Volume 8, Issue 1
Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem

Wei Wei and Hua Dai

10.4208/eajam.070517.180917a

East Asian J. Appl. Math., 8 (2018), pp. 82-99.

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  • Abstract

Based on the generalised Arnoldi procedure, we develop an implicitly restarted generalised Arnoldi method for solving the large-scale polynomial eigenvalue problem. By combining implicit restarting with the refinement scheme, we present an implicitly restarted refined generalised Arnoldi (IRGAR) method. To avoid repeated converged eigenpairs in the later iteration, we develop a novel non-equivalence low-rank deflation technique and propose a deflated and implicitly restarted refined generalised Arnoldi method (DIRGAR). Some numerical experiments show that this DIRGAR method is efficient and robust.

  • History

Published online: 2018-02

  • AMS Subject Headings

65F15

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