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# Cornelius Lanczos

Cornelius Lanczos (Hungarian: Lánczos Kornél, Hungarian pronunciation: [ˈlaːntsoʃ]) (until 1906) Löwy (Lőwy) Kornél was born on February 2, 1893, and died on June 25, 1974. He was a Hungarian mathematician and physicist.

He was born in Székesfehérvár to Karl Löwy (Lőwy Károly) and Adél Hahn.

Lanczos' Ph.D. thesis (1921) was on relativity theory. In 1924 he discovered an exact solution of the Einstein field equation which represents 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 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.

He 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; some even name Carl Friedrich Gauss as a progenitor of the FFT.)

Working in Los Angeles 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 which 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.

Lanczos was an outstanding physics teacher. Books such as The Variational Principles of Mechanics (1949) show his explanatory ability and enthusiasm for the subject.

During the McCarthy era Lanczos came under suspicion for possible Communist links. In 1952 he chose to leave the U.S. and move to the School of Theoretical Physics at the Dublin Institute for Advanced Studies in Ireland where he succeeded Schrödinger[1]. When at D.I.A.S. he wrote the classic book, "Applied Analysis" (1956).

References

1. ^ Louis Komzsik (2003). The Lanczos Method:Evolution and Application. SIAM. p. 79.

* Lanczos, Cornelius; and William R. Davis (ed.) (1998). Collected published papers with commentaries. Raleigh, N.C.: North Carolina State University. ISBN 0-929493-01-X.

* Lanczos, Cornelius (1970). The Variational Principles of Mechanics. Toronto: University of Toronto Press. ISBN 0-8020-1743-6.

* Lanczos, Cornelius (1962). "The splitting of the Riemann tensor". Rev. Modern Phys. 34: 379. doi:10.1103/RevModPhys.34.379.

* Lanczos, Cornelius (1924). "Über eine stationäre Kosmologie im Sinne der Einsteinischen Gravitationstheorie". ZeitschrARRAY. Phys. 21: 73. doi:10.1007/BF01328251.

External links

* O'Connor, John J.; Robertson, Edmund F., "Cornelius Lanczos", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Lanczos.html .

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

* Photo gallery of Lanczos by Nicholas Higham

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