This award supports Professor Ralph Byers of the University of Kansas for collaborative research in mathematics with Professors Angelika Bunse-Gerstner and Volker Mehrmann at the University of Bielefeld, Federal Republic of Germany. They are working on numerical methods for structured eigenvalue problems and control. The distance from a controllable pair to the nearest uncontrollable pair is closely related to the conditioning of control problems. The collaborators will design numerical methods to measure such distances. They will study real, complex and structured perturba- tions. This work will help engineers amd scientists to recognize ill-conditioned problems and to formulate mathematical models hat avoid ill-conditioning. Structured eigenvalue problems arise frequently in control and other engineering and scientific computations. Progress in numerical mehtods has lagged behind progress in computer architecture, so it is difficult to take advantage of the parallelism and theoretical peak computation rate of advanced computers. The collaborators will assemble a set of basic procedures for structured eigenvalue problems. By designing computer algorithms that exploit the mathematical properties of structured matrices, this work will help engineers and scientists solve large computational problems.
