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 inSIAM journal on scientific computing Vol. 19; no. 5; pp. 1486 - 1494
Main Authors Quintana-Ortí, Gregorio, Sun, Xiaobai, Bischof, Christian H.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.09.1998
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
Column pivoting
Block algorithm
QR factorization
Matrices
Performance
Algorithm
Factorization
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ISSN1064-8275
1095-7197
DOI10.1137/S1064827595296732

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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.
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ISSN:1064-8275
1095-7197
DOI:10.1137/S1064827595296732