Hierarchical Approach for Deriving a Reproducible LU factorization

Roman Iakymchuk 1 Stef Graillat 2 David Defour 3 Erwin Laure 1 Enrique Quintana-Ortí 4
2 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
3 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : 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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Contributor : Roman Iakymchuk <>
Submitted on : Tuesday, January 3, 2017 - 9:59:42 AM
Last modification on : Friday, August 31, 2018 - 9:25:55 AM
Long-term archiving on : Tuesday, April 4, 2017 - 1:10:38 PM


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  • HAL Id : hal-01419813, version 2


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



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