arrow
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

Export citation
  • 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.

  • AMS Subject Headings

65F15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-8-82, author = {}, 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 JO - East Asian Journal on Applied Mathematics VL - 1 SP - 82 EP - 99 PY - 2018 DA - 2018/02 SN - 8 DO - http://doi.org/10.4208/eajam.070517.180917a UR - https://global-sci.org/intro/article_detail/eajam/10886.html KW - Polynomial eigenvalue problem, generalised Arnoldi method, refinement, implicit restarting, 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
Copy to clipboard
The citation has been copied to your clipboard