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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.
https://hal.inria.fr/hal-00908496
Contributor : Marc Baboulin Connect in order to contact the contributor
Submitted on : Saturday, November 23, 2013 - 7:18:01 PM
Last modification on : Monday, May 16, 2022 - 4:46:01 PM
Contributor : Marc Baboulin Connect in order to contact the contributor
Submitted on : Saturday, November 23, 2013 - 7:18:01 PM
Last modification on : Monday, May 16, 2022 - 4:46:01 PM
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