关于一般耦合矩阵方程的迭代对称解

ON THE ITERATIVE SYMMETRIC SOLUTIONS OF THE GENERAL COUPLED MATRIX EQUATIONS

本文构造了一个有效的迭代方法(CGL)去求解一般耦合矩阵方程的对称解.若一般耦合矩阵方程关于对称解相容,则对于任意给定的初始对称矩阵组,利用所构造的迭代算法,都能在有限步迭代出所求问题的一组对称解,若选用一些特殊的初值,则可获得矩阵方程的极小范数对称解.最后的数值例子表明了所给算法的有效性.

In this paper, a conjugate gradient-like iterative method （CGL） is presented to find the symmetric solutions of the general coupled matrix equations. When the general coupled matrix equations has symmetric solutions, then we can find the symmetric solutions by CGL iterative method for any symmetrical initial matrix group within finite iterative steps. Also, the least norm symmetric solution can be obtained by properly choosing a group of initial matrices. Finally, we test the algorithm and show its effectiveness by using a numerical example.