Blendenpik: Supercharging lapack's least-squares solver

Haim Avron*, Petar Maymounkov, Sivan Toledo

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

139 Scopus citations


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.

Original languageEnglish
Pages (from-to)1217-1236
Number of pages20
JournalSIAM Journal on Scientific Computing
Issue number3
StatePublished - 2010


  • Dense linear least squares
  • Randomized numerical linear algebra
  • Randomized preconditioners


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