大型线性方程组的迭代求解(英文)

Iterative Solution of Large-Scale Linear Equations

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.

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.