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

美德合作研究：结构化特征值问题与控制的数值方法

• 批准号: 8922444
• 负责人: Ralph Byers
• 金额: --
• 依托单位: University of Kansas Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-08-01 至 1994-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8922444&HistoricalAwards=false
• 关键词: US; Federal; Republic; Germany; Cooperative

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.

该奖项支持堪萨斯大学的Ralph Byers教授与联邦德国比勒费尔德大学的Angelika Bunse-Gerstner教授和Volker Mehrmann教授进行数学合作研究。他们正在研究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密切相关。合作者将设计数值方法来测量这些距离。他们将研究真实的、复杂的和结构化的扰动。这项工作将有助于工程师和科学家认识病态问题，并制定数学模型帽子避免病态。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。数值方法的进展落后于计算机体系结构的进展，因此很难利用先进计算机的并行性和理论峰值计算速度。合作者将为结构特征值问题组装一套基本程序。通过设计利用结构矩阵的数学性质的计算机算法，这项工作将帮助工程师和科学家解决大型计算问题。