求解病态线性方程组的收缩Lanczos方法  

The Deflated Lanczos Method for Ill-conditioned Linear Systems

作　　者：李欣[1] 朱景福[2] 

机构地区：[1]黑龙江八一农垦大学数学系,大庆163319 [2]黑龙江八一农垦大学信息技术学院,大庆163319

出　　处：《数学的实践与认识》2007年第23期38-42,共5页Mathematics in Practice and Theory

基　　金：黑龙江省自然科学基金(ZTA2005-30)

摘　　要：Lanczos方法是求解大型线性方程组的常用方法.遗憾的是,在Lanczos过程中通常会发生算法中断或数值不稳定的情况.将给出求解大型对称线性方程组的收缩Lanczos方法,即DLanczos方法.新算法将采用增广子空间技术,在Lanczos过程中向Krylov子空间加入少量绝对值较小的特征值所对应的特征向量进行收缩.数值实验表明,新算法比Lanczos方法收敛速度更快,并且适合求解病态对称线性方程组.The Lanczos method is usually used for Large symmetric linear systems. Unfortunately, the Lanczos process is susceptible to possible breakdown and numerical instabilities. The deflated Lanczos method is presented in this paper, that is DLanczos method. In the new method, augmented Krylov Subspace technique is used by adding to a few approximate eigenvectors associated to zero. Numerical experiments show that DLanczos method is much better than Lanczos method for symmetric linear systems, and the new methods are suitable for ill-conditioned symmetric linear systems.

关 键 词：对称线性方程组 Krylov予空间 LANCZOS方法 收缩技术 病态方程组 

分 类 号：O241.6[理学—计算数学]