| 解线性方程组的迭代方法研究 |
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| 引用本文： | 刘长河. 解线性方程组的迭代方法研究[J]. 北京建筑工程学院学报, 2013, 29(4): 65-67 |
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| 作者姓名： | 刘长河 |
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| 作者单位： | 北京建筑大学理学院,北京,100044 |
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| 摘 要： | 用求解线性方程组的多参数投影法推出Jacobi迭代法和Gauss-Seidel迭代法,并指出了松弛迭代法和Gauss-Seidel迭代法的内在联系.从最优化的观点分析了Jacobi迭代法收敛速度较慢的原因,即其下降矩阵与步长向量两者并非最优组合.并对Jacobi迭代法,Gauss-Seidel迭代法具有相当的收敛速度给出了合理的解释.
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| 关 键 词： | 线性方程组 投影法 Jacobi迭代法 Gauss-Seidel迭代法 松弛迭代法 |
Research on Iteration Methods for Solving System of Linear Equations |
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| Liu Changhe. Research on Iteration Methods for Solving System of Linear Equations[J]. Journal of Beijing Institute of Civil Engineering and Architecture, 2013, 29(4): 65-67 |
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| Authors: | Liu Changhe |
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| Affiliation: | Liu Changhe ( School of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044) |
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| Abstract: | In this paper, Jacobi iteration methods for system of linear equations are derived from mulit- parameter projection methods. The reason, which Jacobi iteration method converge is slower, is researched from the view of optimization, and its descent matrices and step-size vectors are not optimization combinations. The internal relations between successive over relaxation method and Gauss- Seidel iteration method are indicated. It is explained why Jacobi iteration method and Gauss-Seidel iteration method converge at the same velocity |
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| Keywords: | system of linear equations projection method Jacobi iteration method Gauss-Seideliteration method successive over relaxation method. |
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