Two algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of Sylvester matrix equations

In this paper, we propose two iterative algorithms for finding the Hermitian reflexive and skew-Hermitian solutions of the Sylvester matrix equation AX + XB = C, respectively. We prove that the first (second) algorithm converges to the Hermitian reflexive (skew-Hermitian) solution for any initial Hermitian reflexive (skew-Hermitian) matrix. Finally, two numerical examples illustrate the theoretical results. (C) 2010 Elsevier Ltd. All rights reserved.