Randomized algorithms for the low-rank approximation of matrices.

Liberty, Edo; Woolfe, Franco; Martinsson, Per-Gunnar; Rokhlin, Vladimir; Tygert, Mark · Proc Natl Acad Sci U S A · 2007

basic_science · Level V

Where this comes from

Abstract

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.