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

The QR factorization with column pivoting (QRP), originally suggested by Golub [Numer. Math., 7 (1965), 206--216], is a popular approach to computing rank-revealing factorizations. Using Level 1 BLAS, it was implemented in LINPACK, and, using Level 2 BLAS, in LAPACK. While the Level 2 BLAS version d...

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Bibliographic Details
Published in:SIAM journal on scientific computing 1998-09, Vol.19 (5), p.1486-1494
Main Authors: QUINTANA-ORTI, G, XIAOBAI SUN, BISCHOF, C. H
Format: Article
Language:English
Subjects:
Algorithms
Array processors
Computer science
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
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Summary:The QR factorization with column pivoting (QRP), originally suggested by Golub [Numer. Math., 7 (1965), 206--216], is a popular approach to computing rank-revealing factorizations. 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 sizes due to cache effects. 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 AXP platforms show considerable performance improvements.
ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827595296732