In this paper, we consider finding the interval constrained symmetric solutions of the matrix equation  That is: Given matrices A, B, L and U, find a symmetric matrix X such that  and  where  means that  and  are nonnegative matrices. By presenting an iterative method for solving matrix inequality  the necessary and sufficient conditions for the solvability of the matrix equation  with  are established. Numerical experiments to illustrate the efficiency of the method are also given.

iterative method, matrix equation, matrix inequality.