Hierarchical approach for deriving a reproducible unblocked LU factorization

Roman Iakymchuk 1 Stef Graillat 2 David Defour 3 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 in a high performance and stable algorithm for the (blocked) LU factorization.
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https://hal.archives-ouvertes.fr/hal-01419813
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Roman Iakymchuk, Stef Graillat, David Defour, Enrique Quintana-Ortí. Hierarchical approach for deriving a reproducible unblocked LU factorization. International Journal of High Performance Computing Applications, SAGE Publications, 2019, pp.#1094342019832968. ⟨10.1177/1094342019832968⟩. ⟨hal-01419813v4⟩

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