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A refined jacobi-davidson method and its correction equation

✍ Scribed by Shaoqiang Feng; Zhongxiao Jia

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
602 KB
Volume
49
Category
Article
ISSN
0898-1221

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✦ Synopsis

A central problem in the Jacobi-Davidson method is to expand a projection subspace by solving a 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 unique 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. Numerical experiments are conducted and efficiency of the refined method is confirmed. (~) 2005 Elsevier Ltd. All rights reserved.

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