期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 104, 期 51, 页码 20167-20172出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.0709640104
关键词
matrix; SVD; PCA
资金
- Grants-in-Aid for Scientific Research [25000003, 26820298, 16H00923] Funding Source: KAKEN
- NIEHS NIH HHS [27302C0031] Funding Source: Medline
- Directorate For Geosciences
- Division Of Earth Sciences [847368] Funding Source: National Science Foundation
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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