| 一个拟极小化左共轭梯度算法及其数值表现 |
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| 引用本文： | 王丽平,陈晓红. 一个拟极小化左共轭梯度算法及其数值表现[J]. 计算数学, 2009, 31(2): 127-136 |
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| 作者姓名： | 王丽平 陈晓红 |
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| 作者单位： | 南京航空航天大学数学系,南京,210016;南京航空航天大学数学系,南京,210016 |
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| 摘 要： | 左共轭梯度法是求解大型稀疏线性方程组的一种新兴的Krylov子空间方法.为克服该算法数值表现不稳定、迭代中断的缺点,本文对原方法进行等价变形,得到左共轭梯度方向的另一迭代格式,给出一个拟极小化左共轭梯度算法.数值结果证实了该变形算法与原算法的相关性.
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| 关 键 词： | 迭代法 左共轭梯度法 左共轭梯度方向 拟极小化 |
| 收稿时间： | 2007-04-17 |
A QUASI-MINIMIZED LEFT CONJUGATE GRADIENT METHOD AND ITS NUMERICAL BEHAVIOR |
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| Wang Liping,Chen Xiaohong. A QUASI-MINIMIZED LEFT CONJUGATE GRADIENT METHOD AND ITS NUMERICAL BEHAVIOR[J]. Mathematica Numerica Sinica, 2009, 31(2): 127-136 |
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| Authors: | Wang Liping Chen Xiaohong |
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| Affiliation: | Department of Mathematics;Nanjing University of Aeronautics and Astronautics;Nanjing 210016;China |
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| Abstract: | The left conjugate gradient method is a recently developed Krylov subspace method which aims to solve large-scale sparse linear systems.In order to overcome the drawbacks of numerical instability and possible breakdowns in the iteration,we transform the formula of the left conjugate gradient method into an equivalent version to generate the left conjugate gradient directions.And this technique is used to construct a quasi-minimized left conjugate gradient method.The numerical results reported in this paper ... |
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| Keywords: | iterative method left conjugate gradient method left conjugate gradient direction quasi minimization |
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