An iterative method for the least squares symmetric solutions of the generalized coupled Sylvester matrix equations

摘要

In this paper, an iterative method is proposed to solve the minimum Frobenius norm residual problem: min equations with unknown symmetric matrices X and Y. By this method, its solutions can be obtained for any initial symmetric matrices X1 and Y1 in finite iterative steps. In addition, the least-norm solutions can also be obtained by choosing a special kind of initial symmetric matrices.