Householder Symposium XV, 2002

On July 4, 1993, Alston Scott Householder, past president of SIAM, died of a massive stroke. He is survived by his wife Heidi, his daughter Jackie, and his son John. Two weeks before his death he had attended the Householder Symposium at Lake Arrowhead, California, the twelth in a series research of gatherings he had first started at Gatlinburg Tennessee in 1959. Alston was feeble but alert, and he enjoyed the opportunity to see old friends once again. He will be greatly missed.

He was born on May 5, 1904 in Rockford Illinois and shortly thereafter moved to Alabama, where he spent his childhood. He received his BA in 1925 from Northwestern and his MA from Cornell in 1927, both degrees in philosophy. Until 1937 he held various teaching positions in mathematics.

In 1937 Householder received his Ph.D. in mathematics from the University of Chicago. His subject was the calculus of variations, but mathematical biology was his first love. He joined the Committee for Mathemtical Biology, a group of enthusiastic youngsters that collected around the charismatic figure of Nicolas Rashevsky, and for the next eight years devoted himself to the area.

Householder left the Committee in 1944 to help with the war effort. In 1946 he joined the Mathematics Division of Oak Ridge National Laboratory and became its director in 1948. It was here that he turned from mathematical biology to numerical analysis. In 1969 he retired from ORNL and became a professor of Mathematics at the University of Tennessee, serving for a while as acting chairman. In 1974 he retired to Malibu California.

People of my generation think of Alston chiefly as a numerical analyst specializing in linear algebra. His interests and accomplishments, however, were much broader. They include his research in mathematical biology and numerical analysis as well as his professional and educational contributions.

Although Householder published work in mathematical biology spans only eight years, he was quite influential. John Hearon, retired from the National Institutes of Health, summarized his contributions as follows:

It is almost impossible to recall the difficulties (on a fiscal shoe string in a not entirely cordial scientific community) and the magnitude of the task faced by the original group of the Committee at the University of Chicago. Hypothesis, conjecture and tentative theory flew in all directions and there was a period of great ferment. In the midst of this, to every area to which he addressed himself Householder brought organization and systemization. He was then, and for some years to come, the only one of the group formally trained as a mathematician. It showed. He brought to every problem he undertook unification, generality of method and, in the end, simplicity. During the relatively brief period under discussion he published 33 papers and a monograph on topics which included the theory of neural nets, excitation, sensory discrimination, gestalt, binocular vision, diffusion reaction equations and enzyme kinetics, psychophysics and factor analysis.

Householder published little during his first years at Oak Ridge, and one
might have reasonably concluded that his productive years were over and he
had settled in as an administrator. What was really happening was that he
was retraining himself as a numerical analysts. The first fruit of his efforts
was his book *Principles of Numerical Analysis* which, in the words
of Jim Wilkinson, ``was the first really modern treatment of Numerical
Analysis.''

Householder is best known for his contributions to numerical linear algebra. Again Jim Wilkinson:

In the 1950's our knowledge of this topic was in a rather chaotic state. A large number of algorithms had been developed but no systematic study of their inter-relationships had been undertaken. It is primarily due to the work of Householder that order has emerged from this chaos. In a remarkable series of papers he effectively classified the algorithms for solving linear equations and computing eigensystems, showing that in many cases essentially the same algorithm had been presented in a large variety of superficially quite different algorithms. The resulting classification made it possible to concentrate on the the most profitable lines of research and in this way his work was directly responsible for the development of many of the most effective algorithms in use today. Of particular importance is his appreciation of the value of elementary hermitian matrices in numerical analysis.

But Householder was more than just an organizer of other peoples' ideas. To cite just one example, The ``elementary hermitian matrices'' mentioned by Wilkinson are now universally known as Householder transformations and are one of the most widely used tools in matrix computations.

Householder was also responsible for promoting the use of norms in numerical
linear algebra, where they have played an important role in error analysis.
In addition, with F. L. Bauer and other collaborators, he showed that norms
could be used to derive localization for eigenvalues, an important contribution
to pure linear algebra. The final result of his labors was his highly influential
book *The Theory of Matrices in Numerical Analysis.*

Just before and after his retirement, Householder worked on the solution of nonlinear equations in a single unknown. In a short book on the subject he stressed its historical development, from König's theorem to Ruitishauser's qd-algorithm.

Householder's professional contributions are too numerous to list in their entirety. He was vice president of the American Mathematical Society, and president of SIAM and the Association for Computing Machinery. He served on the editorial boards of Psychometrika, Numerische Mathematik, Linear Algebra and Its Applications, and was editor in chief of the SIAM Journal on Numerical Analysis. He made his personal bibliography available in the form of a KWIK index on numerical algebra (he read French, German, and Russian with ease). And he organized the influential Gatlinburg conferences, which continue now under the name of the Householder Symposia.

While he was at ORNL, Householder was a Ford Professor at the University of Tennessee, where I took two courses from him. He taught Wednesday afternoons and Saturday mornings, which ensured that his classes were not overattended. Alston was not a polished lecturer, but his material, its clarity and organization, more than made up for it. Saturdays he would have us work problems from his texts - Alston never believed in armchair mathematics. I came away from his courses with an appreciation for the power of matrix methods and a sense of the history of the subject.

But Householder's greatest bequest is a personal one. Over time, I have collected a number of recollections and testimonials concerning Alston, and they all mention his integrity, his ability to work with difficult people, his evenhandedness. It is said that intellectual disciplines take on the coloration of their founders. If that is so, the general good will that prevails in numerical linear algebra is in no small part due to Householder's legacy of decency.

G. W. StewartUniversity of Maryland