Harmonic and refined Rayleigh–Ritz for the polynomial eigenvalue problem |
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Authors: | Michiel E. Hochstenbach Gerard L. G. Sleijpen |
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Affiliation: | 1. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, The Netherlands;2. Mathematical Institute, Utrecht University, P.O. Box 80.010, NL‐3508 TA Utrecht, The Netherlands |
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Abstract: | 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. |
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Keywords: | polynomial eigenvalue problem harmonic Rayleigh– Ritz refined Rayleigh– Ritz interior eigenvalues Jacobi– Davidson subspace extraction subspace method subspace expansion Rayleigh– Ritz |
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