| 对称正定矩阵的多级迭代法 |
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| 引用本文： | 鲁雪晶,刘仲云,张育林. 对称正定矩阵的多级迭代法[J]. 数学理论与应用, 2013, 0(1): 7-12 |
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| 作者姓名： | 鲁雪晶 刘仲云 张育林 |
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| 作者单位： | 长沙理工大学数学与计算科学学院;Minho大学数学系 |
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| 基金项目： | Supported by the National Natural Science Foundation of China under Grant No.10771022;Supported by FEDER Funds through“Programa Operacional Factores de Competitividade-COMPETE”;Supported by Portuguese Funds through“Fundao para a Ciência e aTecnologia”,within the Project PEst-C/MAT/UI0013/2011 and PTDC/MAT/112273/2009,Portugal |
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| 摘 要： | 本文主要研究解对称正定矩阵的多级迭代法，并对其收敛性进行证明。最后用数值实验验证此方法的有效性．多级迭代法特别适用于并行计算，并且可以被理解为古典迭代法的扩展，或共轭梯度法的预处理子。
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| 关 键 词： | 线性方程组 对称正定阵 多级分裂 迭代法 收敛性 |
Multistage Iterative Methods for Symmetric Positive Definite Matrices |
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| Lu Xuejing,Liu Zhongyun,Zhang Yulin. Multistage Iterative Methods for Symmetric Positive Definite Matrices[J]. Mathematical Theory and Applications, 2013, 0(1): 7-12 |
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| Authors: | Lu Xuejing Liu Zhongyun Zhang Yulin |
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| Affiliation: | 1.School of Mathematics and Computing Science,Changsha University of Science & Technology, Changsha 410114,China)(2.Centro de Matemática,Universidade do Minho,4710-057 Braga,Portugal) |
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| Abstract: | In this paper a multistage iterative method for solving the symmetric positive definite linear systems is established and the convergence of the method is proved. A numerical example is given to illustrate the effectiveness of our method. The method is especially suitable for parallel computation, and can be viewed as a extension of the classical iterative method or as a preconditioner for the conjugate gradient method. |
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| Keywords: | Linear Systems Symmetric Positive Definite Matrix Multistage Splitting Iterative Method Convergence |
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