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

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.