Error estimation of the homotopy perturbation method to solve second kind Volterra integral equations with piecewise smooth kernels: Application of the CADNA …
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 …
discontinuous kernel obtained from the load leveling and energy system problems. For …
Resiliency in numerical algorithm design for extreme scale simulations
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 …
Extreme Scale Simulations' held March 1–6, 2020, at Schloss Dagstuhl, that was attended …
Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic
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 …
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 …
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 …
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
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 …
(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 …
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 …
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?
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 …
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 …
significantly affect computed results, especially in parallel codes like OpenMP ones. In this …