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A fast randomized algorithm for overdetermined linear least-squares regression
Open accessAbstract
We introduce a randomized algorithm for overdetermined linear least-squares regression. Given an arbitrary full-rank m × n matrix A with m ≥ n , any m × 1 vector b , and any positive real number ε, the procedure computes an n × 1 vector x such that x minimizes the Euclidean norm ‖ Ax − b ‖ to relative precision ε. The algorithm typically requires 𝒪((log( n )+log(1/ε)) mn + n 3 ) floating-point operations. This cost is less than the 𝒪( mn 2 ) required by the classical schemes based on QR -decompositions or bidiagonalization. We present several numerical examples illustrating the performance of the algorithm.
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Cites
Randomized algorithms for the low-rank approximation of matrices
Liberty, E., Woolfe, F., Martinsson, P.-G., Rokhlin, V., & Tygert, M. (2007) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0709640104 · Cited by 559
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Computational Advertising: Techniques for Targeting Relevant Ads
Woodruff, D. P. (2014) · Foundations and Trends® in Theoretical Computer Science · doi:10.1561/0400000060 · Cited by 866
Metadata
- Authors
- Rokhlin, V., & Tygert, M.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 2008-09-09
- Volume
- 105
- Issue
- 36
- Pages
- 13212-13217
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2107599050
- Cited by
- 183
- References
- 1
- FWCI
- 7.84
- Type
- journal article
- Language
- en
- Open access
- green
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