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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.
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关键词:
- 非奇异$\emph{\textbf{M}}$-矩阵 /
- $\emph{\textbf{H}}$-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 -
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