Symmetric Solution of a Class of Matrix Equations and its Optimal Approximation Solution

In this paper,an iterative method is presented to find the symmetric solution of the matrix equations AiXBi + CiXDi = Fi (i = 1,2).By this iterative method,the solvability of the matrix equations can be determined automatically. A symmetric solution can be obtained within finite iterative steps when the matrix equations is consistent,and the symmetric solution with least norm can be obtained by choosing a special kind of initial symmetric matrices. In addition,the optimal approximation solution to a given symmetric matrix can be obtained.