Abstract. In this paper, we propose some new algorithms based on Her- mitian and skew-Hermitian splitting methods for solving a class of Sylvester equations AX + XB = C, where both coecient matrices A and B are (non- Hermitian) positive semi-denite, and at least one of them is positive denite, and obtain some HSS-like iterations for solving Sylvester equations. Some numerical examples illustrating the eectiveness of these algorithms are pre- sented.

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