关键词：数据传输；算法；QR；CARRQR；数值等级
摘 要：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 e ective tool in revealing the rank in practical problems.Our main motivation for introducing CARRQR is that it minimizes data transfer, modulo poly-logarithmic 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.