A Fast Randomized Algorithm for Orthogonal Projection
SIAM Journal on Scientific Computing
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Fast approximation of matrix coherence and statistical leverage
The Journal of Machine Learning Research
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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.