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Séminaire du LRI
Fast and reliable solutions for numerical linear algebra solvers in high-performance computing (HDR defense)
Marc Baboulin

05 December 2012, 10h00 - 05 December 2012, 11h30
Salle/Bat : 435/PCRI-N
Contact : marc.baboulin@lri.fr

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Résumé :
Recent years have seen an increase in peak ``local" speed through parallelism in terms of multicore processors and GPU accelerators. At the same time, the cost of communication between memory hierarchies and/or between processors have become a major bottleneck for most linear algebra algorithms. In this presentation we explain how hybrid multicore+GPU systems can be used efficiently to enhance performance of linear algebra libraries. We illustrate this approach by considering hybrid factorizations where we split the computation over a multicore and a graphic processor and where the amount of communication is significantly reduced.
Next we describe a class of randomized algorithms that accelerate factorization of general or symmetric indefinite systems on multicore or hybrid multicore+GPU systems. Randomization prevents the communication overhead due to pivoting, is computationally inexpensive and requires very little storage. The resulting solvers outperform existing routines while providing us with a satisfying accuracy.
Finally we present numerical tools that enable us to assess the quality of the computed solution of overdetermined linear least squares. Our method is based on deriving exact values or statistical estimates for the condition number of these problems. We describe algorithms and software to compute these quantities using HPC libraries.

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