Harmonic and refined Rayleigh-Ritz for the polynomial eigenvalue problem

M.E. Hochstenbach, G.L.G. Sleijpen

Research output: Contribution to journalArticleAcademicpeer-review

18 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)35-54
JournalNumerical Linear Algebra with Applications
Volume15
Issue number1
DOIs
Publication statusPublished - 2008

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