华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (4): 26-34.

• 应用数学与基础数学 • 上一篇    下一篇

预条件AOR和2PPJ迭代法收敛性的注记

刘庆兵 1、2
陈果良 1
  

  1. 1. 华东师范大学~~数学系, 上海\; 200241;\quad 2. 浙江万里学院~~数学研究所, 浙江~~宁波\; 315100
  • 收稿日期:2008-10-06 修回日期:2008-12-06 出版日期:2009-07-25 发布日期:2009-07-25
  • 通讯作者: 陈果良

Note on the convergence of AOR and 2PPJ iterative methods

LIU Qing-bing$^{1,2}$, CHEN Guo-liang

  

  1. 1. {\it Department of Mathematics,\ East China Normal University,\ Shanghai} 200241, {\it China}

    2. {\itInstitute of Mathematics, Zhejiang Wanli University, Ningbo Zhejiang}\, 315100

  • Received:2008-10-06 Revised:2008-12-06 Online:2009-07-25 Published:2009-07-25
  • Contact: CHEN Guo-liang

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摘要： 分析了系数矩阵是$\emph{\textbf{M}}$-矩阵时预条件AOR和2PPJ迭代法的收敛性,
指出了已有结果的一些错误并给出了正确的收敛定理. 同时,
利用$\emph{\textbf{H}}$-分裂理论,
讨论了系数矩阵是$\emph{\textbf{H}}$-矩阵时预条件AOR的收敛性并给出了参数的收敛区间.

关键词: 非奇异矩阵, 矩阵, AOR迭代法, 2PPJ迭代法, 矩阵分裂, 非奇异矩阵, 矩阵, AOR迭代法, 2PPJ迭代法, 矩阵分裂

Abstract: This paper analyzed the convergence of preconditioned AOR and 2PPJ iterative
methods when the coefficient matrix is an $\emph{\textbf{M}}$-matrix, and pointed out
some errors of known results and established correct convergence theorems. Meanwhile, by
the $\emph{\textbf{H}}$-splitting theory, the convergence of the preconditioned AOR
iterative method for the case of the coefficient matrix being an
$\emph{\textbf{H}}$-matrix was discussed and the convergence interval of parameters was

Key words: matrices, AOR iterative method, 2PPJ iterative method, matrix-splitting, nonnegative matrices, matrices, AOR iterative method, 2PPJ iterative method, matrix-splitting

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