Ralph Byers 1955 – 2007

After a long and hard fight against cancer, Ralph Byers passed away on Saturday December 15, 2007. He is survived by his wife Margaret Bayer and his daughters Ruth and Nora. Ralph received his bachelors degree in Mathematics from McGill University in 1977, his masters degree in 1980 and his doctorate in Applied Mathematics from Cornell University in 1983 under the supervision of Charles Van Loan. He spent post-doc periods at Northern Illinois University from 1983 to 1985 and North Carolina State University from 1985 to 1987. Since 1987 he had been a professor of Mathematics at the University of Kansas. He had visiting positions at Universität Bielefeld in 1990, Lawrence Berkeley National Laboratory in 2003, and TU Berlin in 2004. Ralph served as associate editor of Systems and Control Letters from 1993 to 1998 and Linear Algebra and its Applications since 2003. 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 received the prestigious triennial Householder award (shared with J. Demmel) for his Ph.D. Thesis [1] in which he made a breakthrough towards the problem, known as Van Loan’s curse, of finding a numerically strongly stable method of complexityn3 for the solution of Hamiltonian and symplectic eigenvalue problems. These problems are at the heart of numerical methods in many control applications, in particular in optimal control of continuous and discrete time systems. Ralph’s contributions to these eigenvalue problems and their generalizations, together with the associated methods for solving algebraic Riccati equations, [3,6,9,13,15,20,45,42] present the state of the art in solving these problems. Ralph, together with coauthors also implemented these methods as production code [38]. By carefully analyzing the (potentially numerically unstable) sign function method and by providing a step-size control for the Kleinman–Newton method for the algebraic Riccati equations, Ralph and his coauthors were instrumental to make these methods standard techniques in the solution of Riccati equations [9,20,23,24,25,55], in particular for large scale control problems on parallel computer architectures [39,41]. In his research, Ralph always had a strong interest in the conditioning of numerical problems and the stability analysis of numerical methods in the presence of round-off errors or perturbations. This has led to many contributions on the conditioning of matrix equations and invariant subspaces [2,4,5,8,47]. His interest in considering the extreme and worst case analysis also led to his research on distance problems. The determination of the distance of a control system to the nearest unstable or uncontrollable system are very important problems in the analysis of robustness of real world control applications. Ralph was one of the first to derive numerically stable methods for the computation of such distances [10,14,29,36,51].