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A class of communication-avoiding algorithms for solving general dense linear systems on CPU/GPU parallel machines

Marc Baboulin, Simplice Donfack, Laura Grigori, Adrien Remy, Stanimire Tomov, Jack Dongarra
Laboratoire de Recherche en Informatique – Universite Paris-Sud 11 (LRI), Universite Paris XI – Paris Sud
hal-00656457, version 2, 2012

@article{baboulin2012class,

   title={A class of communication-avoiding algorithms for solving general dense linear systems on CPU/GPU parallel machines},

   author={Baboulin, Marc and Donfack, Simplice and Grigori, Laura and Remy, Adrien and Tomov, Stanimire and Dongarra, Jack},

   year={2012}

}

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We study several solvers for the solution of general linear systems where the main objective is to reduce the communication overhead due to pivoting. We first describe two existing algorithms for the LU factorization on hybrid CPU/GPU architectures. The first one is based on partial pivoting and the second uses a random preconditioning of the original matrix to avoid pivoting. Then we introduce a solver where the panel factorization is performed using a communication-avoiding pivoting heuristic while the update of the trailing submatrix is performed by the GPU. We provide performance comparisons for these solvers on current hybrid multicore-GPU parallel machines.
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