In this paper, we consider finding the interval constrained solutions of the matrix equation  That is: Given matrices A, B, C, D, Land U, find Xsuch that  and  where  means that  and  are nonnegative matrices. We propose an iterative method for solving matrix inequality least squares problem. According to the results obtained by an iterative method and known results about the matrix equations, the consistent conditions and the general expressions for the solutions of the matrix equation are given. Numerical experiments are given to illustrate the efficiency of the method.

nonnegative matrix, iterative method, matrix equation, matrix inequality.