Cornelius Lanczos

He was born in Fehérvár (Alba Regia), Fejér County, Kingdom of Hungary to Jewish parents,{{citation needed|date=July 2023}} Károly Lőwy and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on relativity theory.{{cite arXiv |last=Lanczos |first=Cornelius |authorlink= |eprint=physics/0408079 |title=The relations of the homogeneous Maxwell's equations to the theory of functions |class= |year=2004}} 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."Barbara Gellai (2010) The Intrinsic Nature of Things: the life and science of Cornelius Lanczos, American Mathematical Society {{ISBN|978-0-8218-5166-1}}{{rp|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.{{rp|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.{{rp|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.{{rp|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{{cite book|title=The Lanczos Method: Evolution and Application|author=Louis Komzsik|page=79|publisher=SIAM|year=2003}} and stayed until his death in 1974.[https://www.dias.ie/2010/07/09/lanczos-c/ Cornelius Lanczos] at Dublin Institute for Advanced Studies

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."{{cite journal|author=Todd, John|author-link=John Todd (computer scientist)|title=Review: Applied Analysis, by C. Lanczos|journal=Bull. Amer. Math. Soc.|year=1958|volume=64|issue=4|pages=210–211|url=https://www.ams.org/journals/bull/1958-64-04/S0002-9904-1958-10215-3/|doi=10.1090/s0002-9904-1958-10215-3|doi-access=free}}

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.{{cite journal|title=Gauss and the History of the Fast Fourier Transform|author1=Michael T. Heideman |author2=Don H. Johnson |author3=C. Sidney Burrus |page=14|journal=IEEE ASSP Magazine|date=October 1984}}). Lanczos was the one who introduced Chebyshev polynomials to numerical computing.

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.

His book The Variational Principles of Mechanics (1949){{cite journal|author=Lewis, D. C.|title=Review: The variational principles of mechanics, by C. Lanczos|journal=Bull. Amer. Math. Soc.|year=1951|volume=57|issue=1, Part 1|pages=88–91|url=https://www.ams.org/journals/bull/1951-57-01/S0002-9904-1951-09462-8/|doi=10.1090/s0002-9904-1951-09462-8|doi-access=free}} is a graduate text on mechanics. In the preface of the first edition it is described as a two-semester graduate course of three hours weekly.

• 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}}, [https://www.science.org/doi/10.1126/science.170.3963.1183.a 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}}

• {{cite journal |last=Lanczos |first=Kornel |title=Über eine stationäre Kosmologie im Sinne der Einsteinschen Gravitationstheorie |journal=Zeitschrift für Physik |publisher=Springer Science and Business Media LLC |volume=21 |issue=1 |year=1924 |issn=1434-6001 |doi=10.1007/bf01328251 |pages=73–110 |bibcode=1924ZPhy...21...73L |s2cid=122902359 |language=de}} Translated reprint {{Cite journal |last=Lanczos |first=K. (Kornel) |author-link=Cornelius Lanczos |title=On a Stationary Cosmology in the Sense of Einstein's Theory of Gravitation |journal=General Relativity and Gravitation |volume=29 |pages=363–399 |year=1997 |doi=10.1023/A:1010277120072 |url=https://link.springer.com/article/10.1023/A:1010277120072|url-access=subscription }}
• {{cite journal |last=Lanczos |first=Kornel |url=https://nvlpubs.nist.gov/nistpubs/jres/045/jresv45n4p255_A1b.pdf |format=PDF |title=An iteration method for the solution of the eigenvalue problem of linear differential and integral operators |journal=Journal of Research of the National Bureau of Standards |volume=45 |issue=4 |date=October 1950 |location=Los Angeles}} Research Paper 2133. September 1949.
• {{cite journal |last=Lanczos |first=C. |title=The Splitting of the Riemann Tensor |journal=Reviews of Modern Physics |publisher=American Physical Society (APS) |volume=34 |issue=3 |date=1962-07-01 |issn=0034-6861 |doi=10.1103/revmodphys.34.379 |pages=379–389 |bibcode=1962RvMP...34..379L }}

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{{Reflist}}

• {{cite book|author=Brendan Scaife|author-link=Brendan Scaife|title=Studies in Numerical Analysis: Papers in Honour of Cornelius Lanczos|location=Dublin; London; New York|publisher=Academic Press|year=1974|isbn=0-12-621150-7|url-access=registration|url=https://archive.org/details/studiesinnumeric0000unse}}

• {{MacTutor Biography|id=Lanczos}}
• {{MathGenealogy|id=148153}}
• [https://web.archive.org/web/20061205022927/http://physics.ncsu.edu/lanczos/ Cornelius Lanczos, Collected published papers with commentaries], published by North Carolina State University
• [http://www.maths.manchester.ac.uk/~higham/photos/lanczos/index.htm Photo gallery of Lanczos] by Nicholas Higham
• [http://guettel.com/lanczos/ Series of historic video tapes] produced in 1972, digitalized on the occasion of the 120th anniversary of Cornelius Lanczos's birth

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Category:1893 births

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Category:People from Székesfehérvár

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Category:Victims of McCarthyism