矩阵方程AXB+CYD=E的反中心对称极小范数最小二乘解

Least Squares Anti-centro-symetric Solution of the Matrix Equation AXB+CYD=E

利用矩阵的Kronec ker积和Moore-Penrose广义逆以及拉直算子,研究矩阵方程AXB+CYD=E的反中心对称极小范数最小二乘解,得到了解的表达式,并给出了数值算法和例子。

By using Moore-Penrose generalized inverse and the Kronecker product of matrices and straightening operator,the expression of the least squares anti-centro-symetric soluion of the marix equation AXB+CYD=E with the least norm is derived,and it provides a numerical algorithm and numerical experiment.