复参数HSS迭代法求解非Hermitian正定线性方程组

Complex Parameter HSS Iteration Method for Non-Hermition Linear Equations

将实参数的Hermitian/斜-Hermitian分裂(HSS)迭代法推广到复参数Hermitian/斜-Hermitian分裂(CHSS)迭代法,并证实CHSS迭代法是无条件收敛的。理论分析显示:CHSS迭代法的致缩因子的上界依赖系数矩阵Hermitian部分的谱,与矩阵的特征向量无关。数值例子显示方法的有效性。

In this paper,a real parameter for the Hermitian and skew-Hermitian splitting(HSS) iteration method was extended to a complex parameter for the Hermitian and skew-Hermitian splitting(CHSS) iteration method.It is shown that the CHSS iteration method converges unconditionally to the unique solution of the system of linear equations.Theoretical analysis shows that an upper bound of the contraction factor of the CHSS iteration method depends on the spectrum of the Hermitian part,and is independent of the eigenvectors of the matrices involved.Numerical examples are given to illustrate the efficiency of the presented methods.