物理化学学报 >> 2009, Vol. 25 >> Issue (10): 2143-2146.doi: 10.3866/PKU.WHXB20091016

研究论文 上一篇    下一篇

大型线性方程组的迭代求解

陈飞武, 赵小红   

  1. 北京科技大学化学系, 北京 100083
  • 收稿日期:2009-05-29 修回日期:2009-07-16 发布日期:2009-09-29
  • 通讯作者: 陈飞武 E-mail:chenfeiwu@sas.ustb.edu.cn

Iterative Solution of Large-Scale Linear Equations

CHEN Fei-Wu, ZHAO Xiao-Hong   

  1. Department of Chemistry, University of Science and Technology Beijing, Beijing 100083, P. R. China
  • Received:2009-05-29 Revised:2009-07-16 Published:2009-09-29
  • Contact: CHEN Fei-Wu E-mail:chenfeiwu@sas.ustb.edu.cn

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摘要：

将求解大型标准特征值问题的Davidson方法推广到求解大型线性方程组. 推广后的方法既可以用于求解对称问题, 又可以用于求解非对称问题. 数值计算结果显示, 该方法对这两类问题的求解分别优于共轭梯度方法和双共轭梯度方法.

关键词: 线性方程组, Davidson方法, 共轭梯度方法, 双共轭梯度方法

Abstract:

The Davidson's method originally developed for eigenvalue problems was extended to solve large-scale linear equations. It can be used for symmetrical and nonsymmetrical matrices. Numerical results presented in this study demonstrate that the present scheme is much more effective than conjugate gradient method and biconjugate gradient method for symmetrical and nonsymmetrical problems, respectively.

Key words: Linear equations, Davidson’s method, Conjugate gradient method, Biconjugate gradient method