Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

Details Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

2009-09-22

arxiv.org/abs/0909.4061v2

Mathematics

Numerical Analysis

Scientific paper

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 performing low-rank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. This paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions. These methods use random sampling to identify a subspace that captures most of the action of a matrix. The input matrix is then compressed---either explicitly or implicitly---to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization. In many cases, this approach beats its classical competitors in terms of accuracy, speed, and robustness. These claims are supported by extensive numerical experiments and a detailed error analysis.

Affiliated with

Also associated with

No associations

Rating

Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-301399