Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem
Year: 2018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 1 : pp. 82–99
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.070517.180917a
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 1 : pp. 82–99
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Polynomial eigenvalue problem generalised Arnoldi method refinement implicit restarting non-equivalence low-rank deflation.