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Cornelius Lanczos

February 13, 2023

"Lanczos" redirects here. For resampling method, see Lanczos resampling.

Cornelius (Cornel) Lanczos (Hungarian: Lánczos Kornél, pronounced [ˈlaːnt͡soʃ ˈkorneːl]; born as Kornél Lőwy, until 1906: Löwy (Lőwy) Kornél; February 2, 1893 – June 25, 1974) was a Hungarian-American and later Hungarian-Irish mathematician and physicist. According to György Marx he was one of The Martians.[2]

Cornelius Lanczos
Born(1893-02-02)February 2, 1893
Székesfehérvár, Kingdom of Hungary
DiedJune 25, 1974(1974-06-25) (aged 81)
Budapest
NationalityHungarian
Alma materUniversity of Budapest
University of Szeged
Known forLanczos algorithm
Lanczos tensor
Lanczos resampling
Lanczos approximation
Lanczos sigma factor
Lanczos differentiator
Lanczos–van Stockum dust
Spouse(s)Mária Erzsébet Rump (1928–1939)
Ilse Hildebrand (1954–1974)
AwardsChauvenet Prize (1960)[1]
Scientific career
FieldsMathematics
Theoretical physics
InstitutionsUniversity of Freiburg
Purdue University
Boeing
Institute of Numerical Analysis
Dublin Institute for Advanced Studies
Frankfurt University
ThesisRelation of Maxwell's Aether Equations to Functional Theory (1921)
Doctoral advisorRudolf Ortvay
Other academic advisorsLoránd Eötvös
Lipót Fejér,
Erwin Madelung

Biography

He was born in Fehérvár (Alba Regia), Fejér County, Kingdom of Hungary to Károly Lőwy and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on relativity theory. He sent his thesis copy to Albert Einstein, and Einstein wrote back, saying: "I studied your paper as far as my present overload allowed. I believe I may say this much: this does involve competent and original brainwork, on the basis of which a doctorate should be obtainable ... I gladly accept the honorable dedication."[3]: 20 

In 1924 he discovered an exact solution of the Einstein field equation representing a cylindrically symmetric rigidly rotating configuration of dust particles. This was later rediscovered by Willem Jacob van Stockum and is known today as the van Stockum dust. It is one of the simplest known exact solutions in general relativity and is regarded as an important example, in part because it exhibits closed timelike curves. Lanczos served as assistant to Albert Einstein during the period of 1928–29.[3]: 27 

In 1927 Lanczos married Maria Rupp. He was offered a one-year visiting professorship from Purdue University. For a dozen years (1927–39) Lanczos split his life between two continents. His wife Maria Rupp stayed with Lanczos' parents in Székesfehérvár year-around while Lanczos went to Purdue for half the year, teaching graduate students matrix mechanics and tensor analysis. In 1933 his son Elmar was born; Elmar came to Lafayette, Indiana with his father in August 1939, just before WW II broke out.[3]: 41 & 53  Maria was too ill to travel and died several weeks later from tuberculosis. When the Nazis purged Hungary of Jews in 1944, of Lanczos' family, only his sister and a nephew survived. Elmar married, moved to Seattle and raised two sons. When Elmar looked at his own firstborn son, he said: "For me, it proves that Hitler did not win."

During the McCarthy era, Lanczos came under suspicion for possible communist links.[3]: 89  In 1952, he left the U.S. and moved to the School of Theoretical Physics at the Dublin Institute for Advanced Studies in Ireland, where he succeeded Erwin Schrödinger[4] and stayed until his death in 1974.[5]

In 1956 Lanczos published Applied Analysis. The topics covered include "algebraic equations, matrices and eigenvalue problems, large scale linear systems, harmonic analysis, data analysis, quadrature and power expansions...illustrated by numerical examples worked out in detail." The contents of the book are stylized "parexic analysis lies between classical analysis and numerical analysis: it is roughly the theory of approximation by finite (or truncated infinite) algorithms."[6]

Research

Lanczos did pioneering work along with G. C. Danielson on what is now called the fast Fourier transform (FFT, 1940), but the significance of his discovery was not appreciated at the time, and today the FFT is credited to Cooley and Tukey (1965). (As a matter of fact, similar claims can be made for several other mathematicians, including Carl Friedrich Gauss.[7]). Lanczos was the one who introduced Chebyshev polynomials to numerical computing. He discovered the diagonalizable matrix.

Working in Washington DC at the U.S. National Bureau of Standards after 1949, Lanczos developed a number of techniques for mathematical calculations using digital computers, including:

In 1962, Lanczos showed that the Weyl tensor, which plays a fundamental role in general relativity, can be obtained from a tensor potential that is now called the Lanczos potential.

Lanczos resampling is based on a windowed sinc function as a practical upsampling filter approximating the ideal sinc function. Lanczos resampling is widely used in video up-sampling for digital zoom applications and image scaling.

Books such as The Variational Principles of Mechanics (1949)[8] is a classic graduate text on mechanics. He shows his explanatory ability and enthusiasm as a physics teacher: in the preface of the first edition he says it is taught for a two-semester graduate course of three hours weekly.

Publications

Books

  • 1949: The Variational Principles of Mechanics (dedicated to Albert Einstein), University of Toronto Press ISBN 0-8020-1743-6, followed by 1962, 1966, 1970 editions. ISBN 0-486-65067-7
  • 1956: Applied Analysis, Prentice Hall
  • 1961: Linear Differential Operators, Van Nostrand Company, ISBN 048665656X
  • (1962: The Variational Principles of Mechanics, 2nd ed.)
  • (1966: The Variational Principles of Mechanics, 3rd ed.)
  • 1966: Albert Einstein and the cosmic world order: six lectures delivered at the University of Michigan in the Spring of 1962, Interscience Publishers
  • 1966: Discourse on Fourier Series, Oliver & Boyd
  • 1968: Numbers without End, Edinburgh: Oliver & Boyd
  • (1970: The Variational Principles of Mechanics, 4th ed.)
  • 1970: Judaism and Science, Leeds University Press ISBN 085316021X (22 pages, S. Brodetsky Memorial Lecture)
  • 1970: Space through the Ages (the Evolution of the geometric Ideas from Pythagoras to Hilbert and Einstein), Academic Press ISBN 0124358500, Review by Max Jammer on Science Magazine, December 11, 1970.
  • 1974: The Einstein Decade (1905 — 1915), Granada Publishing ISBN 0236176323
  • 1998: (William R. Davis, editor) Cornelius Lanczos: Collected Published Papers with Commentaries, North Carolina State University ISBN 0-929493-01-X

Articles

  • Lanczos, Kornel (1924). "Über eine stationäre Kosmologie im Sinne der Einsteinschen Gravitationstheorie". Zeitschrift für Physik (in German). Springer Science and Business Media LLC. 21 (1): 73–110. doi:10.1007/bf01328251. ISSN 1434-6001.
  • 1949: "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators" Journal of Research of the National Bureau of Standards, Journal of Research of the National Bureau of Standards, Research Paper 2133. Vol. 45, No. 4, October 1950. Los Angeles, September, 1949.
  • Lanczos, C. (1962-07-01). "The Splitting of the Riemann Tensor". Reviews of Modern Physics. American Physical Society (APS). 34 (3): 379–389. doi:10.1103/revmodphys.34.379. ISSN 0034-6861.

See also

References

  1. ^ Lanczos, Cornelius (1958). "Linear Systems in Self-Adjoint Form". Amer. Math. Monthly. 65: 665–679. doi:10.2307/2308707.
  2. ^ A marslakók legendája – György Marx.
  3. ^ a b c d Barbara Gellai (2010) The Intrinsic Nature of Things: the life and science of Cornelius Lanczos, American Mathematical Society ISBN 978-0-8218-5166-1
  4. ^ Louis Komzsik (2003). The Lanczos Method: Evolution and Application. SIAM. p. 79.
  5. ^ Cornelius Lanczos at Dublin Institute for Advanced Studies
  6. ^ Todd, John (1958). "Review: Applied Analysis, by C. Lanczos". Bull. Amer. Math. Soc. 64 (4): 210–211. doi:10.1090/s0002-9904-1958-10215-3.
  7. ^ Michael T. Heideman; Don H. Johnson; C. Sidney Burrus (October 1984). "Gauss and the History of the Fast Fourier Transform". IEEE ASSP Magazine: 14.
  8. ^ Lewis, D. C. (1951). "Review: The variational principles of mechanics, by C. Lanczos". Bull. Amer. Math. Soc. 57 (1, Part 1): 88–91. doi:10.1090/s0002-9904-1951-09462-8.

External links

February 13, 2023
cornelius, lanczos, lanczos, redirects, here, resampling, method, lanczos, resampling, cornelius, cornel, lanczos, hungarian, lánczos, kornél, pronounced, ˈlaːnt, soʃ, ˈkorneːl, born, kornél, lőwy, until, 1906, löwy, lőwy, kornél, february, 1893, june, 1974, h. Lanczos redirects here For resampling method see Lanczos resampling Cornelius Cornel Lanczos Hungarian Lanczos Kornel pronounced ˈlaːnt soʃ ˈkorneːl born as Kornel Lowy until 1906 Lowy Lowy Kornel February 2 1893 June 25 1974 was a Hungarian American and later Hungarian Irish mathematician and physicist According to Gyorgy Marx he was one of The Martians 2 Cornelius LanczosBorn 1893 02 02 February 2 1893Szekesfehervar Kingdom of HungaryDiedJune 25 1974 1974 06 25 aged 81 BudapestNationalityHungarianAlma materUniversity of BudapestUniversity of SzegedKnown forLanczos algorithmLanczos tensorLanczos resamplingLanczos approximationLanczos sigma factorLanczos differentiatorLanczos van Stockum dustSpouse s Maria Erzsebet Rump 1928 1939 Ilse Hildebrand 1954 1974 AwardsChauvenet Prize 1960 1 Scientific careerFieldsMathematicsTheoretical physicsInstitutionsUniversity of FreiburgPurdue UniversityBoeingInstitute of Numerical AnalysisDublin Institute for Advanced Studies Frankfurt UniversityThesisRelation of Maxwell s Aether Equations to Functional Theory 1921 Doctoral advisorRudolf OrtvayOther academic advisorsLorand EotvosLipot Fejer Erwin MadelungBiography EditHe was born in Fehervar Alba Regia Fejer County Kingdom of Hungary to Karoly Lowy and Adel Hahn Lanczos Ph D thesis 1921 was on relativity theory He sent his thesis copy to Albert Einstein and Einstein wrote back saying I studied your paper as far as my present overload allowed I believe I may say this much this does involve competent and original brainwork on the basis of which a doctorate should be obtainable I gladly accept the honorable dedication 3 20 In 1924 he discovered an exact solution of the Einstein field equation representing a cylindrically symmetric rigidly rotating configuration of dust particles This was later rediscovered by Willem Jacob van Stockum and is known today as the van Stockum dust It is one of the simplest known exact solutions in general relativity and is regarded as an important example in part because it exhibits closed timelike curves Lanczos served as assistant to Albert Einstein during the period of 1928 29 3 27 In 1927 Lanczos married Maria Rupp He was offered a one year visiting professorship from Purdue University For a dozen years 1927 39 Lanczos split his life between two continents His wife Maria Rupp stayed with Lanczos parents in Szekesfehervar year around while Lanczos went to Purdue for half the year teaching graduate students matrix mechanics and tensor analysis In 1933 his son Elmar was born Elmar came to Lafayette Indiana with his father in August 1939 just before WW II broke out 3 41 amp 53 Maria was too ill to travel and died several weeks later from tuberculosis When the Nazis purged Hungary of Jews in 1944 of Lanczos family only his sister and a nephew survived Elmar married moved to Seattle and raised two sons When Elmar looked at his own firstborn son he said For me it proves that Hitler did not win During the McCarthy era Lanczos came under suspicion for possible communist links 3 89 In 1952 he left the U S and moved to the School of Theoretical Physics at the Dublin Institute for Advanced Studies in Ireland where he succeeded Erwin Schrodinger 4 and stayed until his death in 1974 5 In 1956 Lanczos published Applied Analysis The topics covered include algebraic equations matrices and eigenvalue problems large scale linear systems harmonic analysis data analysis quadrature and power expansions illustrated by numerical examples worked out in detail The contents of the book are stylized parexic analysis lies between classical analysis and numerical analysis it is roughly the theory of approximation by finite or truncated infinite algorithms 6 Research EditLanczos did pioneering work along with G C Danielson on what is now called the fast Fourier transform FFT 1940 but the significance of his discovery was not appreciated at the time and today the FFT is credited to Cooley and Tukey 1965 As a matter of fact similar claims can be made for several other mathematicians including Carl Friedrich Gauss 7 Lanczos was the one who introduced Chebyshev polynomials to numerical computing He discovered the diagonalizable matrix Working in Washington DC at the U S National Bureau of Standards after 1949 Lanczos developed a number of techniques for mathematical calculations using digital computers including the Lanczos algorithm for finding eigenvalues of large symmetric matrices the Lanczos approximation for the gamma function the conjugate gradient method for solving systems of linear equations In 1962 Lanczos showed that the Weyl tensor which plays a fundamental role in general relativity can be obtained from a tensor potential that is now called the Lanczos potential Lanczos resampling is based on a windowed sinc function as a practical upsampling filter approximating the ideal sinc function Lanczos resampling is widely used in video up sampling for digital zoom applications and image scaling Books such as The Variational Principles of Mechanics 1949 8 is a classic graduate text on mechanics He shows his explanatory ability and enthusiasm as a physics teacher in the preface of the first edition he says it is taught for a two semester graduate course of three hours weekly Publications EditBooks Edit 1949 The Variational Principles of Mechanics dedicated to Albert Einstein University of Toronto Press ISBN 0 8020 1743 6 followed by 1962 1966 1970 editions ISBN 0 486 65067 7 1956 Applied Analysis Prentice Hall 1961 Linear Differential Operators Van Nostrand Company ISBN 048665656X 1962 The Variational Principles of Mechanics 2nd ed 1966 The Variational Principles of Mechanics 3rd ed 1966 Albert Einstein and the cosmic world order six lectures delivered at the University of Michigan in the Spring of 1962 Interscience Publishers 1966 Discourse on Fourier Series Oliver amp Boyd 1968 Numbers without End Edinburgh Oliver amp Boyd 1970 The Variational Principles of Mechanics 4th ed 1970 Judaism and Science Leeds University Press ISBN 085316021X 22 pages S Brodetsky Memorial Lecture 1970 Space through the Ages the Evolution of the geometric Ideas from Pythagoras to Hilbert and Einstein Academic Press ISBN 0124358500 Review by Max Jammer on Science Magazine December 11 1970 1974 The Einstein Decade 1905 1915 Granada Publishing ISBN 0236176323 1998 William R Davis editor Cornelius Lanczos Collected Published Papers with Commentaries North Carolina State University ISBN 0 929493 01 XArticles Edit Lanczos Kornel 1924 Uber eine stationare Kosmologie im Sinne der Einsteinschen Gravitationstheorie Zeitschrift fur Physik in German Springer Science and Business Media LLC 21 1 73 110 doi 10 1007 bf01328251 ISSN 1434 6001 1949 An iteration method for the solution of the eigenvalue problem of linear differential and integral operators Journal of Research of the National Bureau of Standards Journal of Research of the National Bureau of Standards Research Paper 2133 Vol 45 No 4 October 1950 Los Angeles September 1949 Lanczos C 1962 07 01 The Splitting of the Riemann Tensor Reviews of Modern Physics American Physical Society APS 34 3 379 389 doi 10 1103 revmodphys 34 379 ISSN 0034 6861 See also EditThe Martians scientists References Edit Lanczos Cornelius 1958 Linear Systems in Self Adjoint Form Amer Math Monthly 65 665 679 doi 10 2307 2308707 A marslakok legendaja Gyorgy Marx a b c d Barbara Gellai 2010 The Intrinsic Nature of Things the life and science of Cornelius Lanczos American Mathematical Society ISBN 978 0 8218 5166 1 Louis Komzsik 2003 The Lanczos Method Evolution and Application SIAM p 79 Cornelius Lanczos at Dublin Institute for Advanced Studies Todd John 1958 Review Applied Analysis by C Lanczos Bull Amer Math Soc 64 4 210 211 doi 10 1090 s0002 9904 1958 10215 3 Michael T Heideman Don H Johnson C Sidney Burrus October 1984 Gauss and the History of the Fast Fourier Transform IEEE ASSP Magazine 14 Lewis D C 1951 Review The variational principles of mechanics by C Lanczos Bull Amer Math Soc 57 1 Part 1 88 91 doi 10 1090 s0002 9904 1951 09462 8 Brendan Scaife 1974 Studies in Numerical Analysis Papers in Honour of Cornelius Lanczos Dublin London New York Academic Press ISBN 0 12 621150 7 External links EditO Connor John J Robertson Edmund F Cornelius Lanczos MacTutor History of Mathematics archive University of St Andrews Cornelius Lanczos at the Mathematics Genealogy Project Cornelius Lanczos Collected published papers with commentaries published by North Carolina State University Photo gallery of Lanczos by Nicholas Higham Series of historic video tapes produced in 1972 digitalized on the occasion of the 120th anniversary of Cornelius Lanczos s birth Retrieved from https en wikipedia org w index php title Cornelius Lanczos amp oldid 1136393877, wikipedia, wiki, book, books, library,

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