Numerical Methods and Mathematics for Structured Eigenvalue and Inverse Eigenvalue Problems

结构化特征值和逆特征值问题的数值方法和数学

• 批准号: 8820882
• 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: 1989
• 资助国家: 美国
• 起止时间: 1989-04-01 至 1991-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8820882&HistoricalAwards=false
• 关键词: Numerical; Methods; Mathematics; Structured; Eigenvalue

The investigator will design numerical methods for structured eigenvalue problems that arise in Engineering and Scientific computation. Goals include improved numerical stability and improved performance on computers with advanced architectures. Toward this end, the investigator will complete a small set of algorithms that serve as "ingredients" in recipes for structure preserving algorithms. Possible "ingredients" include tearing methods like Divide and Conquer, simultaneous diagonalization, and variant QR and Jacobi algorithms. The second area of study is methods for assigning eigenvalues by state and output feedback to regions of the complex plane. Robust assignment to regions improves reliability of linear control systems by making them less likely to fail due to perturbations or uncertainty in the data. Research will be in the direction of selecting structured objective functions and designing specialized optimization methods. The third area of study is computational measure of the distance from a controllable pair to the nearest uncontrollable pair. Success here hopefully will generalize to a means of estimating the distance of a generic matrix pencil to an algebraic variety of nongeneric pencils and to general condition estimators.

研究人员将设计用于工程和科学计算中出现的结构特征值问题的数值方法。目标包括提高的数值稳定性和具有高级体系结构的计算机的性能。为此，研究人员将完成一系列的算法，这些算法用作保存算法的结构配方中的“成分”。可能的“成分”包括撕裂方法，例如分裂和征服，同时对角线化以及变体QR和Jacobi算法。研究的第二个领域是通过状态分配特征值的方法，并将输出反馈分配给复杂平面的区域。对区域的强大分配可通过使线性控制系统的可靠性提高，从而使它们由于数据中的扰动或不确定性而导致失败的可能性降低。研究将朝着选择结构化目标函数和设计专业优化方法的方向。研究的第三个领域是从可控对到最近不可控制的对的距离的计算度量。希望这里的成功能够概括为估计通用基质铅笔距离的一种方法，并估计多种非元素铅笔和一般状况估计器的距离。