Mathematical Sciences: Matrix Differential Equations and Their Applications

数学科学：矩阵微分方程及其应用

• 批准号: 9123448
• 负责人: Moody Chu
• 金额: $ 7.87万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123448&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Matrix; Differential; Equations; Mathematical; Sciences; Matrix; Differential; Equations

This research is concerned with the dynamics of matrix differential equations and their applications. The equations are cast in a fairly general framework, generalizing special instances found in some important numerical algorithms. The dynamics of each matrix differential equation will be explored via computer experiments, high resolution graphics and symbolic manipulations, in conjunction with analysis. The objective is to better understand the dynamics of matrix differential equations, and to study the closely related questions regarding the eigenvalues and singular values of specially structured matrices. This study is expected to find important applications ranging from development of novel computational algorithms to theoretic solutions of new problems in differential equations and linear algebra.

这项研究涉及矩阵微分方程及其应用的动态。 这些方程是在相当通用的框架中施放的，在某些重要的数值算法中概括了特殊实例。 每个矩阵微分方程的动力学将通过计算机实验，高分辨率图形和符号操作探索，并结合分析。 目的是更好地了解矩阵微分方程的动力学，并研究有关特殊结构矩阵的特征值和奇异值的密切相关的问题。 预计这项研究将发现重要的应用，从新的计算算法的发展到微分方程和线性代数中新问题的理论解决方案。