Cornelius Lanczos

Cornelius (Cornel) Lanczos (Hungarian: Lánczos Kornél, [ˈlaːnt͡soʃ ˈkorneːl], born as Kornél Lőwy, until 1906: Löwy (Lőwy) Kornél) was a Hungarian mathematician and physicist, who was born in Székesfehérvár, Fejér County, Kingdom of Hungary on February 2, 1893, and died on June 25, 1974. According to György Marx he was one of The Martians.

He was born in Fehérvár (Alba Regia), in Fejér County, to dr. Károly Lőwy and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on relativity theory. He sent his thesis copy to 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."

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) Lanzos 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 era, Lanczos came under suspicion for possible communist 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 1968.

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."

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.). 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) 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 thought for a two-semester graduate course of three hours weekly.

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

• 1924: "Über eine stationäre Kosmologie im Sinne der Einsteinischen Gravitationstheorie", Zeitschrift für Physik 21: 73 doi:10.1007/BF01328251
• 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.
• 1962: "The splitting of the Riemann tensor", Reviews of Modern Physics 34(3): 379 doi:10.1103/RevModPhys.34.379