Extrapolating the Arnoldi Algorithm To Improve Eigenvector Convergence

2021/03/15 by Sara Pollock, Pollock, Sara, L. Ridgway Scott +1 · 3 citations
Computer Science · Physics and Astronomy · #65B05 #65F15 #FOS: Mathematics #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Neural Networks and Applications #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2103.08635

openalex publication_date 2021/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• SLEPc
• Numerics of Gram-Schmidt orthogonalization

Cited by

• Momentum accelerated power iterations and the restarted Lanczos method
• Random Walks, Faber Polynomials and Accelerated Power Methods
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