Per-Gunnar Martinsson

TL;DR: This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation, and presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions.

TL;DR: In this article, a modular framework for constructing randomized algorithms that compute partial matrix decompositions is presented, which uses random sampling to identify a subspace that captures most of the action of a matrix and then the input matrix is compressed to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization.

TL;DR: Two recently proposed randomized algorithms for the construction of low-rank approximations to matrices are described and shown to be considerably more efficient and reliable than the classical (deterministic) ones; they also parallelize naturally.

TL;DR: In this article, the authors present a modular framework for constructing randomized algorithms that compute partial matrix decompositions, which use random sampling to identify a subspace that captures most of the action of a matrix.

TL;DR: In this article, the authors presented a randomized procedure for the approximation of A with a matrix Z of rank k. The procedure relies on applying A T to a collection of l random vectors, where l is an integer equal to or slightly greater than k; the scheme is efficient whenever A and A T can be applied rapidly to arbitrary vectors.