An iterative method for the least squares solutions of the linear matrix equations with some constraint

In this paper, an iterative method is presented to solve the following constrained minimum Frobenius norm residual problem: [GRAPHICS] where A(i) is a linear operator from R-mxn onto R-pixqi, C-i is an element of R-pixqi, i = 1, 2, ... , r, S = {X : X = B(X)}, and B is a linear self- conjugate involution operator. By this method, for any initial matrix X-0 is an element of S, a solution can be obtained in finite iteration steps in the absence of roundoff errors. The least norm solution can be derived when an appropriate initial matrix is chosen. In addition, the optimal approximation solution in the solution set of the above problem to a given matrix can also be derived by this method. Several numerical examples are given to show the efficiency of the proposed iterative method.