Abstract
The solution to many scientific and engineering problems requires the determination of the numerical rank of matrices. We present new parallel algorithms for computing rank-revealing QR (RRQR) factorizations of dense matrices on multicomputers, based on a serial approach developed by C. H. Bischof and G. Quintana-Orti. The parallel implementations include the usual QR factorization with column pivoting, and a new faster approach that consists of two stages: a QR factorization with local column pivoting and a reliable rank-revealing algorithm appropriate for triangular matrices. Our parallel implementations include the BLAS-2 and BLAS-3 QR factorizations without pivoting since they are a good reference point, though they are not appropriate for rank-revealing purposes.
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