We show in this paper 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 aordable computational price while providing us with a satisfying accuracy when compared to partial pivoting. This random transformation called Partial Random

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... uttery Transformation (PRBT) is optimized in terms of data storage and ops count. We propose a solver where PRBT and the LU factorization with no pivoting take advantage of the latest generation of hybrid multicore/GPU machines and we compare its Gop/s performance with a solver implemented in a current parallel library.