一类矩阵方程的反中心对称最小二乘解

Least-squares Solutions of Matrix Equation Over Anti-centrosymmetric Matrices

研究矩阵方程AX+B Y=Z的最小二乘反中心对称解,给出了AX+B Y=Z的反中心对称最小二乘解,导出了AX+B Y=Z有反中心对称解的充分必要条件。在AX+B Y=Z的反中心对称最小二乘解集合中求与给定矩阵最佳逼近的解,给出求解最佳逼近解的数值算法与数值例子。

The least-squares solutions of the matrix equation AX＋BY=Z with respect to anti-centrosymmetric matrices A and B is considered.The general expression of the solution is given and some necessary and sufficient conditions are derived for the solvability of the matrix equation AX＋BY=Z.The optimal approximation to given matrices from the least-squares solution set of AX＋BY=Z is provided.The algorithm and numerical example for solving optimal approximation solution are included.