  This paper introduces and analyzes a preconditioned modified of the Hermitian
and skew-Hermitian splitting (PMHSS). The large sparse continuous Sylvester
equations are solved by PMHSS iterative algorithm based on nonHermitian,
complex, positive definite/semidefinite, and symmetric matrices. We prove that
the PMHSS is converged under suitable conditions. In addition, we propose an
accelerated PMHSS method consisting of two preconditioned matrices and two
iteration parameters {\alpha}, \b{eta}. Theoretical analysis showed that the
convergence speed of the accelerated PMHSS is faster compared to the PMHSS.
Also, the robustness and efficiency of the proposed two iterative algorithms
were demonstrated in numerical experiments.
