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.
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download

Contributor : Roman Iakymchuk <>
Submitted on : Thursday, February 2, 2017 - 4:52:32 PM
Last modification on : Friday, August 31, 2018 - 9:25:55 AM
Long-term archiving on : Friday, May 5, 2017 - 11:48:59 AM


Files produced by the author(s)


  • HAL Id : hal-01419813, version 3


Roman Iakymchuk, Stef Graillat, David Defour, Erwin Laure, Enrique Quintana-Ortí. Hierarchical Approach for Deriving a Reproducible LU factorization. 2016. ⟨hal-01419813v3⟩



Record views


Files downloads