期刊
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
卷 38, 期 4, 页码 1454-1485出版社
SIAM PUBLICATIONS
DOI: 10.1137/17M1111590
关键词
dimension reduction; matrix approximation; numerical linear algebra; randomized algorithm; single-pass algorithm; sketching; streaming algorithm; subspace embedding
资金
- ONR award [N00014-11-1002]
- Gordon & Betty Moore Foundation
- DARPA award [FA8750-17-2-0101]
- European Commission under the ERC Future Proof grant
- SNF [200021-146750, CRSII2-147633]
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image, or sketch, of the matrix. These methods can preserve structural properties of the input matrix, such as positive-semidefiniteness, and they can produce approximations with a user-specified rank. The algorithms are simple, accurate, numerically stable, and provably correct. Moreover, each method is accompanied by an informative error bound that allows users to select parameters a priori to achieve a given approximation quality. These claims are supported by numerical experiments with real and synthetic data.
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