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Harmonic and refined Rayleigh–Ritz for the polynomial eigenvalue problem
Author(s) -
Hochstenbach Michiel E.,
Sleijpen Gerard L. G.
Publication year - 2008
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.562
Subject(s) - mathematics , rayleigh–ritz method , eigenvalues and eigenvectors , subspace topology , polynomial , convergence (economics) , harmonic , ritz method , rayleigh quotient iteration , rayleigh scattering , mathematical analysis , linear system , boundary value problem , physics , optics , quantum mechanics , economics , economic growth , preconditioner
After reviewing the harmonic Rayleigh–Ritz approach for the standard and generalized eigenvalue problem, we discuss several extraction processes for subspace methods for the polynomial eigenvalue problem. We generalize the harmonic and refined Rayleigh–Ritz approaches which lead to new approaches to extract promising approximate eigenpairs from a search space. We give theoretical as well as numerical results of the methods. In addition, we study the convergence of the Jacobi–Davidson method for polynomial eigenvalue problems with exact and inexact linear solves and discuss several algorithmic details. Copyright © 2008 John Wiley & Sons, Ltd.