| 线性方程组的多维投影算法 |
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| 引用本文： | 顾阿伦,孙永广.线性方程组的多维投影算法[J].运筹与管理,2006,15(4):17-21. |
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| 作者姓名： | 顾阿伦 孙永广 |
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| 作者单位： | 清华大学,能源经济环境研究院,北京,100084 |
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| 摘 要： | 本文分析了求解线性方程组的一维投影算法即最小剩余法。定义了长轴陷阱及陷阱深度，用它们刻划了该算法迭代过程中锯齿现象的几何特征。本文给出了基于残差序列的避开长轴陷阱的扰动技巧，即多维投影算法。数值试验表明，投影算法要优于现在流行的主要算法。
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| 关 键 词： | 应用数学 线性方程组 投影算法 长轴陷阱 陷阱深度 |
| 文章编号： | 1007-3221(2006)04-0017-05 |
| 收稿时间： | 11 29 2005 12:00AM |
| 修稿时间： | 2005年11月29 |
Multidimensional Project Algorithm for Solving Linear Equations |
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| GU A-lun,SUN Yong-guang.Multidimensional Project Algorithm for Solving Linear Equations[J].Operations Research and Management Science,2006,15(4):17-21. |
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| Authors: | GU A-lun SUN Yong-guang |
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| Institution: | Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China |
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| Abstract: | The one-dimension projection algorithm, which is the minimum residual method, based on residual space for solving linear equations, is analyzed in this paper. The definitions of long axis trap and trap depth are given. The geometrical feature of the algorithm is characterized. The method of perturbation based on residual series, which keeps residuals off the long axis trap, is presented in this paper. That is the multi - dimension projection method. The numerical experimentation shows that the method is superior to the present popular dominant algorithms. |
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| Keywords: | applied mathematics linear equations project algorithm long axis trap trap depth |
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