Gautschi, Walter SIAM oral history | 102746796

Description

Walter Gautschi discussed his varied work in numerical analysis and a variety of prominent mathematicians that he has interacted with. Gautschi had fairly humble beginnings as the son of a shoe store manager with deep roots in Switzerland. Talented at mathematics from a young age, Gautschi nearly pursued his other passion, music, and continued taking piano and composition lessons as a student. Mathematics eventually emerged as his calling, and he attended the University of Basel, where his instructors included Andreas Speiser and Alexander Ostrowski, a dominating figure under whom Gautschi eventually completed a thesis in graphical methods. Gautschi recalls an early talk he gave at a GAMM (the German equivalent of SIAM) conference in which Richard Grammel, upon whose work his thesis built, made some disparaging remarks about his talk. Undaunted, Gautschi completed his thesis, broadening his work so that it became applicable to numerical methods as well.

Gautschi relates fascinating stories about his mentor, Ostrowski. Born in Ukraine, he left Kiev to study in Germany—first to Marburg under Kurt Hensel and later to Göttingen, where he worked with David Hilbert, Edmund Landau, and Felix Klein—and eventually landed a professorship in Basel in 1927. Ostrowski became interested in linear algebra and iterative methods in the US when he met Herman Goldstine at the Bureau of Standards. Indeed, Gautschi tells about how Ostrowski, upon hearing a lecture by Goldstine on the use of iterative methods for solving eigenvalue problems for matrices, pointed out that Carl Jacobi had already done such work; henceforth it has been called the Jacobi Method.

Starting in 1956, Gautschi spent a few years at the Bureau of Standards, where he joined other Swiss mathematicians, including Peter Henrici and Eduard Stiefel. After a brief stint at American University, Alston Householder enticed him to Oak Ridge where he spent four years before moving to Purdue University in 1963. Gautschi has remained at Purdue ever since, advising a handful of PhD students and postdocs, including Hiroki Yanagiwara, with whom Gautschi collaborated to solve a problem in Chebyshev quadrature. Gautschi also dedicated much of his time to editing the journal Mathematics of Computation, which he did for twelve years.

Gautschi's interest in three-term recurrence relations was initially sparked by the enthusiasm of Milton Abramowitz (who had tapped Gautschi to write two chapters for the National Bureau of Standards' Handbook of Mathematical Functions) for J.C. P. Miller's backwards recurrence. Gautschi's inclinations often lead him to uncover older, original work on a topic, which sometimes spark new ideas. In tracing the roots of Miller's ideas, for example, he went from Oskar Perron's book on continued fractions to Niels Nörlund’s book from the 1920s on difference equations to a paper on hypergeometric functions by Salvatore Pincherle, where he found the theorem he was looking for. It is now widely used in difference equations.

Gautschi's work on orthogonal polynomials began, while he was at Oak Ridge, with an innocent request from a chemist. Gautschi thought the request would have a simple answer from Francis Begnaud Hildebrand's exposition of Gaussian quadrature and orthogonal polynomials, but it turned out to be far more complicated. The problem led him to explore the condition of confluent Vandermonde matrices and related problems. He has recently written a book and a Matlab software package on orthogonal polynomials and their computational aspects. His recent work also has touched on the circle theorem for Gauss-Lobatto, Gauss-Radau, and Gauss-Kronrod formulas. He has also collaborated extensively with Gradimir V. Milovanović on Gaussian quadrature, orthogonal polynomials, and moment-preserving spline approximation.

Date

2004-12-07

Contributor

Davis, Philip, Interviewer

Gautschi, Walter, Interviewee

Publisher

SIAM and U.S. Department of Energy

Place of Publication

West Lafayette, Indiana, United States

Extent

30 p.

Format

PDF

Copyright Holder

Computer History Museum

Subject

Graphical methods; Ordinary differential equation (ODE); Three-term recurrence relation; Orthogonal polynomial; Moment-preserving spline approximation; Gaussian quadrature

Collection Title

Society for Industrial and Applied Mathematics (SIAM) oral history collection

Credit

Gift of SIAM and the US Department of Energy

Lot Number

X6673.2013

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