矩阵方程AXB+CYD=E的双中心最小二乘问题  

Least Squares Double Center Problem of the Matrix Equation AXB+CYD=E with the Least Norm

作　　者：梁艳芳[1] 袁仕芳[1] 

机构地区：[1]五邑大学数学与计算科学学院,广东江门529020

出　　处：《五邑大学学报（自然科学版）》2014年第4期6-12,共7页Journal of Wuyi University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11301397);江门市科技攻关项目

摘　　要：利用矩阵的Kronecker积、列拉直算子和Moore-Penrose广义逆,讨论矩阵方程AXB+CYD=E的双中心最小二乘问题,得到双中心极小范数最小二乘解和对称双中心极小范数最小二乘解的表达式,给出求双中心极小范数最小二乘解的数值解法和数值例子.Given matrices of A∈R^m×n , B∈R^n×s , C∈Rm×k , D∈Rk×s ,E∈R^m×s using the Kronecker product, the Vec-operation and Moore-Penrose generalized inverse of matrices, we derive the expressions of the least squares double center solution with the least norm and the least squares symmetric double center solution with the least norm of the matrix equation ＋ =AXB CYD E . We also provide a numerical algorithm and numerical experiments for finding the least squares double center solution with the least norm.

关 键 词：双中心矩阵 对称双中心矩阵 最小二乘解 极小范数解 MOORE-PENROSE广义逆 KRONECKER积 

分 类 号：O241.2[理学—计算数学]