| 改进的古典迭代法对于M-矩阵谱半径的比较结果 |
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| 引用本文： | 孙丽英,薛占熬.改进的古典迭代法对于M-矩阵谱半径的比较结果[J].河南师范大学学报(自然科学版),2005,33(1):14-17,48. |
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| 作者姓名： | 孙丽英 薛占熬 |
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| 作者单位： | 1. 广东教育学院,数学系,广州,510310
2. 河南师范大学,计算机与信息技术学院,河南,新乡,453007 |
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| 基金项目： | 广东省高校自然科学基金资助项目(Z03095) |
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| 摘 要： | 近四十年来许多文章致力于研究在系数矩阵是M 矩阵的情形下,线性方程组的预处理子的修改与完善,目的是为了改善古典迭代法(Jacobi,Gauss Seidel迭代法等)的收敛速度.本文对其中的Milaszewicz的方法(见文献1])做出改进,将其结论中的预处理子参数化,并对参数的选择给出必要条件,以保证这种预处理方法收敛,从而得到在这种改进的预处理方法下,Jacobi及Gauss Seidel迭代法的迭代矩阵谱半径的比较结果.
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| 关 键 词： | Jacobi GaussSeidel迭代法 M矩阵 正则分裂 谱半径 |
| 文章编号： | 1000-2367(2005)01-0014-04 |
Comparison Results of the Spectral Radius of the Modified Classical Iterative Methods for M-matrix |
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| SUN Li-ying,XUE Zhan-ao.Comparison Results of the Spectral Radius of the Modified Classical Iterative Methods for M-matrix[J].Journal of Henan Normal University(Natural Science),2005,33(1):14-17,48. |
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| Authors: | SUN Li-ying XUE Zhan-ao |
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| Institution: | SUN Li-ying~1,XUE Zhan-ao~2 |
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| Abstract: | In the last four decades many articles have been devoted to the modifications and improvements of classes of preconditioners for linear systems whose matrix coefficient is an M-matrix in order to improve on the convergence rates of the classical iterative schemes (Jacobi, Gauss-Seidel, etc. ).In this paper, we parametrize Milaszewicz's preconditioner by using the idea in 1],sufficient conditions on the α_i's are given that guarantee convergence of this method; then we get the comparison theorem of the spectral radius between the iteration matrices of the modified Gauss-Seidel and Jacobi type iterative schemes. |
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| Keywords: | Jacobi and Gauss-Seidel iterative method M-matrix regular splitting spectral radius |
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