矩阵方程AXA^H=B的Hermitian R-对称形式的最小二乘解  

Least Squares Solution for Hermitian R-symmetric Matrices of Matrix Equation AXA^H= B

作　　者：张秀英 ZHANG Xiu-ying(International Education Teachers School, Changchun Normal University, Changchun Jilin 130032, China)

机构地区：[1]长春师范大学国际教师教育学院,吉林长春130032

出　　处：《长春师范大学学报》2018年第12期4-9,12,共7页Journal of Changchun Normal University

基　　金：长春师范大学自然科研项目"指数积分方法实施的高效算法设计研究"(长师[2016]第03号)

摘　　要：本文以Hermitian R-对称矩阵的结构为基础,研究了复矩阵方程AXA^H=B的Hermitian R-对称解的结构.首先利用奇异值分解,给出了其Hermitian R-对称形式的最小二乘解的表达式;进一步利用商奇异值分解,得到其极小范数最小二乘解的表达式.Based on the structure of Hermitian R-symmetric matrices,least squares solutions to the matrix equation AXA^H=B in the set of Hermitian R-symmetric matrices are considered.Using SVDs,the analytic expressions are obtained,then general form for the minimal norm least squares solutions is derived by Q-SVD.

关 键 词：最小二乘解 极小范数解 HERMITIAN R-对称 奇异值分解 

分 类 号：O24[理学—计算数学]