| 一类矩阵的AOR迭代收敛性分析及其与SOR迭代的比较 |
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| 引用本文： | 薛秋芳.一类矩阵的AOR迭代收敛性分析及其与SOR迭代的比较[J].高等学校计算数学学报,2006,28(1):39-49. |
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| 作者姓名： | 薛秋芳 |
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| 作者单位： | 西安理工大学理学院应用数学系,西安,710048 |
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| 基金项目： | 国家自然科学基金资助项目(10071048)． |
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| 摘 要： | 1 引言
许多实际问题最后常归结为解一个或一些矩阵的线性代数方程组Ax=b （1.1）这里讨论A为（1，1）相容次序矩阵的情形。
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| 关 键 词： | 相容次序矩阵 SOR迭代 收敛性分析 AOR迭代 线性代数方程组 |
| 收稿时间： | 01 1 2005 12:00AM |
| 修稿时间： | 2005-01-01 |
THE ANALYSIS OF THE CONVERGENCE OF THE AOR METHOD AND THE COMPARISON WITH THE SOR METHOD |
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| Xue Qiufang.THE ANALYSIS OF THE CONVERGENCE OF THE AOR METHOD AND THE COMPARISON WITH THE SOR METHOD[J].Numerical Mathematics A Journal of Chinese Universities,2006,28(1):39-49. |
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| Authors: | Xue Qiufang |
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| Abstract: | When the coefficient matrix of a linear system is (1.1) consistently ordered matrix and the eigenvalues of its Jacobi matrix are all pure imaginaries or zeroes, the convergence and the optimum parameters of its AOR iterative method are given.Futhermore,we make a comparison between its optimum spectral radius and that of SOR method and draw a conclusion that these two methods have their own advantages respectively under different conditions. Therefore the method to how to choose the better method between AOR and SOR is given. |
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| Keywords: | consistently ordered matrix AOR method SOR method the optimum parameter spectral radius |
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