Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for pe...

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Bibliographic Details
Published in:	SIAM review Vol. 53; no. 2; pp. 217 - 288
Main Authors:	Halko, N., Martinsson, P. G., Tropp, J. A.
Format:	Journal Article
Language:	English
Published:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:	Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Approximation Computer science; control theory; systems Dimensionality reduction Eigenvalues Error analysis Error bounds Error rates Exact sciences and technology Factorization Linear algebra Mathematical vectors Mathematics Matrices Matrix Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Principal components analysis Randomized algorithms Sciences and techniques of general use Studies SURVEY and REVIEW Theoretical computing Matrix approximation 68W20 random matrix Error analysis Random sampling Memory Decomposition method Krylov subspace method Eigenvalue 60B20 Johnson-Lindenstrauss lemma Research Computing dimension reduction Multiprocessor Input Randomization 65F30 Primary Sparse matrix Floating point Robustness pass-efficient algorithm Singular value decomposition Parallel algorithm Data analysis Secondary rank-revealing QR factorization Architecture Rank randomized algorithm streaming algorithm Factorization interpolative decomposition Survey Scientific computation Applied mathematics eigenvalue decomposition Randomness Environment M matrix Principal component analysis
ISSN:	0036-1445, 1095-7200
Online Access:	Get full text
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