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Volume 18, Issue 5
Extrapolating the Arnoldi Algorithm to Improve Eigenvector Convergence

Sara Pollock & L.Ridgway Scott

Int. J. Numer. Anal. Mod., 18 (2021), pp. 712-721.

Published online: 2021-08

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  • Abstract

We consider extrapolation of the Arnoldi algorithm to accelerate computation of the dominant eigenvalue/eigenvector pair. The basic algorithm uses sequences of Krylov vectors to form a small eigenproblem which is solved exactly. The two dominant eigenvectors output from consecutive Arnoldi steps are then recombined to form an extrapolated iterate, and this accelerated iterate is used to restart the next Arnoldi process. We present numerical results testing the algorithm on a variety of cases and find on most examples it substantially improves the performance of restarted Arnoldi. The extrapolation is a simple post-processing step which has minimal computational cost.

  • Keywords

Eigenvalue computation, extrapolation, Arnoldi algorithm

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-18-712, author = {Pollock , Sara and Scott , L.Ridgway}, title = {Extrapolating the Arnoldi Algorithm to Improve Eigenvector Convergence}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {5}, pages = {712--721}, abstract = {

We consider extrapolation of the Arnoldi algorithm to accelerate computation of the dominant eigenvalue/eigenvector pair. The basic algorithm uses sequences of Krylov vectors to form a small eigenproblem which is solved exactly. The two dominant eigenvectors output from consecutive Arnoldi steps are then recombined to form an extrapolated iterate, and this accelerated iterate is used to restart the next Arnoldi process. We present numerical results testing the algorithm on a variety of cases and find on most examples it substantially improves the performance of restarted Arnoldi. The extrapolation is a simple post-processing step which has minimal computational cost.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/19389.html} }
TY - JOUR T1 - Extrapolating the Arnoldi Algorithm to Improve Eigenvector Convergence AU - Pollock , Sara AU - Scott , L.Ridgway JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 712 EP - 721 PY - 2021 DA - 2021/08 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/19389.html KW - Eigenvalue computation, extrapolation, Arnoldi algorithm AB -

We consider extrapolation of the Arnoldi algorithm to accelerate computation of the dominant eigenvalue/eigenvector pair. The basic algorithm uses sequences of Krylov vectors to form a small eigenproblem which is solved exactly. The two dominant eigenvectors output from consecutive Arnoldi steps are then recombined to form an extrapolated iterate, and this accelerated iterate is used to restart the next Arnoldi process. We present numerical results testing the algorithm on a variety of cases and find on most examples it substantially improves the performance of restarted Arnoldi. The extrapolation is a simple post-processing step which has minimal computational cost.

Pollock , Sara and Scott , L.Ridgway. (2021). Extrapolating the Arnoldi Algorithm to Improve Eigenvector Convergence. International Journal of Numerical Analysis and Modeling. 18 (5). 712-721. doi:
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