Parallel codes for computing the numerical rank

Abstract

In this paper we present an experimental comparison of several numerical tools for computing the numerical rank of dense matrices. The study includes the well-known SVD, the URV decomposition, and several rank-revealing QR factorizations: the QR factorization with column pivoting, and two QR factorizations with restricted column pivoting. Two different parallel programming methodologies are analyzed in our paper. First, we present block-partitioned algorithms for the URV decomposition and rank-revealing QR factorizations which provide efficient implementations on shared memory environments. Furthermore, we also present parallel distributed algorithms, based on the message-passing paradigm, for computing rank-revealing QR factorizations on multicomputers.