Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations

The consistent conditions and the general expressions about the Hermitian solutions of the linear matrix equations A X B = C and (A X, X B) = (C. D) are studied in depth, where A, B, C and D are given matrices of suitable sizes. The Hermitian minimum F-norm solutions are obtained for the matrix equations A X B = C and (A X, X B) = (C, D) by Moore-Penrose generalized inverse, respectively. For both matrix equations, we design iterative methods according to the fundamental idea of the classical conjugate direction method for the standard system of linear equations. Numerical results show that these iterative methods are feasible and effective in actual computations of the solutions of the above-mentioned two matrix equations. Copyright (C)c 2006 John Wiley & Sons, Ltd.