__NOTOC__ Cornelius (Cornel) Lanczos ( hu, Lánczos Kornél, ; 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.

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."Barbara Gellai (2010) ''The Intrinsic Nature of Things: the life and science of Cornelius Lanczos'', American Mathematical Society 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. 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. 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 McCarthy (also spelled MacCarthy or McCarty) may refer to: * MacCarthy, a Gaelic Irish clan * McCarthy, Alaska, United States * McCarty, Missouri, United States * McCarthy Road, a road in Alaska * McCarthy (band), an indie pop band * Château MacC ...

era, Lanczos came under suspicion for possible

communist Communism (from Latin la, communis, lit=common, universal, label=none) is a far-left sociopolitical, philosophical, and economic ideology and current within the socialist movement whose goal is the establishment of a communist society, a s ...

links. 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 and stayed until his death in 1974. 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."

Research

Lanczos did pioneering work along with G. C. Danielson on what is now called the

fast Fourier transform A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in th ...

(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.). Lanczos was the one who introduced

Chebyshev polynomials The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshe ...

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 In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

of large symmetric matrices, * the Lanczos approximation for the gamma function, * the

conjugate gradient method In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterativ ...

for solving systems of linear equations. In 1962, Lanczos showed that the

Weyl tensor In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal forc ...

, which plays a fundamental role in general relativity, can be obtained from a

tensor potential In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tenso ...

that is now called the Lanczos potential. Lanczos resampling is based on a windowed

sinc function In mathematics, physics and engineering, the sinc function, denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatornamex = \frac. Alternatively, the u ...

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) is a classic

graduate text on mechanics Graduate may refer to: Education * The subject of a graduation, i.e. someone awarded an academic degree ** Alumnus, a former student who has either attended or graduated from an institution * High school graduate, someone who has completed high ...

. 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 , followed by 1962, 1966, 1970 editions. * 1956: ''Applied Analysis'',

Prentice Hall Prentice Hall was an American major educational publisher owned by Savvas Learning Company. Prentice Hall publishes print and digital content for the 6–12 and higher-education market, and distributes its technical titles through the Safari B ...

* 1961: ''Linear Differential Operators'', Van Nostrand Company, * (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 (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
Review
by

Max Jammer Max Jammer (מקס ימר; born Moshe Jammer, ; April 13, 1915 – December 18, 2010), was an Israeli physicist and philosopher of physics. He was born in Berlin, Germany. He was Rector and Acting President at Bar-Ilan University from 1967 to 1 ...

on Science Magazine, December 11, 1970. * 1974: ''The Einstein Decade (1905 — 1915)'', Granada Publishing *1998: (William R. Davis, editor) ''Cornelius Lanczos: Collected Published Papers with Commentaries'',

North Carolina State University North Carolina State University (NC State) is a public land-grant research university in Raleigh, North Carolina. Founded in 1887 and part of the University of North Carolina system, it is the largest university in the Carolinas. The universit ...

Articles

* * 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 The ''Journal of Research of the National Institute of Standards and Technology'' is the flagship peer-reviewed scientific journal of the National Institute of Standards and Technology. It has been published since 1904. Its former name was ''Jour ...

, Research Paper 2133. Vol. 45, No. 4, October 1950. Los Angeles, September, 1949. *

References

External links

* *
Cornelius Lanczos, Collected published papers with commentaries
published by North Carolina State University

by Nicholas Higham
Series of historic video tapes
produced in 1972, digitalized on the occasion of the 120th anniversary of Cornelius Lanczos's birth {{DEFAULTSORT:Lanczos, Cornelius 1893 births 1974 deaths People from Székesfehérvár Hungarian Jews Hungarian emigrants to the United States 20th-century Hungarian mathematicians American expatriates in the Republic of Ireland 20th-century Hungarian physicists Irish mathematicians Numerical analysts Relativity theorists Jewish physicists Austro-Hungarian mathematicians Academics of the Dublin Institute for Advanced Studies Fellows of the American Physical Society