Journal of East China Normal University(Natural Sc ›› 2009, Vol. 2009 ›› Issue (4): 26-34.

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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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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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