解线性方程组的预条件Gauss-Seidel型迭代法

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基金项目: 教育部“新世纪人才支持计划”基金资助项目(2004);四川省应用基础研究基金资助项目(05JY029-068-2)

Preconditioned Gauss-Seidel Type Iterative Methods for Solving Linear Systems

School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China

摘要: 给出了解线性方程组的预条件Gauss-Seidel型方法,提出了选取合适的预条件因子．并讨论了对Z-矩阵应用这种方法的收敛性,给出了收敛最快时的系数取值．最后给出数值例子，说明选取合适的预条件因子应用Gauss-Seidel方法求解线性方程组是有效的．
- Gauss-Seidel方法 /
- 预条件迭代法 /
- Z-矩阵
Abstract: The preconditioned Gauss-Seidel type iterative method for solving linear systems, with the proper choice of the preconditioner, was presented. Convergence of the preconditioned method applied to Z-matrices was discussed. Also the optimal parmeter was presented. Numerical results show that the proper choice of the preconditioner can lead to effective the preconditioned Gauss-Seidel type iterative methods for solving linear systems.
- Gauss-Seidel method /
- preconditioned iterative method /
- Z-matrix

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