TY - JOUR
T1 - Randomized LU decomposition
AU - Shabat, Gil
AU - Shmueli, Yaniv
AU - Aizenbud, Yariv
AU - Averbuch, Amir
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2018/3/1
Y1 - 2018/3/1
N2 - Randomized algorithms play a central role in low rank approximations of large matrices. In this paper, the scheme of the randomized SVD is extended to a randomized LU algorithm. Several error bounds are introduced, that are based on recent results from random matrix theory related to subgaussian matrices. The bounds also improve the existing bounds of already known randomized SVD algorithm. The algorithm is fully parallelized and thus can utilize efficiently GPUs without any CPU–GPU data transfer. Numerical examples, which illustrate the performance of the algorithm and compare it to other decomposition methods, are presented.
AB - Randomized algorithms play a central role in low rank approximations of large matrices. In this paper, the scheme of the randomized SVD is extended to a randomized LU algorithm. Several error bounds are introduced, that are based on recent results from random matrix theory related to subgaussian matrices. The bounds also improve the existing bounds of already known randomized SVD algorithm. The algorithm is fully parallelized and thus can utilize efficiently GPUs without any CPU–GPU data transfer. Numerical examples, which illustrate the performance of the algorithm and compare it to other decomposition methods, are presented.
KW - LU decomposition
KW - Matrix factorizations
KW - Random matrices
KW - Randomized algorithms
UR - http://www.scopus.com/inward/record.url?scp=84975167733&partnerID=8YFLogxK
U2 - 10.1016/j.acha.2016.04.006
DO - 10.1016/j.acha.2016.04.006
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84975167733
SN - 1063-5203
VL - 44
SP - 246
EP - 272
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 2
ER -