A compact Heart iteration for low-rank approximations of large matrices

Abstract

In this paper we present a compact version of the Heart iteration. One that computes low-rank approximations of large sparse matrices. The new iteration is a restarted Krylov method that is based on explicit restarts and Gram–Schmidt orthogonalizations. It is a simple algorithm that requires a minimal amount of computer storage as well as a minimal number of matrix–vector products per iteration. Yet it enjoys a fast rate of convergence. Numerical experiments illustrate the usefulness of the proposed approach.