US-Federal Republic of Germany Cooperative Research: Numerical methods for Structured Eigenvalue Problems and Control

该奖项支持堪萨斯大学的Ralph Byers教授与德意志联邦共和国比勒费尔德大学的Angelika Bunse-Gerstner教授和Volker Mehrmann教授在数学方面的合作研究。他们致力于结构特征值问题和控制的数值方法。从可控对到最近的不可控对的距离与控制问题的条件性密切相关。合作者将设计数字方法来测量这样的距离。他们将研究真实的、复杂的和结构化的扰动。这项工作将帮助工程师和科学家识别病态问题，并建立避免病态的数学模型。结构特征值问题经常出现在控制和其他工程和科学计算中。数值方法的发展滞后于计算机体系结构的发展，因此很难利用先进计算机的并行性和理论峰值计算速度。合作者将汇编一套结构化特征值问题的基本程序。通过设计利用结构化矩阵的数学特性的计算机算法，这项工作将帮助工程师和科学家解决大型计算问题。

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.