Blendenpik: Supercharging LAPACK's Least-Squares Solver

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. Key words. dense linear least squares, randomized numerical linear algebra, randomized preconditioners AMS subject classifications. 65F20, 68W20, 65F10 D...

• Type: Journal
• Year: 2010
• Where: SIAMSC
• Authors: Haim Avron, Petar Maymounkov, Sivan Toledo
• Keywords: Linear Algebra, Numerical Linear Algebra, QR Factorization-based Solvers, SIAMSC 2010