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

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.

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.