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The Jacobi–Davidson method
Author(s) -
Hochstenbach M.E.,
Notay Y.
Publication year - 2006
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201490038
Subject(s) - jacobi method , factorization , krylov subspace , eigenvalues and eigenvectors , subspace topology , computer science , matrix decomposition , incomplete lu factorization , linear system , sparse matrix , matrix (chemical analysis) , algebra over a field , mathematics , iterative method , algorithm , artificial intelligence , pure mathematics , mathematical analysis , computational chemistry , physics , chemistry , materials science , quantum mechanics , composite material , gaussian
The Jacobi–Davidson method is a popular technique to compute a few eigenpairs of large sparse matrices. Its introduction, about a decade ago, was motivated by the fact that standard eigensolvers often require an expensive factorization of the matrix to compute interior eigenvalues. Such a factorization may be infeasible for large matrices as arise in today's large‐scale simulations. In the Jacobi–Davidson method, one still needs to solve “inner” linear systems, but a factorization is avoided because the method is designed so as to favor the efficient use of modern iterative solution techniques, based on preconditioning and Krylov subspace acceleration. Here we review the Jacobi–Davidson method, with the emphasis on recent developments that are important in practical use. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)