In this paper we introduce CARRQR, a communication avoiding rank revealing QR

factorization with tournament pivoting. We show that CARRQR reveals the numerical

rank of a matrix in an analogous way to QR factorization with column pivoting (QRCP).

Although the upper bound of a quantity involved in the characterization of a rank revealing

factorization is worse for CARRQR than for QRCP, our numerical experiments on a set of

challenging matrices show that this upper bound is very pessimistic, and CARRQR is an

effective tool in revealing the rank in practical problems.

Our main motivation for introducing CARRQR is that it minimizes data transfer, modulo

polylogarithmic factors, on both sequential and parallel machines, while previous factorizations

as QRCP are communication sub-optimal and require asymptotically more communication

than CARRQR. Hence CARRQR is expected to have a better performance on current and

future computers, where commmunication is a major bottleneck that highly impacts the

performance of an algorithm.

Communication Avoiding Rank Revealing QR Factorization with Column Pivoting