Iterative Method for Least Squares Reflexive Solution of General Linear Matrix Equation

On the base of conjugate gradient method of solving linear algebraic equations,an iterative method is presented to find the least squares reflexive solution of the general linear matrix equation and its convergence is proved.By the iterative method,the least squares reflexive solution can be obtained within finite iterative steps in the absence of round off errors.And the least squares solution with minimal norm can be obtained by choosing a special initial reflexive matrix.In addition,its optimal approximation matrix to a given matrix can be obtained.The given numerical examples show that the iterative method is quite efficient.