期刊
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
卷 44, 期 2, 页码 246-272出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2016.04.006
关键词
LU decomposition; Matrix factorizations; Random matrices; Randomized algorithms
资金
- Israel Science Foundation [1041/10]
- Israel Ministry of Science and Technology [3-9096, 3-10898]
- US - Israel Binational Science Foundation [BSF 2012282]
- Blavatnik Computer Science Research Fund
- Blavatnik ICRC Funds
- Jyvaskyla University
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. (C) 2016 Elsevier Inc. All rights reserved.
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