循环收缩QMR方法  

Restarted and deflated QMR method

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,黑龙江大庆163319 [2]黑龙江八一农垦大学信息技术学院,黑龙江大庆163319

出　　处：《哈尔滨工业大学学报》2009年第9期225-227,共3页Journal of Harbin Institute of Technology

基　　金：黑龙江省自然科学基金资助项目(ZTA2005-30)

摘　　要：在利用QMR方法求解非对称线性方程组的Lanczos过程中通常会发生算法中断或数值不稳定的情况.为解决这个问题并进一步提高收敛速度,本文在QMR方法解非对称线性方程组时,利用增广子空间技术向Krylov子空间加入少量模较小的特征值所对应的特征向量进行收缩,给出求解非对称线性方程组的收缩QMR方法.同时为减少存储量和计算量,给出收缩QMR方法的循环格式.数值实验表明,新方法比Lanczos方法和QMR方法的收敛速度更快.The Lanczos process is susceptible to possible breakdown and numerical instabilities in solving nonsymmetric linear equations with QMR method. To overcome this problem and improve the convergence, the augmented Krylov subspaee technique is used by adding a few approximate eigenvectors associated to the eigenvalues that are close to zero and the deflated QMR method is given for nonsymmetric linear systems. In order to reduce computations and memories, restarted version of the deflated QMR method is presented. Numerical experiments show that the new methods are much better than Lanczos method and QMR method for solving nonsymmetric linear equations.

关 键 词：非对称线性方程组 KRYLOV子空间 LANCZOS方法 QMR方法 收缩技术 

分 类 号：O241.6[理学—计算数学]