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Towards Fast, Accurate and Reproducible LU Factorization

Roman Iakymchuk 1 David Defour 2 Stef Graillat 3
2 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
3 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : The process of finding the solution of a linear system of equations is often the core of many scientific applications. Usually, this process relies upon the LU factorization, which is also the most compute-intensive part of it. Although current implementations of the LU fac-torization may reach 70% of the peak performance, their accuracy and, even more, reproducibility cannot be guaranteed, mainly, due to the non-associativity of floating-point operations and dynamic thread scheduling. In this work, we address the problem of reproducibility of the LU factorization due to cancelations and rounding errors, resulting from floating-point arithmetic. Instead of developing a completely independent version of the LU factorization, we benefit from the hierarchical structure of linear algebra libraries and start from develop-ing/enhancing reproducible algorithmic variants for the kernel operations like the ones included in the BLAS library-that serve as building blocks in the LU factorization. In addition, we aim at ensuring the accuracy of these underlying BLAS routines.
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Contributor : Stef Graillat <>
Submitted on : Thursday, July 4, 2019 - 5:23:30 PM
Last modification on : Friday, January 8, 2021 - 5:40:03 PM


  • HAL Id : hal-01539343, version 1


Roman Iakymchuk, David Defour, Stef Graillat. Towards Fast, Accurate and Reproducible LU Factorization. SCAN 2016, 17th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, Sep 2016, Uppsala, Sweden. pp.59-60. ⟨hal-01539343⟩



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