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A fundamental problem when adding column pivoting to the Householder QRfactorization is that only about half of the computation can be cast in termsof high performing matrix-matrix multiplications, which greatly limits thebenefits that can be derived from so-called blocking of algorithms. This paperdescribes a technique for selecting groups of pivot vectors by means ofrandomized projections. It is demonstrated that the asymptotic flop count forthe proposed method is $2mn^2 - (2/3)n^3$ for an $m\times n$ matrix, identicalto that of the best classical unblocked Householder QR factorization algorithm(with or without pivoting). Experiments demonstrate acceleration in speed ofclose to an order of magnitude relative to the {\sc geqp3} function in LAPACK,when executed on a modern CPU with multiple cores. Further, experimentsdemonstrate that the quality of the randomized pivot selection strategy isroughly the same as that of classical column pivoting. The described algorithmis made available under Open Source license and can be used with LAPACK orlibflame.

Householder QR Factorization with Randomization for Column Pivoting (HQRRP). FLAME Working Note #78