%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.98", %%% date = "05 June 2024", %%% time = "07:41:40 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 = "01748 23866 100112 1050327", %%% 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 1.98, the year coverage looked %%% like this: %%% %%% 1921 ( 1) 1956 ( 4) 1991 ( 12) %%% 1922 ( 2) 1957 ( 4) 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: 30 %%% TechReport: 34 %%% Unpublished: 4 %%% %%% Total entries: 895 %%% %%% 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)"} @String{j-PHYS-REV-B-CMMP= "Physical Review B: Condensed Matter and Materials Physics"} @String{j-PHYS-REV-LET= "Physical Review Letters"} @String{j-PHYS-TEACHER= "The Physics Teacher"} @String{j-PHYS-TODAY= "Physics Today"} @String{j-PHYSIKAL-Z= "{Physikalische Zeitschrift}"} @String{j-PROC-NATL-ACAD-SCI-USA= "Proceedings of the National Academy of Sciences of the United States of America"} @String{j-PROC-SPIE= "Proceedings of the SPIE --- The International Society for Optical Engineering"} @String{j-PROG-PART-NUCL-PHYS= "Progress in Particle and Nuclear Physics"} @String{j-QUART-APPL-MATH= "Quarterly of Applied Mathematics"} @String{j-RELIABLE-COMPUTING= "Reliable Computing = Nadezhnye vychisleniia"} @String{j-REV-MOD-PHYS= "Reviews of Modern Physics"} @String{j-SCI-EDUC-SPRINGER= "Science \& Education (Springer)"} @String{j-SCI-PROG= "Scientific Programming"} @String{j-SCIENCE= "Science"} @String{j-SCPE= "Scalable Computing: Practice and Experience"} @String{j-SIAM-J-APPL-MATH= "SIAM Journal on Applied Mathematics"} @String{j-SIAM-J-MAT-ANA-APPL= "SIAM Journal on Matrix Analysis and Applications"} @String{j-SIAM-J-MATH-ANA= "SIAM Journal on Mathematical Analysis"} @String{j-SIAM-J-NUM-ANALYSIS-B= "Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis"} @String{j-SIAM-J-NUMER-ANAL= "SIAM Journal on Numerical Analysis"} @String{j-SIAM-J-OPT= "SIAM Journal on Optimization"} @String{j-SIAM-J-SCI-COMP= "SIAM Journal on Scientific Computing"} @String{j-SIAM-J-SCI-STAT-COMP= "SIAM Journal on Scientific and Statistical Computing"} @String{j-SIAM-NEWS= "SIAM News"} @String{j-SIAM-REVIEW= "SIAM Review"} @String{j-SYST-CONTROL-LETT= "Systems and Control Letters"} @String{j-TOMS= "ACM Transactions on Mathematical Software"} @String{j-USSR-COMP-MATH-MATH-PHYS= "U.S.S.R. Computational Mathematics and Mathematical Physics"} @String{j-Z-ANGE-MATH-PHYS= "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik = Journal of Applied Mathematics and Physics}"} @String{j-Z-PHYSIK= "{Zeitschrift f{\"u}r Physik}"}

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

@String{pub-ACADEMIC= "Academic Press"} @String{pub-ACADEMIC:adr= "New York, USA"} @String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, USA"} @String{pub-AIP= "American Institute of Physics"} @String{pub-AIP:adr= "Woodbury, NY, USA"} @String{pub-AKADEMIE-VERLAG= "Akademie-Verlag"} @String{pub-AKADEMIE-VERLAG:adr= "Berlin, Germany"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-AW= "Ad{\-d}i{\-s}on-Wes{\-l}ey"} @String{pub-AW:adr= "Reading, MA, USA"} @String{pub-BIRKHAUSER= "Birkh{\"a}user Verlag"} @String{pub-BIRKHAUSER:adr= "Basel, Switzerland"} @String{pub-BIRKHAUSER-BOSTON= "Birkh{\"a}user Boston Inc."} @String{pub-BIRKHAUSER-BOSTON:adr= "Cambridge, MA, USA"} @String{pub-BLAISDELL= "Blaisdell Pub. Co."} @String{pub-BLAISDELL:adr= "Waltham, MA, USA"} @String{pub-CAMBRIDGE= "Cambridge University Press"} @String{pub-CAMBRIDGE:adr= "Cambridge, UK"} @String{pub-CHAPMAN-HALL-CRC= "Chapman and Hall/CRC"} @String{pub-CHAPMAN-HALL-CRC:adr= "Boca Raton, FL, USA"} @String{pub-CLARENDON= "Clarendon Press"} @String{pub-CLARENDON:adr= "New York, NY, USA"} @String{pub-DOVER= "Dover Publications, Inc."} @String{pub-DOVER:adr= "New York, NY, USA"} @String{pub-DUNOD= "Dunod"} @String{pub-DUNOD:adr= "Paris, France"} @String{pub-ELSEVIER= "Elsevier"} @String{pub-ELSEVIER:adr= "Amsterdam, The Netherlands"} @String{pub-HALSTED= "Halsted Press"} @String{pub-HALSTED:adr= "New York, USA"} @String{pub-HARVARD= "Harvard University Press"} @String{pub-HARVARD:adr= "Cambridge, MA, USA"} @String{pub-IBM= "IBM Corporation"} @String{pub-IBM:adr= "San Jose, CA, USA"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-JOHNS-HOPKINS= "The Johns Hopkins University Press"} @String{pub-JOHNS-HOPKINS:adr= "Baltimore, MD, USA"} @String{pub-KLUWER= "Kluwer Academic Publishers Group"} @String{pub-KLUWER:adr= "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-INTERSCIENCE= "Interscience Publishers"} @String{pub-INTERSCIENCE:adr= "New York, NY, USA"} @String{pub-MATH-ASSOC-AMER= "Mathematical Association of America"} @String{pub-MATH-ASSOC-AMER:adr= "Washington, DC, USA"} @String{pub-MCGRAW-HILL= "Mc{\-}Graw-Hill"} @String{pub-MCGRAW-HILL:adr= "New York, NY, USA"} @String{pub-MIR= "Mir Publishers"} @String{pub-MIR:adr= "Moscow, Russia"} @String{pub-NAUKA= "Nauka"} @String{pub-NAUKA:adr= "Moscow, Russia"} @String{pub-NBS= "U.S. National Bureau of Standards"} @String{pub-NBS:adr= "Gaithersburg, MD, USA"} @String{pub-NORTH-HOLLAND= "North-Hol{\-}land"} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-NORTH-OXFORD= "North Oxford Academic"} @String{pub-NORTH-OXFORD:adr= "Oxford, England"} @String{pub-NTIS= "National Technical Information Service"} @String{pub-NTIS:adr= "Washington, DC, USA"} @String{pub-OXFORD= "Oxford University Press"} @String{pub-OXFORD:adr= "Walton Street, Oxford OX2 6DP, UK"} @String{pub-PERGAMON= "Pergamon"} @String{pub-PERGAMON:adr= "New York, NY, USA"} @String{pub-PH= "Pren{\-}tice-Hall"} @String{pub-PH:adr= "Upper Saddle River, NJ 07458, USA"} @String{pub-PLENUM= "Plenum Press"} @String{pub-PLENUM:adr= "New York, NY, USA; London, UK"} @String{pub-REIDEL= "D. Reidel"} @String{pub-REIDEL:adr= "Dordrecht, The Netherlands; Boston, MA, USA; Lancaster, UK; Tokyo, Japan"} @String{pub-SIAM= "SIAM Press"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-STANFORD= "Stanford University Press"} @String{pub-STANFORD:adr= "Stanford, CA, USA"} @String{pub-SV= "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-USGPO= "United States Government Printing Office"} @String{pub-USGPO:adr= "Washington, DC, USA"} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"} @String{pub-WORLD-SCI= "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr= "P. O. Box 128, Farrer Road, Singapore 9128"} @String{pub-U-TORONTO= "University of Toronto Press"} @String{pub-U-TORONTO:adr= "Toronto, ON, Canada"} @String{pub-WRE= "Weapons Research Establishment"} @String{pub-WRE:adr= "Salisbury, Australia"}

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

@String{ser-LNCS= "Lecture Notes in Computer Science"} @String{ser-LNCSE= "Lecture Notes in Computational Science and Engineering"} @String{ser-LNM= "Lecture Notes in Mathematics"}

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

@String{ser-BOSTON-STUD-PHILOS-SCI= "Boston Studies in the Philosophy of Science"}

%%% ==================================================================== %%% 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", booktitle = "Conference Proceedings", title = "The Calculation of the Eigenvectors of Codiagonal Matrices Produced by the {Givens} and {Lanczos} Processes", publisher = pub-WRE, address = pub-WRE:adr, 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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @InProceedings{Blondin:1994:CMA, author = "John Blondin and James Stone", title = "Computational Magnetohydrodynamics in Astrophysics", crossref = "Brown:1994:PCL", pages = "431--451", 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{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", 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{Boley:1994:LMC, author = "Daniel Boley", title = "{Lanczos} Methods in Control and Signal Processing", crossref = "Brown:1994:PCL", pages = "375--376", 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{Brown:1994:BHT, author = "David Brown", title = "Black Hole Thermodynamics in a Box", crossref = "Brown:1994:PCL", pages = "548--550", year = "1994", bibdate = "Sat Jun 18 12:37:25 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @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", 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{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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", 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", 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{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", 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{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", URL = "http://etna.mcs.kent.edu/vol.2.1994/pp1-21.dir/pp1-21.pdf", 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", 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{Carey:1994:LBM, author = "Cheryl M. M. Carey and Gene H. Golub and Kincho H. Law", title = "A {Lanczos}-based method for structural dynamic reanalysis problems", journal = j-INT-J-NUMER-METHODS-ENG, volume = "37", number = "16", pages = "2857--2883", day = "30", month = aug, year = "1994", CODEN = "IJNMBH", DOI = "https://doi.org/10.1002/nme.1620371610", ISSN = "0029-5981 (print), 1097-0207 (electronic)", ISSN-L = "0029-5981", MRclass = "65F15 (15A18)", MRnumber = "95d:65032", bibdate = "Mon Jan 15 16:19:27 1996", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", acknowledgement = ack-nhfb, 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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @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", 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{Carlson:1994:PQC, author = "Carl E. Carlson", title = "Perturbative {QCD} Calculations of Heavy Meson Decays", crossref = "Brown:1994:PCL", pages = "605--607", 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{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", 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{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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @InProceedings{Chu:1994:ECT, 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; MathSciNet database", 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; MathSciNet database", 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; MathSciNet database", acknowledgement = ack-nhfb, } @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; MathSciNet database", 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; MathSciNet database", 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; MathSciNet database", 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", 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; MathSciNet database", acknowledgement = ack-nhfb, } @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; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", 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; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", 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; MathSciNet database", 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; MathSciNet database", acknowledgement = ack-nhfb, } @InProceedings{Dolan:1994:LT, author = "P. Dolan and A. H. Taub", title = "{Lanczos} {$H$}-tensor", crossref = "Brown:1994:PCL", pages = "488--489", year = "1994", bibdate = "Sat Jun 11 17:22:09 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @InProceedings{Drake:1994:EES, author = "G. W. F. Drake", title = "Essentially Exact Solutions of the Helium Problem", crossref = "Brown:1994:PCL", pages = "251--254", year = "1994", bibdate = "Sat Jun 11 17:22:09 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @InProceedings{Dunn:1994:PWE, author = "C. T. Dunn", title = "Plasma Waves in the Electron Foreshock", crossref = "Brown:1994:PCL", pages = "461--463", year = "1994", bibdate = "Sat Jun 18 13:03:35 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @InProceedings{Edgar:1994:LTD, author = "S. Brian Edgar", title = "The {Lanczos} {$H$}-Tensor, Dimension and Tensor Identities", crossref = "Brown:1994:PCL", pages = "494--496", year = "1994", bibdate = "Sat Jun 18 13:03:35 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", 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; MathSciNet database", 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; MathSciNet database", 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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", 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; MathSciNet database", 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; MathSciNet database", 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; MathSciNet database", 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; MathSciNet database", 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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", 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; MathSciNet database", 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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @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", bibdate = "Sat Jun 18 13:16:40 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", acknowledgement = ack-nhfb, } @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", 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=42615; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42615&PLACEBO=IE.pdf", acknowledgement = ack-nhfb, 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", ISSN = "1358-6254", 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", series = "Technical report", URL = "http://epubs.cclrc.ac.uk/bitstream/1345/RAL-TR-97-058.pdf; 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", bibsource = "http://www.gbhap-us.com/journals/728/728-top.htm; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", 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", bibsource = "http://etna.mcs.kent.edu/; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", 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", bibsource = "http://www.elsevier.com/locate/laa; 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, 1996).", URL = "http://www.elsevier.com/cas/tree/store/laa/sub/1998/275-276/1-3/6047.pdf; http://www.elsevier.com/cgi-bin/cas/tree/store/laa/cas_sub/browse/browse.cgi?year=1998&volume=275-276&issue=1-3&aid=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", 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/5058/31/5/abstract.htm; 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)", bibdate = "Sat Dec 31 06:28:14 2005", 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; https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib; MathSciNet database", URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/31/12/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/31/12/fulltext.pdf", 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; MathSciNet database", 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", CODEN = "NLAAEM", DOI = "https://doi.org/10.1002/(SICI)1099-1506(199805/06)5", ISSN = "1070-5325 (print), 1099-1506 (electronic)", ISSN-L = "1070-5325", MRclass = "65Fxx", MRnumber = "1 627 045", 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=61002412; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=61002412&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 = "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", CODEN = "IJNMBH", DOI = "https://doi.org/10.1002/(SICI)1097-0207(19980930)43", 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 = "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, year = "1998", CODEN = "IJNMBH", DOI = "https://doi.org/10.1002/(SICI)1097-0207(19980615)42", 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", } @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", 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", note = "Large scale eigenvalue problems (Argonne, IL, 1997)", URL = "http://etna.mcs.kent.edu/vol.7.1998/pp90-103.dir/pp90-103.pdf", acknowledgement = ack-nhfb, 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", 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/30481", acknowledgement = ack-nhfb, 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", month = nov, 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/8081001/80810125.htm; http://link.springer.de/link/service/journals/00211/papers/8081001/80810125.pdf", 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", bibdate = "Fri Jul 16 10:38:58 MDT 1999", bibsource = "http://www.ams.org/mcom/1998-67-224; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", URL = "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00973-9&u=/mcom/1998-67-224/", 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", DOI = "https://doi.org/10.1109/SC.1998.10033", bibdate = "Wed Mar 06 06:37:52 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www.supercomp.org/sc98/papers/", URL = "http://www.supercomp.org/sc98/TechPapers/sc98_FullAbstracts/Wu1023/index.htm", 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", 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{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", bibdate = "Mon Jan 2 07:55:27 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/S002199919895971X", 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)", ISSN-L = "0895-4798", bibdate = "Sat Jan 22 14:39:14 MST 2000", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/20/4; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/31780", 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", CODEN = "NUMMA7", ISSN = "0029-599X (print), 0945-3245 (electronic)", ISSN-L = "0029-599X", bibdate = "Mon Oct 18 10:45:13 MDT 1999", bibsource = "http://link.springer-ny.com/link/service/journals/00211/tocs/t9083001.htm; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", URL = "http://link.springer-ny.com/link/service/journals/00211/bibs/9083001/90830053.htm; http://link.springer-ny.com/link/service/journals/00211/papers/9083001/90830053.pdf", 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", CODEN = "NUALEG", ISSN = "1017-1398 (print), 1572-9265 (electronic)", ISSN-L = "1017-1398", bibdate = "Mon Sep 29 08:36:58 MDT 2003", bibsource = "http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/20/15/abstract.htm; 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", ISSN = "0006-3835 (print), 1572-9125 (electronic)", ISSN-L = "0006-3835", bibdate = "Wed Jan 4 15:06:03 MST 2006", bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=39&issue=4; http://www.mai.liu.se/BIT/contents/bit39.html; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/bit.bib; OCLC Article1st database", URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=39&issue=4&spage=603", acknowledgement = ack-nhfb, 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", bibdate = "Mon May 20 06:37:48 MDT 2002", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; OCLC Proceedings database", 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", bibsource = "http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", URL = "http://ipsapp007.kluweronline.com/content/getfile/5058/19/3/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/19/3/fulltext.pdf", 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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", series = "GAKUTO Internat. Ser. Math. Sci. Appl.", acknowledgement = ack-nhfb, } @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", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/9/2; https://www.math.utah.edu/pub/bibnet/authors/g/gould-nicholas-ian.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", 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", 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/S0898122199002758", 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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; http://www3.interscience.wiley.com/journalfinder.html", note = "Czech-US Workshop in Iterative Methods and Parallel Computing, Part I (Milovy, 1997).", URL = "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=62002985; 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", bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/parco/cas_free/browse/browse.cgi?year=1999&volume=25&issue=5; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", 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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; MathSciNet database", 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", 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/S0021999199963064", 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", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/21/4; 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", URL = "http://www.ams.org/journal-getitem?pii=S0025-5718-99-01163-1; http://www.ams.org/mcom/2000-69-232/S0025-5718-99-01163-1/S0025-5718-99-01163-1.dvi; http://www.ams.org/mcom/2000-69-232/S0025-5718-99-01163-1/S0025-5718-99-01163-1.pdf; http://www.ams.org/mcom/2000-69-232/S0025-5718-99-01163-1/S0025-5718-99-01163-1.ps; 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", 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/5058/3/23/abstract.htm; 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; 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/s/stiefel-eduard.bib; https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; 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; https://www.math.utah.edu/pub/bibnet/subjects/fastmultipole.bib; 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", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; 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; http://www.mai.liu.se/BIT/contents/bit40.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=40&issue=3&spage=471", 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", bibsource = "http://www.interscience.wiley.com/jpages/0020-7608; 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/70002215/START; http://www3.interscience.wiley.com/cgi-bin/fulltext/70002215/FILE?TPL=ftx_start; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=70002215&PLACEBO=IE.pdf", 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", URL = "http://www.elsevier.nl/gej-ng/10/30/19/126/25/39/abstract.html; http://www.elsevier.nl/gej-ng/10/30/19/126/25/39/article.pdf", acknowledgement = ack-nhfb, 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/autho