| 预处理后关于IMGS和SOR迭代法的一个比较定理 |
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| 引用本文： | 雷刚.预处理后关于IMGS和SOR迭代法的一个比较定理[J].贵州大学学报(自然科学版),2012,29(1):17-19. |
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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（ZK11015） |
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| 摘 要： | 对于迭代法解线性方程组,运用矩阵分裂理论及比较定理,对超松弛迭代法(即SOR方法)和预条件P=I+Cα后的Gauss-Seidel迭代法(称为IMGS方法)的收敛速度进行比较,得到较好结果,最后给出一个数值例子。
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| 关 键 词： | 预条件 收敛性 M-矩阵 SOR迭代法 IMGS迭代法 |
A Comparison Theorem in the IMGS and SOR Iterative Method |
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| LEI Gang.A Comparison Theorem in the IMGS and SOR Iterative Method[J].Journal of Guizhou University(Natural Science),2012,29(1):17-19. |
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| Authors: | LEI Gang |
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| Institution: | LEI Gang ( Department of Mathematics , Baoji University of Arts and Sciences, Baoji 721013, China) |
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| Abstract: | The linear systems were solved by the iterative method. The matrix iterative analysis and matrix comparison theorems were used to compare the convergence speed in the successive over-relaxation iterative method （SOR method） and the Gauss-Seidel method of the preconditioner P = I ＋ Ca （IMGS method ）, the comparison conclusion is better. And the numerical example was given. |
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| Keywords: | precondition nonsingular M-matrix SOR iterative method IMGS iterative method |
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