NDLI: Computing rank-revealing QR factorizations of dense matrices

Content Provider	ACM Digital Library
Author	Quintana-ortí, G. Bischof, Christian H.
Copyright Year	1998
Abstract	We develop algorithms and implementations for computing rank-revealing QR (RRQR) factorizations of dense matrices. First, we develop an efficient block algorithm for approximating an RRQR factorization, employing a windowed version of the commonly used Golub pivoting strategy, aided by incremental condition estimation. Second, we develop efficiently implementable variants of guaranteed reliable RRQR algorithms for triangular matrices originally suggested by Chandrasekaran and Ipsen and by Pan and Tang. We suggest algorithmic improvements with respect to condition estimation, termination criteria, and Givens updating. By combining the block algorithm with one of the triangular postprocessing steps, we arrive at an efficient and reliable algorithm for computing an RRQR factorization of a dense matrix. Experimental results on IBM RS/6000 SGI R8000 platforms show that this approach performs up to three times faster that the less reliable QR factorization with column pivoting as it is currently implemented in LAPACK, and comes within 15% of the performance of the LAPACK block algorithm for computing a QR factorization without any column exchanges. Thus, we expect this routine to be useful in may circumstances where numerical rank deficiency cannot be ruled out, but currently has been ignored because of the computational cost of dealing with it.
Starting Page	226
Ending Page	253
Page Count	28
File Format	PDF
ISSN	00983500
e-ISSN	15577295
DOI	10.1145/290200.287637
Volume Number	24
Issue Number	2
Journal	ACM Transactions on Mathematical Software (TOMS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1998-06-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	QR factorization Block algorithm Least-squares systems Numerical rank Rank-revealing orthogonal factorization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Software

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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