A refined Jacobi-Davidson method and its correction equation

作者：Feng SQ^*; Jia ZX

来源：Computers & Mathematics with Applications, 2005, 49(2-3): 417-427.

DOI：10.1016/j.camwa.2003.01.018

• Jacobi-Davidson method
• refined Jacobi-Davidson method
• Ritz value
• Ritz vector
• refined eigenvector approximation
• correction equation
• Rayleigh quotient

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.

• 出版日期2005-2
• 单位大连理工大学