Extrapolating the Arnoldi Algorithm to Improve Eigenvector Convergence

Extrapolating the Arnoldi Algorithm to Improve Eigenvector Convergence

Year:    2021

Author:    Sara Pollock, L.Ridgway Scott

International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 5 : pp. 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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2021-IJNAM-19389

International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 5 : pp. 712–721

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Eigenvalue computation extrapolation Arnoldi algorithm

Author Details

Sara Pollock

L.Ridgway Scott