求解复对称线性系统的改进EPGS迭代法

Improved EPGS Iterative Method for Solving Complex Symmetric Linear Systems

本文主要讨论求解复对称线性系统的EPGS迭代法。基于矩阵块三角分裂思想,我们对该方法引入一个加速参数后,得到了改进EPGS迭代法(IEPGS)。我们对IEPGS迭代法进行收敛性分析,给出了收敛性条件,并得到了最优迭代参数及相应的最优收敛因子。数值实验的结果进一步表明了该方法的有效性。

In this paper, we mainly discuss the EPGS iterative method for solving complex symmetric linear systems. Based on the idea of triangular splitting of matrix blocks, we introduce an acceleration parameter to this method and obtain the improved EPGS iterative method (IEPGS). We analyze the convergence of IEPGS iteration method, give the condition of convergence, and obtain the optimal iteration parameters and the corresponding optimal convergence factors. Numerical experiments show that the method is effective.