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拉尔夫·拜尔斯教授与德国联邦共和国比勒菲尔德大学的安吉利卡·邦斯 - 格斯特纳教授和沃尔克·穆尔曼（Angelika Bunse-Gerstner）和沃尔克·梅尔曼（Volker Mehrmann）合作研究。他们正在研究用于结构化特征值问题和控制的数值方法。从可控对到最近不可控制的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此类距离。他们将研究真实，复杂和结构化的努力。这项工作将帮助工程师AMD科学家认识到条件不足的问题，并制定数学模型帽子避免了不良条件。结构化特征值问题在控制以及其他工程和科学计算中经常出现。数值MEHTODS的进展落后于计算机架构的进展，因此很难利用高级计算机的并行性和理论峰值计算率。合作者将组装一组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。