The Story of the Butterflies

Marc Baboulin (University of Paris-Sud)

Frank Adams 1,

We present an overview of how random butterfly transformations (RBT) can accelerate the solution of linear systems by preventing the communication overhead due to pivoting. We explain how it has been successfully applied to dense general and symmetric indefinite linear systems, resulting in efficient RBT solvers for current parallel architectures, including multicore, GPU and Intel Xeon Phi. We also present experiments on direct sparse factorizations (serial and parallel). In particular we describe how RBT can be combined with sparsity-preserving strategies. 

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