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Implicitly Restarted Refined Partially Orthogonal Projection Method with Deflation

Part of: Numerical linear algebra

Published online by Cambridge University Press:  31 January 2017

Wei Wei  and
Hua Dai
Wei Wei*
Affiliation:
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Hua Dai*
Affiliation:
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
*
*Corresponding author. Email addresses:[email protected] (W. Wei), [email protected] (H. Dai)
*Corresponding author. Email addresses:[email protected] (W. Wei), [email protected] (H. Dai)
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Abstract

In this paper we consider the computation of some eigenpairs with smallest eigenvalues in modulus of large-scale polynomial eigenvalue problem. Recently, a partially orthogonal projection method and its refinement scheme were presented for solving the polynomial eigenvalue problem. The methods preserve the structures and properties of the original polynomial eigenvalue problem. Implicitly updating the starting vector and constructing better projection subspace, we develop an implicitly restarted version of the partially orthogonal projection method. Combining the implicit restarting strategy with the refinement scheme, we present an implicitly restarted refined partially orthogonal projection method. In order to avoid the situation that the converged eigenvalues converge repeatedly in the later iterations, we propose a novel explicit non-equivalence low-rank deflation technique. Finally some numerical experiments show that the implicitly restarted refined partially orthogonal projection method with the explicit non-equivalence low-rank deflation technique is efficient and robust.

Keywords

Polynomial eigenvalue problempartially orthogonal projection methodrefinementimplicitly restartingnon-equivalence low-rank deflation

MSC classification

Secondary: 65F15: Eigenvalues, eigenvectors
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 1 , February 2017 , pp. 1 - 20
Copyright
Copyright © Global-Science Press 2017 

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