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

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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. 
@article{PDMA_2012_5_a64,
     author = {V. S. Usatyuk},
     title = {The implementation of the parallel orthogonalization algorithms in the shortest integer lattices basis problem},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {120--122},
     publisher = {mathdoc},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2012_5_a64/}
}
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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/