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Harmonic projection methods for large non‐symmetric eigenvalue problems
Author(s) -
Morgan Ronald B.,
Zeng Min
Publication year - 1998
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/(sici)1099-1506(199801/02)5:1<33::aid-nla125>3.0.co;2-1
Subject(s) - eigenvalues and eigenvectors , mathematics , rayleigh–ritz method , subspace topology , mathematical analysis , projection (relational algebra) , eigenvalue perturbation , divide and conquer eigenvalue algorithm , boundary value problem , ritz method , algorithm , physics , quantum mechanics
Abstract The problem of finding interior eigenvalues of a large nonsymmetric matrix is examined. A procedure for extracting approximate eigenpairs from a subspace is discussed. It is related to the Rayleigh–Ritz procedure, but is designed for finding interior eigenvalues. Harmonic Ritz values and other approximate eigenvalues are generated. This procedure can be applied to the Arnoldi method, to preconditioning methods, and to other methods for nonsymmetric eigenvalue problems that use the Rayleigh–Ritz procedure. The subject of estimating the boundary of the entire spectrum is briefly discussed, and the importance of preconditioning for interior eigenvalue problems is mentioned. © 1998 John Wiley & Sons, Ltd.