迭代求解非Hermitian正定线性方程组的衍生多分裂方法（英文）  

The Derived Multisplitting Method for Iteratively Solving Non-Hermitian Positive Definite Linear Systems

作　　者：温瑞萍[1] 李苏丹 

机构地区：[1]太原师范学院工程科学计算山西省高校重点实验室,山西太原030012

出　　处：《应用数学》2018年第1期1-11,共11页Mathematica Applicata

基　　金：supported by NSF of China(11371275);NSF of Shanxi Province(201601D011004)

摘　　要：本文研究迭代求解非Hermitian正定线性方程组的问题.在系数矩阵HS分裂的基础上,提出了一种新的衍生并行多分裂迭代方法.通过参数调节分配反Hermitian部分给Hermitian部分的多分裂来衍生出非Hermitian正定系数矩阵的并行多分裂迭代格式,并利用优化技巧来获得权矩阵.同时,建立算法的收敛理论.最后用数值实验表明了新方法的有效性和可行性.In this paper, we propose a derived multisplitting method for iteratively solving non-Hermitian positive definite linear systems Ax=b. Based on the Hermitian and skew-Hermitian（HS） splitting A=H＋S,we further derive the multisplitting of A by splitting the Hermitian part H into multisplitting scheme. Moreover, by choosing the weighting matrices based on the optimization models, the convergence of the multisplitting iteration method is established. Finally, the numerical examples show the feasibility and effectiveness of the derived multisplitting method.

关 键 词：多分裂 Hermitian与反Hermitian分裂 非Hermitian正定 收敛性 

分 类 号：O241.6[理学—计算数学]