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

Wei Wei & Hua Dai

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

Published online: 2018-02

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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.

  • Keywords

Polynomial eigenvalue problem generalised Arnoldi method refinement implicit restarting non-equivalence low-rank deflation

  • AMS Subject Headings

65F15

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-82, author = {Wei Wei and Hua Dai}, title = {Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {1}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.070517.180917a}, url = {http://global-sci.org/intro/article_detail/eajam/10886.html} }
TY - JOUR T1 - Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem AU - Wei Wei & Hua Dai JO - East Asian Journal on Applied Mathematics VL - 1 SP - 82 EP - 99 PY - 2018 DA - 2018/02 SN - 8 DO - http://dor.org/10.4208/eajam.070517.180917a UR - https://global-sci.org/intro/article_detail/eajam/10886.html KW - Polynomial eigenvalue problem KW - generalised Arnoldi method KW - refinement KW - implicit restarting KW - non-equivalence low-rank deflation AB -

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.

Wei Wei & Hua Dai. (1970). Implicitly Restarted Refined Generalised Arnoldi Method with Deflation for the Polynomial Eigenvalue Problem. East Asian Journal on Applied Mathematics. 8 (1). 82-99. doi:10.4208/eajam.070517.180917a
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