Blendenpik: Supercharging LAPACK's Least-Squares Solver

• Main Authors: Maymounkov, Petar Borissov (Contributor), Toledo, Sivan (Contributor), Avron, Haim (Author)
• Other Authors: Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: Society for Industrial and Applied Mathematics, 2011-02-16T15:50:47Z.
• Subjects: Article
• Online Access: Get fulltext

 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.