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Studies on Jacobi–Davidson, Rayleigh quotient iteration, inverse iteration generalized Davidson and Newton updates
Author(s) -
Zhou Yunkai
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.490
Subject(s) - rayleigh quotient iteration , mathematics , subspace topology , quotient , type (biology) , rayleigh quotient , inverse , algebra over a field , iterative method , mathematical analysis , pure mathematics , mathematical optimization , power iteration , eigenvalues and eigenvectors , geometry , ecology , physics , quantum mechanics , biology
We study Davidson‐type subspace eigensolvers. Correction equations of Jacobi–Davidson and several other schemes are reviewed. New correction equations are derived. A general correction equation is constructed, existing correction equations may be considered as special cases of this general equation. The main theme of this study is to identify the essential common ingredient that leads to the efficiency of a diverse form of Davidson‐type methods. We emphasize the importance of the approximate Rayleigh‐quotient‐iteration direction. Copyright © 2006 John Wiley & Sons, Ltd.