Blendenpik: Supercharging LAPACK's Least-Squares Solver
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Avron-2010-BLENDENPIK_ SUPERCHA.pdf
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505.16 KB
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Checksum (MD5)
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Author(s)
Maymounkov, Petar Borissov
Toledo, Sivan
Avron, Haim
Date Issued
April 2010
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Avron, Haim, Petar Maymounkov, and Sivan Toledo. “Blendenpik: Supercharging LAPACK's Least-Squares Solver.” SIAM Journal on Scientific Computing 32.3 (2010): 1217. c2010 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
Several innovative random-sampling and random-mixing techniques for solving problems in linear algebra have been proposed in the last decade, but they have not yet made a significant impact on numerical linear algebra. We show that by using a high-quality implementation of one of these techniques, we obtain a solver that performs extremely well in the traditional yardsticks of numerical linear algebra: it is significantly faster than high-performance implementations of existing state-of-the-art algorithms, and it is numerically backward stable. More specifically, we describe a least-squares solver for dense highly overdetermined systems that achieves residuals similar to those of direct QR factorization-based solvers (lapack), outperforms lapack by large factors, and scales significantly better than any QR-based solver.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/090767911
