| 预处理后多分裂下的SOR迭代法收敛性分析 |
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| 引用本文： | 雷刚.预处理后多分裂下的SOR迭代法收敛性分析[J].四川工业学院学报,2012(2):88-90. |
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| 作者姓名： | 雷刚 |
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| 作者单位： | 宝鸡文理学院数学系,陕西宝鸡721013 |
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| 基金项目： | 国家自然科学基金资助项目（10071048）; 宝鸡文理学院重点项目基金资助 |
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| 摘 要： | 使用预处理方法解大型线性方程组Ax=b,结合矩阵分裂理论,给出预处理后多种分裂形式的SOR迭代方法,并与一般的预处理方法进行比较分析,证明分裂后的迭代法能加速SOR迭代法的收敛性。最后用数值例子加以验证。
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| 关 键 词： | 预处理 收敛性 SOR迭代法 M-矩阵 谱半径 |
The Convergence Analysis of the Multi-splitting SOR Iterative Method after Precondition |
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| LEI Gang.The Convergence Analysis of the Multi-splitting SOR Iterative Method after Precondition[J].Journal of Sichuan University of Science and Technology,2012(2):88-90. |
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| Authors: | LEI Gang |
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| Affiliation: | LEI Gang(Department of Mathematics,Baoji University of Arts and Sciences,Baoji 721013 China) |
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| Abstract: | Precondition method is used to solve the large linear systemAx=b in this paper.Combined matrix iterative analysis and comparison theorem,it presents multi-splitting SOR iterative method and compares it with general precondition approach,then proves that the multi-splitting method can not only accelerate the convergence of SOR iterative method,but also surpass the general precondition SOR method.Finally,a numerical example is given. |
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| Keywords: | precondition convergence SOR iteration method M-matrix Spectral radius |
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