Mathematical Sciences: Matrix Differential Equations and Their Applications

本研究涉及矩阵的动力学 微分方程及其应用 了方程 在一个相当通用的框架中进行转换， 在一些重要的数值算法中发现的实例。 的 将探讨每个矩阵微分方程的动力学 通过计算机实验，高分辨率图形和符号 操作，结合分析。 目标是 更好地理解矩阵微分方程的动力学， 并研究与此密切相关的问题， 特殊结构矩阵的特征值和奇异值。 这项研究有望找到重要应用 从开发新的计算算法， 微分方程新问题的理论解， 线性代数

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.