Randomized methods for matrix computations

TL;DR

This paper introduces randomized algorithms for matrix factorization that are faster and require less communication, especially useful for large matrices and low-rank approximations.

Contribution

It presents new randomized algorithms that improve efficiency and reduce communication in matrix factorizations compared to traditional methods.

Findings

Algorithms achieve high practical speed for large matrices.

Effective for low-rank approximations and full factorizations.

Require less communication than deterministic algorithms.

Abstract

The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate computations using randomized projections. The algorithms are particularly powerful for computing low-rank approximations to very large matrices, but they can also be used to accelerate algorithms for computing full factorizations of matrices. A key competitive advantage of the algorithms described is that they require less communication than traditional deterministic methods.