| GSOR方法最优迭代参数的简化推导 |
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| 引用本文： | 晁震,张乃敏,陈果良.GSOR方法最优迭代参数的简化推导[J].应用数学与计算数学学报,2014(2):134-139. |
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| 作者姓名： | 晁震 张乃敏 陈果良 |
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| 作者单位： | [1]华东师范大学数学系,上海市核心数学与实践重点实验室上海200241 [2]温州大学数学与信息科学学院,浙江温州325035 |
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| 基金项目： | Project supported by the National Natural Science Foundation of China （61002039）; the Natural Science Foundation of Zhejiang Province of China （Y1110451） |
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| 摘 要： | 对于增广线性系统,Bai等研究了广义SOR方法（Bai Z Z,Parlett B,Wang Z Q.On generaliged successive overrelaxation methods for augmented linear systems.Numerische Mathematik,2005,102（1）：1-38）,并得到其最优迭代参数.给出了另外一种推导最优迭代参数的简化方法,这种方法对于求解其他参数加速定常迭代方法的最优迭代参数非常有意义.
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| 关 键 词： | 最优参数 广义SOR方法 增广线性系统 迭代方法 |
Brief derivation for optimal iteration parameters in GSOR method |
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| CHAO Zhen,ZHANG Nai-min,CHEN Guo-liang.Brief derivation for optimal iteration parameters in GSOR method[J].Communication on Applied Mathematics and Computation,2014(2):134-139. |
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| Authors: | CHAO Zhen ZHANG Nai-min CHEN Guo-liang |
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| Institution: | ( Department of Mathematics, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai 200241, China; 2. College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, Zhejiang Province, China) |
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| Abstract: | For augmented linear systems, Bai, et al. studied the generalized SOR method （Bai Z Z, Parlett B, Wang Z Q. methods for augmented linear systems. 1-38） and obtained the optimal iteration optimal iteration parameters is given in On generalized successive overrelaxation Numerische Mathematik, 2005, 102（1）： parameters. Another short proof for the this paper, which will be very useful for investigating the optimal iteration parameters of other stationary iteration methods with parameter acceleration. |
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| Keywords: | optimal parameter generalized SOR method augmented linear systems iterative method |
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