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.

翻译：本文介绍并分析了对Hermitian和Skew-Hermitian分割(PMHS)的前提条件修改。大型稀有连续的Sylvester方程式由PMHSS基于非Hermitian、复杂、正确定/semidefite和对称矩阵的迭代算法解决。我们证明PMHSS是在适当条件下趋同的。此外,我们提议加速的PMHSS方法由两个先决条件矩阵和两个迭代参数(pha},\b{eta})组成。理论分析表明,加速的Sylvester方程式的趋同速度比PMHSS更快。此外,拟议的两种迭代算法的稳健性和效率在数字实验中得到了证明。