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Harmonic and refined Rayleigh-Ritz for the polynomial eigenvalue problem. (English) Zbl 1212.65150

Summary: 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.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A54 Matrices over function rings in one or more variables
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