矩阵方程AXB+CXTD=E自反最佳逼近解的迭代算法
AN ITERATIVE ALGORITHM FOR THE REFLEXIVE OPTIMAL APPROXIMATION SOLUTION OF MATRIX EQUATIONS AXB + CXTD=E

本文研究了Sylvester矩阵方程AXB+CXTD=E自反(或反自反)最佳逼近解.利用所提出的共轭方向法的迭代算法,获得了一个结果:不论矩阵方程AXB+CXTD=E是否相容,对于任给初始自反(或反自反)矩阵X1,在有限迭代步内,该算法都能够计算出该矩阵方程的自反(或反自反)最佳逼近解.最后,三个数值例子验证了该算法是有效性的.
In this paper, we study the optimal approximation solutin of the Sylvester matrix equations AXB + CXTD=E over reflexive (anti-reflexive) matrices. By using the proposed conjugate direction method, we get a result that whatever matrix equations AXB + CXTD=E are consistent or not, for arbitrary initial reflexive (anti-reflexive) matrix X1, the reflexive (anti-reflexive) optimal approximation solution can be obtained within finite iteration steps in the absence of round-off errors. The effectiveness of the proposed algorithm is verified by three numerical examples