Gene H. Golub

Gene Golub in 2007

Gene Howard Golub (born February 29, 1932 in Chicago , † November 16, 2007 in Stanford ) was one of the most important mathematicians of his generation in the field of numerical mathematics .

Life

Golub was born the son of Eastern European Jewish immigrants during the Great Depression . He and his younger brother grew up in very simple circumstances. The Second World War and the Holocaust did not play a major role in his life at that time, but later shaped him and his worldview very strongly. In 1948 his father died. He graduated from high school in 1949 and then attended community college. There he came into contact with differential and integral calculus , which sparked his interest in mathematics. After two years he successfully applied for admission to the University of Chicagoand studied mathematics there. For his last undergraduate year, he then moved to Urbana-Champaign to study at the University of Illinois at Urbana-Champaign , where he earned his BS in 1953 and his MS in 1954. He learned a lot about statistics and matrices , but in particular he took a programming course for the ILLIAC . His doctoral supervisor was Abraham H. Taub , who introduced him to numerical mathematics. In his doctoral thesis from 1959, The Use of Chebyshev Matrix Polynomials in the Iterative Solution of Linear Equations Compared to the Method of Successive Overrelaxation , he dealt with the iterative solution of linear systems of equations with the help of the SOR method and its relationship to Chebyshev polynomials . Towards the end of his dissertation, Taub invited Richard Varga to Illinois. Golub and Varga discovered they were working on similar things and wrote an essay together.

After completing his dissertation, Golub went to Cambridge University on a National Science Foundation scholarship . There he worked a lot with William Kahan , made contacts with James H. Wilkinson and heard lectures from Cornelius Lanczos , from whom he first learned about the existence of singular value decomposition . He also met Antony Jameson there, whom he introduced to numerical mathematics. In 1960 he returned to the USA. He initially worked for various institutes such as the Lawrence Berkeley National Laboratory , but then applied to various universities.

In 1962 he received a position from George Forsythe at Stanford University and became a professor there in 1970, which he remained until the end of his life. So he worked in one of the world's best computer science departments, together with Donald Knuth , Edward J. McCluskey and George Forsythe. Wilkinson, Germund Dahlquist and Peter Henrici were frequent visitors. Over time, Golub had 30 PhD students including Richard P. Brent , Michael Heath , Michael Overton , Dianne O'Leary , Michael Saunders, and Margaret H. Wright . Golub traveled a lot, was an avid visitor to conferences and often spent long periods of time abroad, for example at the ETH Zurich . He always sought contact with young scientists, brought many people together and offered mathematicians the opportunity to do research at Stanford University. He influenced the careers of numerous mathematicians to a large extent. His house in Stanford was open to everyone. He was only briefly married in the 1990s.

In 1994 he was invited speaker at the International Congress of Mathematicians in Zurich (Matrix computation and the theory of moments).

Golub died after a short illness of acute myeloid leukemia , one day before ETH Zurich would have awarded him an honorary doctorate.

plant

Gene Golub license plate

Golub's best-known work was the development of direct and iterative algorithms for the computation of a singular value decomposition (SVD), together with William Kahan in 1965 and with Christian Reinsch in 1970. These were already part of the first version of MATLAB and are still used today. His best-known book, co- authored with Charles F. Van Loan , is Matrix Computations, as he called numerical linear algebra . The book has been sold over 50,000 times and cited over 10,000 times in academic papers. In total, he published almost 200 articles in specialist journals.

Golub was the one who worked out the solution of the linear systems of equations derived from the least squares method with the help of Householder reflections in detail and made it popular. He also coined the term “total least squares”. Towards the end of the 1970s, he and others developed a quick solver for the discretized Poisson equation in non-regular areas. In the 1980s he made the preconditioning of the CG process known with his work .

He played an essential role in the creation of the NA-Net, the NA-Digest and the International Conference on Industrial and Applied Mathematics (ICIAM). He was for a time President of the Society for Industrial and Applied Mathematics and founder of the SIAM Journal on Scientific Computing and SIAM Journal on Matrix Analysis and Applications. Golub has held ten honorary doctorates, was a member of the National Academy of Sciences (since 1993) and has received the Bolzano Gold Medal.

He was associated with the University of Illinois throughout his life, grateful for the opportunities that education there had opened up for him. He endowed her with the Paul and Cynthia Saylor Professorship from funds he had acquired through his stake in a company founded by Stanford graduates, and to honor the mathematician Paul Saylor.

Part of his inheritance went to SIAM, which uses it to organize the Gene Golub SIAM Summer School every year.

Fonts

• Numerical methods for solving linear least squares problems. In: Numerical Mathematics. Vol. 7, No. 3, 1965, pp. 206-216, doi : 10.1007 / BF01436075 .
• with Charles Van Loan : Matrix Computations (= Johns Hopkins Series in the Mathematical Sciences. 3). Johns Hopkins University Press, Baltimore MD 1983, ISBN 0-8018-3010-9 .
• with James M. Ortega: Scientific Computing and Differential Equations. An Introduction to Numerical Methods. Academic Press, Boston MA et al. 1992, ISBN 0-12-289255-0 .
• with Gérard Meurant: Matrices, Moments and Quadrature. In: David F. Griffiths, G. Alistair Watson (Eds.): Numerical analysis 1993. Proceedings of the 15th Dundee Conference, June-July 1993 (= Pitman Research Notes in Mathematics Series. 303). Longman Scientific & Technical, Harlow 1994, ISBN 0-582-22568-X , pp. 105-156.
• with Moody T. Chu: Inverse Eigenvalue problems. Theory, algorithms, and applications. Oxford University Press, Oxford et al. 2005, ISBN 0-19-856664-6 .

literature

• Raymond H. Chan, Chen Greif, Dianne P. O'Leary: Milestones in Matrix Computation. The Selected Works of Gene H. Golub. With commentaries. Oxford University Press, Oxford 2007, ISBN 978-0-19-920681-0 (the book contains a biography written by Greif, which is also available online ).

Web links

• Literature by and about Gene H. Golub in the catalog of the German National Library
• Gene H Golub Memorial page
• Gene Golub in pictures around the world

Footnotes

1. ↑ G. Golub & W. Kahan: Calculating the singular values ​​and pseudo-inverse of a matrix. In: Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis. Volume 2, 1965, DOI: 10.1137 / 0702016 , pp. 205–224 ( PDF; 6 kB )
2. ^ GH Golub & C. Reinsch: Singular value decomposition and least squares solutions. In: Numerical Mathematics. Volume 14, 1970, DOI: 10.1007 / BF02163027 , pp. 403-420
3. ↑ - ( Memento of the original from June 15, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , accessed June 13, 2011