Randomized algorithms for the low-rank approximation of matrices Export

@article{citeulike:2069894, abstract = {10.1073/pnas.0709640104 We describe two recently proposed randomized algorithms for the construction of low-rank approximations to matrices, and demonstrate their application () 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 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.}, author = {Liberty, Edo and Woolfe, Franco and Martinsson, Per-Gunnar and Rokhlin, Vladimir and Tygert, Mark}, citeulike-article-id = {2069894}, citeulike-linkout-0 = {http://dx.doi.org/10.1073/pnas.0709640104}, citeulike-linkout-1 = {http://www.pnas.org/content/104/51/20167.abstract}, citeulike-linkout-2 = {http://www.pnas.org/content/104/51/20167.full.pdf}, citeulike-linkout-3 = {http://www.pnas.org/cgi/content/abstract/104/51/20167}, citeulike-linkout-4 = {http://view.ncbi.nlm.nih.gov/pubmed/18056803}, citeulike-linkout-5 = {http://www.hubmed.org/display.cgi?uids=18056803}, day = {18}, doi = {10.1073/pnas.0709640104}, journal = {Proceedings of the National Academy of Sciences}, keywords = {algorithms, linearalgebra, matrix, random, rank}, month = {December}, number = {51}, pages = {20167--20172}, posted-at = {2009-09-25 22:40:43}, priority = {2}, title = {Randomized algorithms for the low-rank approximation of matrices}, url = {http://dx.doi.org/10.1073/pnas.0709640104}, volume = {104}, year = {2007} }

TY - JOUR ID - citeulike:2069894 L3 - citeulike-article-id:2069894 N2 - 10.1073/pnas.0709640104 We describe two recently proposed randomized algorithms for the construction of low-rank approximations to matrices, and demonstrate their application () 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 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. IS - 51 JF - Proceedings of the National Academy of Sciences EP - 20172 TI - Randomized algorithms for the low-rank approximation of matrices VL - 104 SP - 20167 KW - algorithms KW - linearalgebra KW - matrix KW - random KW - rank AU - Liberty, Edo AU - Woolfe, Franco AU - Martinsson, Per-Gunnar AU - Rokhlin, Vladimir AU - Tygert, Mark PY - 2007/12/18/ UR - http://dx.doi.org/10.1073/pnas.0709640104 ER -