Geodesic
The implementation of the parallel orthogonalization algorithms in the shortest integer lattices basis problem
Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 120-122 
V. S. Usatyuk. The implementation of the parallel orthogonalization algorithms in the shortest integer lattices basis problem. Prikladnaya Diskretnaya Matematika. Supplement, no. 5 (2012), pp. 120-122. http://geodesic.mathdoc.fr/item/PDMA_2012_5_a64/
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     author = {V. S. Usatyuk},
     title = {The implementation of the parallel orthogonalization algorithms in the shortest integer lattices basis problem},
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     year = {2012},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2012_5_a64/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This article presents a way to significantly increase the performance of lattice basis reduction algorithms (hundredfold to three hundred times) by replacing recursive orthogonalization Gram–Schmidt algorithm by parallel QR algorithms. The paper contains a comparison between implementation of serial column-major Gram–Schmidt and parallel algorithms on NVIDIA CUDA GPU framework using Givens rotation, multicore CPU Intel Math Kernel library, and Householder transformation.

[1] Schnorr C. P., Euchner M., “Lattice basis reduction: Improved practical algorithms and solving subset Sum Problems”, Fundamentals of Computation Theory, Gosen, Germany, 1991, 68–85 | DOI | MR | Zbl

[2] Longley J. W., “Modified Gram–Schmidt process vs. classical Gram–Schmidt”, Commun. Stat. Simul. Comp., 10:5 (1981), 517–527 | DOI | MR | Zbl

[3] Press W. H., Teukolsky S. A., Vetterling W. T., Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, New York, 2007, 1262 pp. | MR | Zbl

[4] CUDA Toolkit 4.1 CUBLAS Library, , January 2012, 99 pp. http://goo.gl/85KwD

[5] Programmy dlya privedeniya bazisa reshëtok, , 2012 http://www.lcrypto.com/lsolv

[6] Lattice SVP and SBP challenge, , 2011 http://www.latticechallenge.org/