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|Title||Accelerating Linear System Solutions Using Randomization Techniques|
|Publication Type||Journal Article|
|Year of Publication||2013|
|Authors||Baboulin, M., J. Dongarra, J. Herrmann, and S. Tomov|
|Journal||ACM Transactions on Mathematical Software (also LAWN 246)|
|Keywords||algorithms, dense linear algebra, experimentation, graphics processing units, linear systems, lu factorization, multiplicative preconditioning, numerical linear algebra, performance, plasma, randomization|
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.