A compact Heart iteration for low-rank approximations of large matrices

In this paper we present a compact version of the Heart iteration. One that computes low-rank approximations of large sparse matrices. The new iteration is a restarted Krylov method that is based on explicit restarts and Gram–Schmidt orthogonalizations. It is a simple algorithm that requires a minim...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2024-02, Vol.437, p.115467, Article 115467
Main Author: Dax, Achiya
Format: Article
Language:English
Subjects:
A reduced storage approach
Large sparse matrices
Low-rank approximations
Restarted Krylov methods
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Summary:In this paper we present a compact version of the Heart iteration. One that computes low-rank approximations of large sparse matrices. The new iteration is a restarted Krylov method that is based on explicit restarts and Gram–Schmidt orthogonalizations. It is a simple algorithm that requires a minimal amount of computer storage as well as a minimal number of matrix–vector products per iteration. Yet it enjoys a fast rate of convergence. Numerical experiments illustrate the usefulness of the proposed approach.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2023.115467