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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (8): 61-65.doi: 10.6040/j.issn.1671-9352.0.2015.402

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基于超松弛迭代的MHSS加速方法

王洋1,赵彦军2*,冯毅夫1   

  1. 1.吉林师范大学数学学院, 吉林 四平 136100;2.东北师范大学人文学院, 吉林 长春 130117
  • 收稿日期:2015-08-24 出版日期:2016-08-20 发布日期:2016-08-08
  • 通讯作者: 赵彦军(1979— ),男,硕士研究生,讲师,研究方向为偏微分方程及其应用、应用时间序列与数据挖掘. E-mail:yjzchsnenu@163.com E-mail:yyang3721@163.com
  • 作者简介:王洋(1982— ),女,博士研究生,讲师,研究方向为微分方程数值解和数值代数. E-mail:yyang3721@163.com
  • 基金资助:
    吉林省教育厅“十三五”科学技术研究规划项目(2016210);四平市科技发展计划项目(2015052);吉林省教育厅项目(2015214)

On successive-overrelaxation acceleration of MHSS iterations

WANG Yang1, ZHAO Yan-jun2*, FENG Yi-fu2   

  1. 1. College of Mathmatics, Jilin Normal University, Siping 136100, Jilin, China;
    2. College of Humanities &
    Sciences of Northeast Normal University, Changchun 130117, Jilin, China
  • Received:2015-08-24 Online:2016-08-20 Published:2016-08-08

摘要: 修正的Hermite/反Hermite分裂(MHSS)迭代方法是一类求解大型稀疏复对称线性代数方程组的无条件收敛的迭代算法。基于超松弛(SOR)迭代技术,本文提出一类MHSS加速方法,分析了MHSS加速方法的收敛性质,给出了MHSS加速方法中参数ω的选取办法。数值实验证明了新方法能够有效地提高MHSS求解线性代数方程组的求解效率。

关键词: 收敛分析, 复对称线性系统, 对称/反对称分裂

Abstract: Modified Hermitian and skew-Hermitian splitting(MHSS)iteration method is an unconditionally convergent method for solving large sparse complex symmetric linear systems. Based on successive-overrelaxation technique, a class of accelerated MHSS iterative method is presented, then convergence theorems is established for the new method. Moreover, a selection method of the parameter ω is given. Numerical experiment demonstrate that new method can effectively improve the efficiency of MHSS iterative method for solving linear algebraic equations.

Key words: Hermitian/skew-Hermitian Splitting, convergence analysis, complex symmetric linear systems

中图分类号: 

  • O241.82
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