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Journal Articles ACM Transactions on Mathematical Software Year : 2013

Accelerating linear system solutions using randomization technique

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.
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Dates and versions

hal-00908496 , version 1 (23-11-2013)

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Marc Baboulin, Jack Dongarra, Julien Herrmann, Stanimire Tomov. Accelerating linear system solutions using randomization technique. ACM Transactions on Mathematical Software, 2013, 39 (2), ⟨10.1145/2427023.2427025⟩. ⟨hal-00908496⟩
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