Randomized LU decomposition

Gil Shabat, Yaniv Shmueli, Yariv Aizenbud, Amir Averbuch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

Randomized algorithms play a central role in low rank approximations of large matrices. In this paper, the scheme of the randomized SVD is extended to a randomized LU algorithm. Several error bounds are introduced, that are based on recent results from random matrix theory related to subgaussian matrices. The bounds also improve the existing bounds of already known randomized SVD algorithm. The algorithm is fully parallelized and thus can utilize efficiently GPUs without any CPU–GPU data transfer. Numerical examples, which illustrate the performance of the algorithm and compare it to other decomposition methods, are presented.

Original languageEnglish
Pages (from-to)246-272
Number of pages27
JournalApplied and Computational Harmonic Analysis
Volume44
Issue number2
DOIs
StatePublished - 1 Mar 2018

Funding

FundersFunder number
United States-Israel Binational Science FoundationBSF 2012282
Israel Science Foundation1041/10
Jyväskylän Yliopisto
Ministry of Science and Technology, Israel3-9096, 3-10898

    Keywords

    • LU decomposition
    • Matrix factorizations
    • Random matrices
    • Randomized algorithms

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