Pré-Publication, Document De Travail Année : 2016

Hierarchical Approach for Deriving a Reproducible LU factorization

Résumé

We propose a reproducible variant of the unblocked LU factorization for graphics processor units (GPUs). For this purpose, we build upon Level-1/2 BLAS kernels that deliver correctly-rounded and reproducible results for the dot (inner) product, vector scaling, and the matrix-vector product. In addition, we draw a strategy to enhance the accuracy of the triangular solve via iterative refinement. Following a bottom-up approach, we finally construct a reproducible unblocked implementation of the LU factorization for GPUs, which accommodates partial pivoting for stability and can be eventually integrated into a (blocked) high performance and stable algorithm for the LU factorization.

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Dates et versions

hal-01419813 , version 1 (20-12-2016)
hal-01419813 , version 2 (03-01-2017)
hal-01419813 , version 3 (02-02-2017)
hal-01419813 , version 4 (18-04-2017)

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  • HAL Id : hal-01419813 , version 2

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Roman Iakymchuk, Stef Graillat, David Defour, Erwin S Laure, Enrique S Quintana-Ortí. Hierarchical Approach for Deriving a Reproducible LU factorization. 2016. ⟨hal-01419813v2⟩
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