  By applying the minimal residual technique to the Hermitian and
skew-Hermitian (HSS) iteration scheme, we introduce a non-stationary iteration
method named minimal residual Hermitian and skew-Hermitian (MRHSS) iteration
method to solve the continuous Sylvester equation. Numerical results verify the
effectiveness and robustness of the MRHSS iteration method versus the HSS
method for the continuous Sylvester equation. Moreover, by numerical
computation, we show that the MRHSS splitting can be used as a splitting
preconditioner and induce accurate, robust and effective preconditioned Krylov
subspace iteration methods for solving the continuous Sylvester equation.
