Accelerating Linear System Solutions Using Randomization Techniques

Marc Baboulin, Jack Dongarra, Julien Herrmann, Stanimire Tomov
2013 ACM Transactions on Mathematical Software  
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
more » ... led Partial Random Buttery 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.
doi:10.1145/2427023.2427025 fatcat:rbb5bn2dbrhq7bhr3wxtfoh45a