@article {icl:721,
	title = {Accelerating Linear System Solutions Using Randomization Techniques},
	journal = {ACM Transactions on Mathematical Software (also LAWN 246)},
	volume = {39},
	year = {2013},
	month = {2013-02},
	abstract = {We illustrate how linear algebra calculations can be enhanced by statistical techniques in the case of a square linear system Ax = b. We study a random transformation of A that enables us to avoid pivoting and then to reduce the amount of communication. Numerical experiments show that this randomization can be performed at a very affordable computational price while providing us with a satisfying accuracy when compared to partial pivoting. This random transformation called Partial Random Butterfly Transformation (PRBT) is optimized in terms of data storage and flops count. We propose a solver where PRBT and the LU factorization with no pivoting take advantage of the current hybrid multicore/GPU machines and we compare its Gflop/s performance with a solver implemented in a current parallel library.},
	keywords = {algorithms, dense linear algebra, experimentation, graphics processing units, linear systems, lu factorization, multiplicative preconditioning, numerical linear algebra, performance, plasma, randomization},
	doi = {10.1145/2427023.2427025},
	url = {http://dl.acm.org/citation.cfm?id=2427025},
	author = {Marc Baboulin and Jack Dongarra and Julien Herrmann and Stanimire Tomov}
}
