贾仲孝,冯绍强.Jacobi-Davidson方法中的修正方程和对应的精化方法[J].数学研究及应用,2005,25(3):515~524 |
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 |
投稿时间:2003-03-17 |
DOI:10.3770/j.issn:1000-341X.2005.03.021 |
中文关键词: 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 |
英文关键词:Jacobi-Davidson method refined Jacobi-Davidson method Ritz value Ritz vector refined eigenvector approximation correction equation Rayleigh quotient. |
基金项目:国家自然科学基金(10471074),国家重点基础研究规划项目(Gl999032805),高等学校骨干教师基金. |
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中文摘要: |
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. |
英文摘要: |
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 computing certain refined approximation eigenvectors from the subspace. A corresponding correction equation is derived for the refined method. |
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