Obituaries: Ralph Byers

January 6, 2008

Ralph Byers, 1955-2007

Ralph Byers passed away on Saturday, December 15, 2007, after a long and hard fight against cancer. He is survived by his wife, Margaret Bayer, and his daughters, Ruth and Nora.

Ralph received a bachelor's degree in mathematics from McGill University in 1977, and a master's (1980) and doctorate (1983) in applied mathematics from Cornell University, under the supervision of Charles Van Loan.

After postdoctoral fellowships at Northern Illinois University (1983–1985) and North Carolina State University (1985–1987), he moved to the University of Kansas in 1987. He spent the remainder of his career as a professor of mathematics at Kansas, with visiting positions at Universität Bielefeld (1990), Lawrence Berkeley National Laboratory (2003), and TU Berlin (2004). He was an associate editor of Systems and Control Letters from 1993 to 1998 and, from 2003 on, of Linear Algebra and its Applications.

Ralph was very well known for his research in applied and numerical linear algebra, in particular in the areas of numerical methods for eigenvalue and control problems. In 1984 he shared the prestigious Householder Award with J.W. Demmel. Ralph was recognized for his PhD thesis, Hamiltonian and Symplectic Algorithms for the Algebraic Riccati Equation, in which he made a breakthrough in the problem of finding a strongly stable numerical method of complexity n^3 for the solution of n x n Hamiltonian and symplectic eigenvalue problems. Numerical methods for these problems and their generalizations to matrix pencils are at the heart of many techniques in robust and optimal control.

Ralph was also one of the first to derive numerically stable methods for computing the distance of a control system to instability and uncontrollability, and he and his co-authors were instrumental in making the sign function method and the Kleinman–Newton method standard techniques for the solution of Riccati equations, in particular for large-scale control problems on parallel computers.

Ralph was at the forefront of research on extending the classical results for standard state–space systems to generalized state–space systems (descriptor systems) and, recently, to higher-order systems and matrix polynomials as well. A highlight in this direction is his work with Peter Benner on a newly designed pencil arithmetic, which allows many computational control problems for generalized state–space systems to be addressed in a uniform way.

Another hard problem that occupied Ralph for many years was the convergence behavior of the QR algorithm and the numerical problems that arise with the use of a large number of shifts to introduce matrix–matrix operations into the iteration. Ralph, together with his PhD student Karen Braman and co-author Roy Mathias, addressed this problem in ground-breaking work for which the group received the 2003 triennial SIAM Activity Group on Applied Linear Algebra Prize and a 2005 SIAM Outstanding Paper Prize. In the last three years, Ralph spent endless hours implementing this new multishift QR algorithm with aggressive deflation so as to make it available to the community within the LAPACK library.

Ralph was always open to new mathematical ideas, but it was a distinct feature of his personality to be extremely careful and thorough when it came to publishing or implementing his results, and to refereeing the work of others. He never took the easy and fast path and was always critical of his own work. Several of my students and postdocs and I, having met Ralph during his research visits in Germany, continued to work with him over the years. We enjoyed this attitude, as well as his warm and friendly nature, and his subtle humor.

Ralph was very much a family man, the well-being of his family and the education and future of his daughters always having the highest priority for him.

The numerical linear algebra community has lost a great scientist and, for many of us, a very good friend.---Volker Mehrmann, Institut für Mathematik, Technische Universität Berlin.

Thanks to Peter Benner, Daniel Kressner, and Hongguo Xu for helpful comments on a draft of this obituary.

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