**Cornelius Lanczos** (until 1906)

**Löwy (Lőwy) Kornél** was a

HungarianHungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...

-Jewish

mathematicianA mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

and

physicistA physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

, who was born on February 2, 1893, and died on June 25, 1974.

He was born in Székesfehérvár to Karl Löwy (

**Lőwy Károly**) and

**Adél Hahn**.

Lanczos'

Ph.D.A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...

thesis (1921) was on relativity theory. In 1924 he discovered an

exact solutionIn general relativity, an exact solution is a Lorentzian manifold equipped with certain tensor fields which are taken to model states of ordinary matter, such as a fluid, or classical nongravitational fields such as the electromagnetic field....

of the Einstein field equation which represents a cylindrically symmetric rigidly rotating configuration of

dustIn general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid....

particles. This was later rediscovered by

Willem Jacob van StockumWillem Jacob van Stockum was a mathematician who made an important contribution to the early development of general relativity....

and is known today as the

van Stockum dustIn general relativity, the van Stockum dust is an exact solution of the Einstein field equation in which the gravitational field is generated by dust rotating about an axis of cylindrical symmetry...

. 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 curveIn mathematical physics, a closed timelike curve is a worldline in a Lorentzian manifold, of a material particle in spacetime that is "closed," returning to its starting point...

s.

Lanczos served as assistant to

Albert EinsteinAlbert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

during the period of 1928–29.

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

fast Fourier transformA fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...

(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 GaussJohann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...

.)

Working in Washington DC at the U.S.

National Bureau of StandardsThe National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

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

- the Lanczos algorithm
The Lanczos algorithm is an iterative algorithm invented by Cornelius Lanczos that is an adaptation of power methods to find eigenvalues and eigenvectors of a square matrix or the singular value decomposition of a rectangular matrix. It is particularly useful for finding decompositions of very...

for finding eigenvalues 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 symmetric and positive-definite. The conjugate gradient method is an iterative method, so it can be applied to sparse systems that are too...

for solving systems of linear equations

In 1962, Lanczos showed that the

Weyl tensorIn 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 force that a body feels when moving along a geodesic...

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

Lanczos potentialThere are two different tensors sometimes referred to as the Lanczos tensor :* A tensor in the theory of quadratic Lagrangians, which vanishes in four dimensions....

.

Lanczos resamplingLanczos resampling is an interpolation method used to compute new values for sampled data. It is often used in multivariate interpolation, for example for image scaling , but can be used for any other digital signal...

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

McCarthyMcCarthyism is the practice of making accusations of disloyalty, subversion, or treason without proper regard for evidence. The term has its origins in the period in the United States known as the Second Red Scare, lasting roughly from the late 1940s to the late 1950s and characterized by...

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 StudiesThe Dublin Institute for Advanced Studies Dublin, Ireland was established in 1940 by the Taoiseach of the time, Éamon de Valera under the . The Institute consists of 3 schools: The , the and the . The directors of these schools are currently Professor Werner Nahm, Professor Luke Drury and...

in Ireland where he succeeded Schrödinger. When at D.I.A.S. he wrote the classic book, "Applied Analysis" (1956).

According to a short speech delivered Oct 1, 2010 during Lanczos' induction to the NIST Portrait Gallery of Distinguished Staff, his daughter-in-law described his return to Hungary in 1939 from his then-position at Purdue University, when he attempted to convince his family to return to the US with him due to the anti-Jewish Nazi threat. His wife was too ill to travel, and died several weeks later from tuberculosis. He was only able to extricate his 5 year old son and return to the US just before the war began. When the Nazis purged Hungary of Jews in 1944, only his aunt and a nephew survived. That son married, moved to Seattle and raised two sons. Upon hearing of the birth of his first grandson by letter while in Ireland, he replied in his own letter that the boy "was proof that Hitler did not win."

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