__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 Hungarian Americans ( Hungarian: ''amerikai magyarok'') are Americans of Hungarian descent. The U.S. Census Bureau has estimated that there are approximately 1.396 million Americans of Hungarian descent as of 2018. The total number of people wit ...

and later Hungarian-Irish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...

. According to

György Marx György Marx (25 May 1927 – 2 December 2002) was a Hungarian physicist, astrophysicist, science historian and professor. He discovered the lepton numbers and established the law of lepton flavor conservation. Life He was the first non-Briti ...

he was one of The Martians.

Biography

He was born in Fehérvár (Alba Regia),

Fejér County Fejér ( hu, Fejér megye, ) is an administrative county (comitatus or megye) in Central Hungary. It lies on the west bank of the river Danube and nearly touches the eastern shore of Lake Balaton. It shares borders with the Hungarian counties V ...

Kingdom of Hungary The Kingdom of Hungary was a monarchy in Central Europe that existed for nearly a millennium, from the Middle Ages into the 20th century. The Principality of Hungary emerged as a Christian kingdom upon the coronation of the first king Stephen ...

to Károly Lőwy and Adél Hahn. Lanczos'

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

thesis (1921) was on

relativity theory The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...

. He sent his thesis copy to

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...

, 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 The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

In 1924 he discovered an exact solution of the

Einstein field equation In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...

representing a cylindrically symmetric rigidly rotating configuration of

dust Dust is made of fine particles of solid matter. On Earth, it generally consists of particles in the atmosphere that come from various sources such as soil lifted by wind (an aeolian process), volcanic eruptions, and pollution. Dust in homes ...

particles. This was later rediscovered by

Willem Jacob van Stockum Willem Jacob van Stockum (20 November 1910 – 10 June 1944) was a Dutch mathematician who made an important contribution to the early development of general relativity. Biography Van Stockum was born in Hattem in the Netherlands. His father wa ...

and is known today as the

van Stockum dust In general relativity, the van Stockum dust is an exact solution of the Einstein field equations in which the gravitational field is generated by dust rotating about an axis of cylindrical symmetry. Since the density of the dust is ''increasing' ...

. 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 curve In mathematical physics, a closed timelike curve (CTC) is a world line in a Lorentzian manifold, of a material particle in spacetime, that is "closed", returning to its starting point. This possibility was first discovered by Willem Jacob van Sto ...

s. Lanczos served as assistant to

during the period of 1928–29. In 1927 Lanczos married Maria Rupp. He was offered a one-year visiting professorship from

Purdue University Purdue University is a public land-grant research university in West Lafayette, Indiana, and the flagship campus of the Purdue University system. The university was founded in 1869 after Lafayette businessman John Purdue donated land and money ...

. 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 Lafayette ( , ) is a city in and the county seat of Tippecanoe County, Indiana, United States, located northwest of Indianapolis and southeast of Chicago. West Lafayette, on the other side of the Wabash River, is home to Purdue University, whi ...

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 The Dublin Institute for Advanced Studies (DIAS) ( ga, Institiúid Ard-Léinn Bhaile Átha Cliath) is a statutory independent research institute in Ireland. It was established in 1940 on the initiative of the Taoiseach, Éamon de Valera, in Dub ...

in Ireland, where he succeeded

Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theory ...

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 Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied in the ...

and

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of ...

: it is roughly the theory of approximation by finite (or truncated infinite)

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

s."

Research

Lanczos did pioneering work along with

G. C. Danielson Gordon Charles Danielson (October 28, 1912 - September 30, 1983) was a Distinguished Professor in Sciences and Humanities in 1964 at Iowa State University at Ames, Iowa. His name was added to the Distinguished Professor Award Wall in Beardsher H ...

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 Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...

.). 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 In linear algebra, a square matrix A is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix P and a diagonal matrix D such that or equivalently (Such D are not unique.) ...

. Working in Washington DC at the U.S.

National Bureau of Standards The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...

after 1949, Lanczos developed a number of techniques for mathematical calculations using digital computers, including: * the

Lanczos algorithm The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power iteration, power methods to find the m "most useful" (tending towards extreme highest/lowest) eigenvalues and eigenvectors of an n \times n ...

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 In mathematics, the Lanczos approximation is a method for computing the gamma function numerically, published by Cornelius Lanczos in 1964. It is a practical alternative to the more popular Stirling's approximation for calculating the gamma functio ...

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 mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. For example, :\begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in the ...

. 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 f ...

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

Lanczos resampling filtering and Lanczos resampling are two applications of a mathematical formula. It can be used as a low-pass filter or used to smoothly interpolate the value of a digital signal between its samples. In the latter case it maps each sample of t ...

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 In computer graphics and digital imaging, image scaling refers to the resizing of a digital image. In video technology, the magnification of digital material is known as upscaling or resolution enhancement. When scaling a vector graphic image, ...

. 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

University of Toronto Press The University of Toronto Press is a Canadian university press founded in 1901. Although it was founded in 1901, the press did not actually publish any books until 1911. The press originally printed only examination books and the university calen ...

, 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 John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in p ...

* 1966: ''Discourse on Fourier Series'',

Oliver & Boyd Oliver and Boyd was a British publishing and printing firm that traded from 1807 or 1808 until 1990.

* 1968: ''Numbers without End'', Edinburgh: Oliver & Boyd * (1970: ''The Variational Principles of Mechanics'', 4th ed.) * 1970: ''Judaism and Science'',

Leeds University Press The University of Leeds is a public research university in Leeds, West Yorkshire, England. It was established in 1874 as the Yorkshire College of Science. In 1884 it merged with the Leeds School of Medicine (established 1831) and was renamed Yorks ...

(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 Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes reference ...

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 ...

Science Magazine ''Science'', also widely referred to as ''Science Magazine'', is the peer-reviewed academic journal of the American Association for the Advancement of Science (AAAS) and one of the world's top academic journals. It was first published in 1880, ...

, December 11, 1970. * 1974: ''The Einstein Decade (1905 — 1915)'',

Granada Publishing Granada (,, DIN: ; grc, Ἐλιβύργη, Elibýrgē; la, Illiberis or . ) is the capital city of the province of Granada, in the autonomous community of Andalusia, Spain. Granada is located at the foot of the Sierra Nevada mountains, at the c ...

*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 Los Angeles ( ; es, Los Ángeles, link=no , ), often referred to by its initials L.A., is the largest city in the state of California and the second most populous city in the United States after New York City, as well as one of the world' ...

, September, 1949. *

References

External links

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

by

Nicholas Higham Nicholas John Higham FRS (born 25 December 1961 in Salford) is a British numerical analyst. He is Royal Society Research Professor and Richardson Professor of Applied Mathematics in the Department of Mathematics at the University of Manchest ...

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