**Walter Gautschi**

Oral History (pdf)

**Interviewer:** Philip J. Davis

**Abstract:**

Walter Gautschi discusses his varied work in numerical analysis and a variety of prominent mathematicians that he has interacted with. He attended the University of Basel, where his instructors included Alexander Ostrowski, under whom Gautschi eventually completed a thesis in graphical methods for ordinary differential equations, later broadening his work so that it became applicable to numerical methods as well.

Starting in 1956, Gautschi spent a few years at the US National Bureau of Standards. After a brief stint at American University, Alston Householder enticed him to Oak Ridge National Laboratory where he spent four years before moving to Purdue University in 1963. Gautschi has remained at Purdue ever since, advising a handful of Ph.D. students and postdocs. He also spent twelve years editing the journal,* Mathematics of Computation*.

Gautschi's interest in three-term recurrence relations was initially sparked by the enthusiasm of Milton Abramowitz 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 a book on continued fractions to a book from the 1920s on difference equations to a paper on hypergeometric functions, 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 to which he thought there would be a simple answer. But it turned out to be far more complicated. The problem led him to explore the condition of certain matrices and related problems. He has recently written a book on orthogonal polynomials and their computational aspects. He has also collaborated with Gradimir V. Milovanović on Gaussian quadrature, orthogonal polynomials, and moment-preserving spline approximation.

**Key words**: graphical methods for ODEs, relaxation methods, three-term recurrence relations, orthogonal polynomials, moment-preserving spline approximation, Gaussian quadrature

**Funding Agency:** US Department of Commerce, US Department of Energy

**Time frame:** 1950's, 1960's, 1970's, 1980's

**People:** Alexander Ostrowski, Richard V. Southwell, Herman Goldstine, Peter Henrici, Eduard Steifel, Milton Abramowitz, J.C.P. Miller, Alston Householder, Gradimir Milovanović

**Location:** University of Basel, National Bureau of Standards, Oak Ridge National Laboratory, Purdue University

**Citation:** Walter Gautschi, Oral history interview by Philip Davis, 7 December, 2004, Purdue University, West Layfayette, IN. Society for Industrial and Applied Mathematics, Philadelphia, PA

**Statement of Use Policy**: Copyright © by the Computer History Museum. Use of this the material for research purposes is allowed. Any such use should cite the SIAM History of Numerical Analysis and Scientific Computing Project (http://history.siam.org). Use of the oral history materials for commercial purposes requires the written permission of the Computer History Museum. Contact the Computer History Museum, 1401 N Shoreline Boulevard, Mountain View, CA 94043-1311 USA for permissions.