论文标题
预处理的MHSS迭代算法及其求解复杂Sylvester矩阵方程的加速方法
Preconditioned MHSS iterative algorithm and its accelerated method for solving complex Sylvester matrix equations
论文作者
论文摘要
本文介绍并分析了对遗传学和偏斜式分裂（PMHSS）的预处理修改。较大的稀疏连续sylvester方程是通过基于非赫米特式，复杂的，正定/半芬矿和对称矩阵的PMHSS迭代算法求解的。我们证明，PMHSS在适当的条件下收敛。此外，我们提出了一种加速PMHSS方法，该方法由两个预处理矩阵和两个迭代参数α，\ b {eta}组成。理论分析表明，与PMHSS相比，加速PMHS的收敛速度更快。同样，在数值实验中证明了所提出的两种迭代算法的鲁棒性和效率。
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 α, \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.
