Abstract: An orthogonal projection iteration method for matrix equations AX=B,XC=D is studied.Firstly,the iterative method is constructed by using the theory of orthogonal projection and the properties of general matrix;secondly,its convergence is proved by using the singular value decomposition,the orthogonal invariance of F-norm and the properties for solutions of the matrix equations and the estimation of its convergence rate is obtained;finally,numerical examples are given to verify the validity of the algorithm.

Key words: matrix equations, general solution, orthogonal projection iteration method, optimal approximation, minimum norm solution