Harmonic and refined Rayleigh–Ritz for the polynomial eigenvalue problem

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.