A Refined Jacobi-Davidson Method and Its Correction Equation
Received:March 17, 2003  
Key Words: Jacobi-Davidson method   refined Jacobi-Davidson method   Ritz value   Ritz vector   refined eigenvector approximation   correction equation   Rayleigh quotient.  
Fund Project:
Author NameAffiliation
JIA Zhong-xiao Dept. of Math.
Tsinghua University
Beijing
China 
FENG Shao-qiang Dept. of Appl. Math.
Dalian University of Technology
Liaoning
China 
Hits: 2424
Download times: 1298
Abstract:
      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.
Citation:
DOI:10.3770/j.issn:1000-341X.2005.03.021
View Full Text  View/Add Comment