Error estimation of the homotopy perturbation method to solve second kind Volterra integral equations with piecewise smooth kernels: Application of the CADNA …

S Noeiaghdam, A Dreglea, J He, Z Avazzadeh… - Symmetry, 2020 - mdpi.com
This paper studies the second kind linear Volterra integral equations (IEs) with a
discontinuous kernel obtained from the load leveling and energy system problems. For …

Resiliency in numerical algorithm design for extreme scale simulations

E Agullo, M Altenbernd, H Anzt… - … Journal of High …, 2022 - journals.sagepub.com
This work is based on the seminar titled 'Resiliency in Numerical Algorithm Design for
Extreme Scale Simulations' held March 1–6, 2020, at Schloss Dagstuhl, that was attended …

Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic

S Graillat, F Jézéquel, R Picot, F Févotte… - Journal of computational …, 2019 - Elsevier
The type length chosen for floating-point numbers (eg 32 bits or 64 bits) may have an impact
on the execution time, especially on SIMD (Single Instruction Multiple Data) units …

A Novel Algorithm to Evaluate Definite Integrals by the Gauss-Legendre Integration Rule Based on the Stochastic Arithmetic: Application in the Model of Osmosis …

S Noeiaghdam, MAF Araghi - Mathematical Modelling of …, 2020 - search.ebscohost.com
Finding the optimal iteration of Gaussian quadrature rule is one of the important problems in
the computational methods. In this study, we apply the CESTAC (Controle et Estimation …

Acceleration of nuclear reactor simulation and uncertainty quantification using low-precision arithmetic

A Cherezov, A Vasiliev, H Ferroukhi - Applied Sciences, 2023 - mdpi.com
In recent years, interest in approximate computing has been increasing significantly in many
disciplines in the context of saving energy and computation cost by trading off on the quality …

A framework for semi-automatic precision and accuracy analysis for fast and rigorous deep learning

C Lauter, A Volkova - 2020 IEEE 27th Symposium on …, 2020 - ieeexplore.ieee.org
Deep Neural Networks (DNN) represent a performance-hungry application. Floating-Point
(FP) and custom floating-point-like arithmetic satisfies this hunger. While there is need for …

Numerical validation of half precision simulations

F Jézéquel, SS Hoseininasab, T Hilaire - Trends and Applications in …, 2021 - Springer
In this article, we show how to control the numerical quality of half precision computations
using stochastic arithmetic. The CADNA library that is used to estimate rounding errors and …

FP-ANR: A representation format to handle floating-point cancellation at run-time

D Defour - 2018 IEEE 25th Symposium on Computer Arithmetic …, 2018 - ieeexplore.ieee.org
When dealing with floating-point numbers, there are several sources of error which can
drastically reduce the numerical quality of computed results. One of those error sources is …

Can we avoid rounding-error estimation in HPC codes and still get trustworthy results?

F Jézéquel, S Graillat, D Mukunoki, T Imamura… - … , VSTTE 2020, and 13th …, 2020 - Springer
Numerical validation enables one to ensure the reliability of numerical computations that
rely on floating-point operations. Discrete Stochastic Arithmetic (DSA) makes it possible to …

Estimation of round-off errors in OpenMP codes

P Eberhart, J Brajard, P Fortin, F Jézéquel - OpenMP: Memory, Devices …, 2016 - Springer
It is crucial to control round-off error propagation in numerical simulations, because they can
significantly affect computed results, especially in parallel codes like OpenMP ones. In this …