线性流形上一类矩阵方程的最佳逼近问题

THE BEST APPROXIMATE PROBLEM OF A CLASS OF MATRIX EQUATION ON THE LINEAR MANIFOLD

本文研究矩阵方程AXB=C在线性流形Γ={X∈SR^(n×n)|||TX-Y||=min}上的最佳逼近问题,得到了问题解的表达式．此外,还给出了求解该问题的数值算法和算例．

In this paper, the best approximate problem of the matrix equation AXB = C is studied on the manifold Г={X∈SR^n×n｜｜TX-Y｜｜=min}. At the same time, the expression of the best approximate solution and the corresponding numerical method are also given, and a numerical example is used to show the feasibility of this method.