Abstract: The numerical algorithm of continuous Sylvester matrix equation is studied deeply, and a parameterized single step HSS iteration method is proposed innovatively. This method has a unique solution idea and its convergence is proved. In order to improve the performance, quasi-optimal parameters are found by minimizing the upper bound of the spectral radius of the iterative matrix. Numerical experiments verify the effectiveness and robustness of the new method, and demonstrate its high efficiency and stability in solving continuous Sylvester matrix equations, which provides a new tool for relevant numerical calculation.

Key words: continuous Sylvester equation, PSHSS iteration method, convergence analysis, numerical experiments