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.