Jacobi-Davidson方法中的修正方程和对应的精化方法  

A Refined Jacobi-Davidson Method and Its Correction Equation

作　　者：贾仲孝[1] 冯绍强[2] 

机构地区：[1]清华大学数学科学系,北京100084 [2]大连理工大学应用数学系,辽宁大连116024

出　　处：《Journal of Mathematical Research and Exposition》2005年第3期515-524,共10页数学研究与评论（英文版）

基　　金：国家自然科学基金(10471074)国家重点基础研究规划项目(G1999032805)高等学校骨干教师基金.

摘　　要：Jacobi-Davidson方法的核心之一是求解用以合理扩展投影子空间的线性修正方程组,众多文献均认为该方程是自然有解的.本文详细研究了修正方程,证明它可能无解,并给出了解存在的条件.同时,为克服近似特征向量的可能不收敛性,提出了精化的Jacobi-Davidson方法,建立了对应的修正方程.A central problem in the Jacobi-Davidson method is to expand a projection subspace by solving certain correction equation. It has been commonly accepted that the correction equation always has a solution. However, it is proved in this paper that this is not true. Conditions are given to decide when it has a unqiue solution or many solutions or no solution. A refined Jacobi-Davidson method is proposed to overcome the possible nonconvergence of Ritz vectors by coinputing certain refined approximation eigenvectors from the subspace. A corresponding correction equation is derived for the refined method.

关 键 词：JACOBI-DAVIDSON方法 精化的Jacobi-Davidson方法 RITZ值 Ritz向量 精化向 量 修正方程 RAYLEIGH商 

分 类 号：O241.6[理学—计算数学]