摘要
本文讨论了子矩阵约束下一类矩阵方程的实矩阵解问题。基于矩阵的奇异值分解和广义奇异值分解方法,给出了该问题有解的充要条件和解的一般表达式。并证明了对任一给定的实矩阵,在上述解集合中必存在唯一的最佳逼近解,给出了最佳逼近解的形式。
The problem of finding real matrix solutions for a class of matrix equation under a submatrix constraint is discussed. Based on the singular value decomposition and generalized singular value decomposition methods, the necessary and sufficient conditions for the existence of solutions and their general expression are given. Moreover, for a given real matrix, we prove a unique optimal approximation solution exists in the above previous solution set, and the expression of the optimal approximation solution is also derived.
出处
《工程数学学报》
CSCD
北大核心
2007年第5期913-918,共6页
Chinese Journal of Engineering Mathematics
关键词
矩阵方程
子矩阵
矩阵范数
最佳逼近
matrix equation
submatrix
matrix norm
optimal approximation
