Randomized algorithms for the low-rank approximation of matrices
We describe two recently proposed randomized algorithms for the construction of low-rank approximations to matrices, and demonstrate their application (inter alia) to the evaluation of the singular value decompositions of numerically low-rank matrices. Being probabilistic, the schemes described here...
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| Published in: | Proceedings of the National Academy of Sciences - PNAS Vol. 104; no. 51; p. 20167 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
18.12.2007
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| ISSN: | 1091-6490, 1091-6490 |
| Online Access: | Get more information |
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| Summary: | We describe two recently proposed randomized algorithms for the construction of low-rank approximations to matrices, and demonstrate their application (inter alia) to the evaluation of the singular value decompositions of numerically low-rank matrices. Being probabilistic, the schemes described here have a finite probability of failure; in most cases, this probability is rather negligible (10(-17) is a typical value). In many situations, the new procedures are considerably more efficient and reliable than the classical (deterministic) ones; they also parallelize naturally. We present several numerical examples to illustrate the performance of the schemes. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 1091-6490 1091-6490 |
| DOI: | 10.1073/pnas.0709640104 |