algebra, including fundamentals,
numerical linear algebra, software packages for
computation in linear algebra, and various
applications, such as quantum computing, control
theory, image compression, and computational biology.
The author addresses combinatorial Matrix theory and
features Matrix notation throughout the text. The book
includes a chapter on software that provides extensive
coverage of MATLAB, Maple, and Mathematica and contains
details of Fortran subroutines available for linear
algebra such as LAPACK and ARPACK. Rather than
presenting long mathematical proofs, the text provides
numerous references for additional information.",
acknowledgement = ack-nhfb # " and " # ack-rah,
keywords = "Maple",
remark = "Associate editors: Richard Brualdi, Anne Greenbaum,
and Roy Mathias.",
subject = "Algebras, Linear",
tableofcontents = "Preliminaries \\
I. Linear algebra \\
1: Vectors, matrices and systems of linear equations /
Jane Day \\
2: Linear independence, span, and bases / Mark Mills
\\
3: Linear transformations / Francesco Barioli \\
4: Determinants and eigenvalues / Luz M. DeAlba \\
5: Inner product spaces, orthogonal projection, least
squares and singular value decomposition / Lixing Han
and Michael Neumann \\
6: Canonical forms / Leslie Hogben \\
7: Unitary similarity, normal matrices, and spectral
theory / Helene Shapiro \\
8: Hermitian and positive definite matrices / Wayne
Barrett \\
9: Nonnegative and stochastic matrices / Uriel G.
Rothblum \\
10: Partitioned matrices / Robert Reams \\
11: Functions of matrices / Nicholas J. Higham \\
12: Quadratic, bilinear and sesquilinear forms /
Raphael Lowey \\
13: Multilinear algebra / J. A. Dias de Silva and
Armando Machado \\
14: Matrix equalities and inequalities / Michael
Tsatsomeros \\
15: Matrix perturbation theory / Ren-Cang Li \\
16: Pseudospectra / Mark Embree \\
17: Singular values and singular value inequalities /
Roy Mathias \\
18: Numerical range / Chi-Kwong Li \\
19: Matrix stability and inertia / Daniel Hershkowitz
\\
20: Inverse eigenvalue problems / Alberto Borobia \\
21: Totally positive and totally negative matrices /
Shaun M. Fallat \\
22: Linear preserver problems / Peter \v Semrl \\
23: Matrices over integral domains / Shmuel Friedland
\\
24: Similarities of families of matrices / Shmuel
Friedland \\
25: Max-plus algebra / Marianne Akian, Ravindra Bapat,
St{\'e}phane Gaubert \\
26: Matrices leaving a cone invariant / Bit-Shun Tam
and Hans Schneider \\
II. Combinatorial matrix theory and graphs \\
27: Combinatorial matrix theory / Richard A. Brualdi
\\
28: Matrices and graphs / Willem H. Haemers \\
29: Digraphs and matrices / Jeffrey L. Stuart \\
30: Bipartite graphs and matrices / Bryan L. Shader \\
31: Permanents / Ian M. Wanless \\
32: D-optimal designs / Michael G. Neubauer and William
Watkins \\
33: Sign pattern matrices / Frank J. Hall and Zhongshan
Li \\
34: Multiplicity lists for the eigenvalues of symmetric
matrices with a given graph / Charles R. Johnson,
Ant{\'o}nio Leal Duarte, and Carlos M. Saiago \\
35: Matrix completion problems / Leslie Hogben and Amy
Wangsness \\
36: Algebraic connectivity / Steve Kirkland \\
III. Numerical methods \\
37: Vector and matrix norms, error analysis, efficiency
and stability / Ralph Byers and Biswa Nath Datta \\
38: Matrix factorizations, and direct solution of
linear systems / Christopher Beattie \\
39: Least squares solution of linear systems / Per
Christian Hansen and Hans Bruun Nielsen \\
40: Sparse matrix methods / Esmond G. Ng \\
41: Iterative solution methods for linear systems /
Anne Greenbaum \\
42: Symmetric matrix eigenvalue techniques / Ivan
Slapni\v car \\
43: Unsymmetric matrix eigenvalue techniques / David S.
Watkins \\
44: The implicitly restarted Arnoldi method / D. C.
Sorensen \\
45: Computation of the singular value decomposition /
Alan Kaylor Cline and Inderjit S. Dhillon \\
46: Computing eigenvalues and singular values to high
relative accuracy / Zlatko Drma{\v{c}} \\
47: Fast matrix multiplication / Dario A. Bini \\
48: Structured matrix computations / Michael Ng \\
49: Large-scale matrix computations / Roland W. Freund
\\
IV. Applications \\
50: Linear programming / Leonid S. Vaserstein \\
51: Semidefinite programming / Henry Wolkowicz \\
52: Random vectors and linear statistical models / Simo
Puntanen and George P. H. Styan \\
53: Multivariate statistical analysis / Simo Puntanen,
George A. F. Seber, and George P. H. Styan \\
54: Markov chains / Beatrice Meini \\
55: Differential equations and stability / Volker
Mehrmann and Tatjana Stykel \\
56: Dynamical systems and linear algebra / Fritz
Colonius and Wolfgang Kliemann \\
57: Control theory / Peter Benner \\
58: Fourier analysis / Kenneth Howell \\
59: Linear algebra and mathematical physics / Lorenzo
Sadun \\
60: Linear algebra in biomolecular modeling / Zhijun Wu
\\
61: Coding theory / Joachim Rosenthal and Paul Weiner
\\
62: Quantum computation / Zijian Diao \\
63: Information retrieval and web search / Amy
Langville and Carl Meyer \\
64: Signal processing / Michael Stewart \\
65: Geometry / Mark Hunacek \\
66: Some applications of matrices and graphs in
Euclidean geometry / Miroslav Fiedler \\
67: Matrix groups / Peter J. Cameron \\
68: Group representations / Randall Holmes and T. Y.
Tam \\
69: Nonassociative algebras / Murray R. Bremner, Lucia
I. Muakami and Ivan P. Shestakov \\
70: Lie algebras / Robert Wilson \\
V. Computational software \\
71: METLAB / Steven J. Leon \\
72: Linear algebra in Maple / David J. Jeffrey and
Robert M. Corless \\
73: Mathematica / Heikki Ruskeep{\"a}{\"a} \\
74: BLAS / Jack Dongarra, Victor Eijkhout, and Julien
Langou \\
75: LAPACK / Zhaojun Bai \\
76: Use of ARPACK and EIGS / D. C. Sorensen \\
77: Summary of Software for Linear Algebra Freely
Available on the Web / Jack Dongarra, Victor Eijkhout,
Julien Langou \\
G-1: Glossary \\
H-1: Notation Index",
}
@Proceedings{Simos:2007:CMS,
editor = "Theodore E. Simos and George Maroulis",
booktitle = "{Computation in Modern Science and Engineering:
Proceedings of the [Fifth] International Conference on
Computational Methods in Science and Engineering 2007
(ICCMSE 2007), Corfu, Greece, 25--30 September 2007}",
title = "{Computation in Modern Science and Engineering:
Proceedings of the [Fifth] International Conference on
Computational Methods in Science and Engineering 2007
(ICCMSE 2007), Corfu, Greece, 25--30 September 2007}",
volume = "2A, 2B",
publisher = pub-AIP,
address = pub-AIP:adr,
bookpages = "xxvi + 730 + 10 (vol. 2A)",
pages = "xxvi + 730 + 10 (vol. 2A)",
year = "2007",
ISBN = "0-7354-0476-3 (set), 0-7354-0477-1 (vol. 1),
0-7354-0478-X (vol. 2)",
ISBN-13 = "978-0-7354-0476-2 (set), 978-0-7354-0477-9 (vol. 1),
978-0-7354-0478-6 (vol. 2)",
ISSN = "0094-243X (print), 1551-7616 (electronic), 1935-0465",
LCCN = "Q183.9 .I524 2007",
bibdate = "Thu Feb 21 14:15:15 2008",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
series = "AIP Conference Proceedings (\#963)",
URL = "http://www.springer.com/physics/atoms/book/978-0-7354-0478-6",
abstract = "All papers have been peer-reviewed. The aim of ICCMSE
2007 is to bring together computational scientists and
engineers from several disciplines in order to share
methods, methodologies and ideas. The potential readers
of these proceedings are all the scientists with
interest in the following fields: Computational
Mathematics, Theoretical Physics, Computational
Physics, Theoretical Chemistry, Computational
Chemistry, Mathematical Chemistry, Computational
Engineering, Computational Mechanics, Computational
Biology and Medicine, Scientific Computation, High
Performance Computing, Parallel and Distributed
Computing, Visualization, Problem Solving Environments,
Software Tools, Advanced Numerical Algorithms, Modeling
and Simulation of Complex Systems, Web-based Simulation
and Computing, Grid-based Simulation and Computing,
Computational Grids, and Computer Science.",
acknowledgement = ack-nhfb,
remark = "Two volumes.",
}
@Book{Olver:2010:NHM,
editor = "Frank W. J. Olver and Daniel W. Lozier and Ronald F.
Boisvert and Charles W. Clark",
key = "NIST",
booktitle = "{NIST} Handbook of Mathematical Functions",
title = "{NIST} Handbook of Mathematical Functions",
publisher = pub-CAMBRIDGE,
address = pub-CAMBRIDGE:adr,
pages = "xv + 951",
year = "2010",
ISBN = "0-521-19225-0",
ISBN-13 = "978-0-521-19225-5",
LCCN = "QA331 .N57 2010",
bibdate = "Sat May 15 09:08:09 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
price = "US\$99.00",
URL = "http://dlmf.nist.gov/;
http://www.cambridge.org/9780521140638",
acknowledgement = ack-nhfb,
remark = "Includes a DVD with a searchable PDF of each
chapter.",
tableofcontents = "1. Algebraic and analytic methods [Ranjan Roy,
Frank W. J. Olver, Richard A. Askey and Roderick S. C.
Wong] \\
2. Asymptotic approximations [Frank W. J. Olver and
Roderick S. C. Wong] \\
3. Numerical methods [Nico M. Temme] \\
4. Elementary functions [Ranjan Roy and Frank W. J.
Olver] \\
5. Gamma function [Richard A. Askey and Ranjan Roy] \\
6. Exponential, logarithmic, sine and cosine integrals
[Nico M. Temme] \\
7. Error functions, Dawson's and Fresnel integrals
[Nico M. Temme] \\
8. Incomplete gamma and related functions [Richard B.
Paris] \\
9. Airy and related functions [Frank W. J. Olver] \\
10. Bessel functions [Frank W. J. Olver and Leonard C.
Maximon] \\
11. Struve and related functions [Richard B. Paris] \\
12. Parabolic cylinder functions [Nico M. Temme] \\
13. Confluent hypergeometric functions [Adri B. Olde
Daalhuis] \\
14. Legendre and related functions [T. Mark Dunster]
\\
15. Hypergeometric function [Adri B. Olde Daalhuis] \\
16. Generalized hypergeometric functions and Meijer
G-function [Richard A. Askey and Adri B. Olde Daalhuis]
\\
17. q-Hypergeometric and related functions [George E.
Andrews] \\
18. Orthogonal polynomials [Tom H. Koornwinder,
Roderick S. C. Wong, Roelof Koekoek and Rene F.
Swarttouw] \\
19. Elliptic integrals [Bille C. Carlson] \\
20. Theta functions [William P. Reinhardt and Peter L.
Walker] \\
21. Multidimensional theta functions [Bernard
Deconinck] \\
22. Jacobian elliptic functions [William P. Reinhardt
and Peter L. Walker] \\
23. Weierstrass elliptic and modular functions [William
P. Reinhardt and Peter L. Walker] \\
24. Bernoulli and Euler polynomials [Karl Dilcher] \\
25. Zeta and related functions [Tom M. Apostol] \\
26. Combinatorial analysis [David M. Bressoud] \\
27. Functions of number theory [Tom M. Apostol] \\
28. Mathieu functions and Hill's equation [Gerhard
Wolf] \\
29. Lam{\'e} functions [Hans Volkmer] \\
30. Spheroidal wave functions [Hans Volkmer] \\
31. Heun functions [Brian D. Sleeman and Vadim
Kuznetsov] \\
32. Painlev{\'e} transcendents [Peter A. Clarkson] \\
33. Coulomb functions [Ian J. Thompson] \\
34. 3j, 6j, 9j symbols [Leonard C. Maximon] \\
35. Functions of matrix argument [Donald St. P.
Richards] \\
36. Integrals with coalescing saddles [Michael V. Berry
and Chris Howls]",
}
@Book{Baaz:2011:KGF,
editor = "Matthias Baaz and Christos H. Papadimitriou and Hilary
W. Putnam and Dana S. Scott and Charles L. {Harper,
Jr.}",
booktitle = "{Kurt G{\"o}del} and the Foundations of Mathematics:
Horizons of Truth",
title = "{Kurt G{\"o}del} and the Foundations of Mathematics:
Horizons of Truth",
publisher =