Obituary: Richard S. Varga

By Volker Mehrmann and Daniel B. Szyld 

Richard S. Varga, a giant in the applied mathematics community, passed away peacefully on February 25, 2022. He was 93 years old.

Richard grew up in Cleveland, Ohio, within a Hungarian-American community. He was very proud of his heritage and often referred to this community in conversation. His father was a tool maker and his mother worked as a secretary at a local Hungarian newspaper; she was also an expert in passementerie sewing (elaborate edging or trimming for clothing or upholstery). During his youth, Richard played ping-pong and was on the wrestling team. He met Esther Marie Pfister within the Hungarian milieu and married her in 1951. They had one daughter, Gretchen, whom he adored. Richard was also especially fond of his two grandsons, Maximilian and Alexander.

Richard received his B.S. in mathematics at Case Institute of Technology (now Case Western Reserve University) in 1950. He was planning to accept a job as an actuary in Cedar Rapids, Iowa, but changed his plans at the urging of Max Morris, a professor at Case who encouraged him to “Bet on himself,” borrow some money, and apply to graduate school at Harvard (it was too late in the year for Richard to receive an assistantship). So he borrowed $1,500 from his father, applied to Harvard in July 1950, and began his graduate studies that September.

Richard earned his Ph.D. from Harvard University in 1954 under the direction of Joseph Walsh; his thesis was titled “Properties of a Special Set of Entire Functions and Their Respective Partial Sums.” He also worked with Garrett Birkhoff while at Harvard, and continued to collaborate with him after graduation on positive matrices (and positive operators on partially ordered vector spaces) as well as iterative methods for linear systems that arise in the discretization of differential equations. 

After Richard’s graduation from Harvard, Paul Garabedian recruited him to work at Westinghouse's Bettis Atomic Power Laboratory in Pittsburgh, Pa. Richard knew that he would not be drafted for the ongoing Korean War if he accepted such an “essential” role. His work at Westinghouse related to the design of nuclear reactors for submarines and aircraft carriers, and some of his early papers addressed the solutions of equations that pertained to these reactors. Soon, Richard was engaging with numerical methods and matrix theory. His first paper in a SIAM journal—which appeared in the Journal of the Society for Industrial and Applied Mathematics, now the SIAM Journal on Applied Mathematics—published in 1957 and is titled “A Comparison of the Successive Overrelaxation Method and Semi-iterative Methods using Chebyshev Polynomials” [7].

In 1958, Richard published a paper with John Holladay entitled “On Powers of Non-negative Matrices” in the Proceedings of the American Mathematical Society (AMS) [6]. This and other works trace his intellectual trajectory in the first decade after his Ph.D. Richard published two papers on alternating implicit methods with Birkhoff [1] and David Young [2], a third on the same topic with James Douglas and R.B. Kellogg [3], and two seminal papers with Gene Golub on “Chebyshev Semi-iterative Methods, Successive Overrelaxation Iterative Methods, and Second Order Richardson Iterative Methods” [4, 5].

Much of this material ended up in Richard’s very influential book Matrix Iterative Analysis, which published in 1962 when he was just 33 years old [8]. Richard received a Guggenheim Fellowship that same year — the first of many honors and awards. He later received a Senior Humboldt Fellowship and the Hans Schneider Prize in Linear Algebra from the International Linear Algebra Society. Richard was also both a SIAM and AMS Fellow, and held honorary degrees from the University of Karlsruhe and the University of Lille. 

In addition to his many contributions in matrix computations and numerical analysis, Richard studied approximation theory as well. He focused especially on Padé approximation and analytic number theory, including high-precision calculations that pertained to disproving the Riemann hypothesis. 

Richard became a professor of mathematics at Case in 1960, then moved to Kent State University 10 years later and stayed there until his retirement in 2007. While at Kent, he created the Institute for Computational Mathematics, which became an important locus of activity that hosted multiple conferences and a large cast of visitors. 

Richard’s editorial work was extensive. He served on the editorial boards of a dozen journals, including the SIAM Journal on Matrix Analysis and Applications. He was also editor-in-chief of Numerische Mathematik for an impressive 16 years, beginning in 1988. Together with Lothar Reichel and Arden Ruttan, Richard founded the Electronic Transactions on Numerical Analysis in 1993 and served as co-editor-in-chief until 2009.

Richard was a “founding father” of the field that we now call numerical linear algebra. In 1958, he attended the Conference on Matrix Computations at Wayne State University with Young, Cornelius Lanczos, Peter Henrici, Heinz Bauer, James H. Wilkinson, Alston Householder, William Kahan, and Herbert Keller. During a 1960 summer session at the University of Michigan, a group of people including Richard, Young, Bauer, Henrici, Wilkinson, Olga Taussky Todd, John Todd, Wallace Givens, and George Forsythe decided to hold another meeting on matrix computations. In 1961, Householder organized such a meeting in Gatlinburg, Tenn. This conference was the first of a series of meetings that took place in Gatlinburg and later elsewhere. Today these meetings take place every three years and are called the Householder Symposia. Richard organized the first conference in the series that was outside of Gatlinburg; it was held in Los Alamos, N.M., in 1972.

Richard had a very congenial personality and was generous with his time. He helped younger researchers in many ways; carefully educated his graduate students in proper mathematical writing, paper review processes, and presentation delivery; and supported them in their careers. 

We recall a moment from a dinner during a past SIAM meeting in Madison, Wis. While at a table with half a dozen younger colleagues, Richard looked around and said, “I think that at one point or another I wrote letters of recommendation for each of you.” He has in fact influenced the careers of many friends and colleagues through his scientific work, conference and editorial contributions, and the example of his life. He will be deeply missed.

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References
[1] Birkhoff, G., & Varga, R.S. (1959). Implicit alternating direction methods. Trans. Amer. Math. Soc., 92, 13-24.
[2] Birkhoff, G., Varga, R.S., & Young, D. (1962). Alternating direction implicit methods. Adv. Comput., 3, 189-273.
[3] Douglas Jr., J., Kellogg, R.B., & Varga, R.S. (1963). Alternating direction iteration methods for n space variables. Math. Comput., 17(83), 279-282.
[4] Golub, G.H., & Varga, R.S. (1961). Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods: Part I. Numer. Mathe., 3(1), 147-156.
[5] Golub, G.H., & Varga, R.S. (1961). Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods: Part II. Numer. Mathe., 3(1), 157-168.
[6] Holladay, J.C., & Varga, R.S. (1958). On powers of non-negative matrices. Proceed. AMS, 9(4), 631-634.
[7] Varga, R.S. (1957). A comparison of the successive overrelaxation method and semi-iterative methods using Chebyshev polynomials. J. Soc. Indust. Appl. Math., 5(2), 39-46.
[8] Varga, R.S. (1962). Matrix iterative analysis. Englewood Cliffs, NJ: Prentice Hall.

Volker Mehrmann is a professor of numerical mathematics at the Technische Universität Berlin, president of the European Mathematical Society, and co-founder of the European Service Network of Mathematics for Industry and Innovation. His research interests include numerical mathematics/scientific computing, applied and numerical linear algebra, control theory, and the theory and numerical solution of differential-algebraic equations.

Daniel B. Szyld is a professor in the Department of Mathematics at Temple University and a former SIAM Vice President-at-Large. He is a SIAM representative to the Mathematical Council of the Americas.