A BLAS-3 version of the QR factorization with column pivoting

The QR factori ation with column pivoting (QRP), originally suggested by Golub [Numer. Math., 7 (1965), 206-216], is a popular approach to computing rank-revealing factori ations. Using Level 1 BLAS, it was implemented in LINPACK, and, using Level 2 BLAS, in LAPACK. While the Level 2 BLAS version delivers superior performance in general, it may result in worse performance for large matrix si es due to cache e ects. We introduce a modification of the QRP algorithm which allows the use of Level 3 BLAS kernels while maintaining the numerical behavior of the LINPACK and LAPACK implementations. Experimental comparisons of this approach with the LINPACK and LAPACK implementations on IBM RS/6000, SGI R8000, and DEC A P platforms show considerable performance improvements.