矩阵方程AXB=C的广义中心对称解及其最佳逼近

Generalized central symmetric solution of matrix equation AXB=C and its optimal approximation

利用矩阵对的广义奇异值分解,给出了矩阵方程AXB=C广义中心对称解的充要条件和通解表达式,证明了在矩阵方程AXB=C的广义中心对称解集合中存在唯一与给定矩阵X*的最佳逼近解,给出了求解最佳逼近解的数值算法和数值例子.

By the generalized singular value decompositions of the matrix pair,the necessary and sufficient conditions is established for the existence and the expressions for the generalized central symmetric solution of the matrix equation AXB =C,the result shows that there is an unique optimal approximation solution to a given matrix in Frobenius norm in the generalized central symmetric solution set of matrix equation AXB =C,and numerical algorithms and numerical experiments are presented to compute the unique optimal approximation solution.