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.

研究者将为工程和科学计算中出现的结构化特征值问题设计数值方法。目标包括改进数字稳定性和改进具有先进体系结构的计算机的性能。为此，研究者将完成一小部分算法，作为结构保存算法配方中的“成分”。可能的“成分”包括撕裂方法，如分而治之，同时对角化，以及变体QR和Jacobi算法。第二个研究领域是根据状态和输出反馈给复平面区域分配特征值的方法。鲁棒区域分配提高了线性控制系统的可靠性，使它们不太可能因数据中的扰动或不确定性而失效。研究方向将是选择结构化的目标函数和设计专业化的优化方法。研究的第三个领域是从可控对到最近的不可控对的距离的计算度量。这里的成功有望推广到估计一般矩阵铅笔到非一般铅笔的代数变化和一般条件估计量的距离的方法。