A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

Autor: Samad Noeiaghdam, Sanda Micula, Juan J. Nieto

Publikováno v: Mathematics, Vol 9, Iss 12, p 1321 (2021)

In this paper, a nonlinear fractional order model of COVID-19 is approximated. For this aim, at first we apply the Caputo–Fabrizio fractional derivative to model the usual form of the phenomenon. In order to show the existence of a solution, the Ba

Externí odkaz: https://doaj.org/article/21a902fffb6b48fb9ae83a36819286f5

Computing multiple roots of polynomials in stochastic arithmetic with Newton method and approximate GCD

Autor: Graillat, Stef, Jézéquel, Fabienne, Queiros Martins, Enzo, Spyropoulos, Maxime

In this article, we propose new methods to compute multiple roots of polynomials in floating-point arithmetic. We rely on stochastic arithmetic that makes it possible to deal with rounding errors. We develop the concept of stochastic GCD that we use

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a98cecb179228a7c5f2460704213d15f
https://hal.archives-ouvertes.fr/hal-03274453

Numerical validation of half precision simulations

Autor: Sara sadat Hoseininasab, Thibault Hilaire, Fabienne Jézéquel

Publikováno v: 1st Workshop on Code Quality and Security (CQS 2021) in conjunction with WorldCIST'21 (9th World Conference on Information Systems and Technologies)
1st Workshop on Code Quality and Security (CQS 2021) in conjunction with WorldCIST'21 (9th World Conference on Information Systems and Technologies), Mar 2021, Terceira Island, Azores, Portugal
RAIM (Rencontres Arithmétiques de l'Informatique Mathématique)
RAIM (Rencontres Arithmétiques de l'Informatique Mathématique), May 2021, Paris, France
Advances in Intelligent Systems and Computing ISBN: 9783030726539
WorldCIST (4)

International audience; 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 detect numerical instabilities in floatin

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::443940b3e9b247e92fc676be1f2b32bc
https://hal.archives-ouvertes.fr/hal-03138494/document

A Novel Technique to Control the Accuracy of a Nonlinear Fractional Order Model of COVID-19: Application of the CESTAC Method and the CADNA Library

Autor: Sanda Micula, Samad Noeiaghdam, Juan J. Nieto

Publikováno v: Minerva: Repositorio Institucional de la Universidad de Santiago de Compostela
Universidad de Santiago de Compostela (USC)
Mathematics, Vol 9, Iss 1321, p 1321 (2021)
Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
instname
Mathematics
Volume 9
Issue 12

In this paper, a nonlinear fractional order model of COVID-19 is approximated. For this aim, at first we apply the Caputo–Fabrizio fractional derivative to model the usual form of the phenomenon. In order to show the existence of a solution, the Ba

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::588b13e62a4f78ef42a6da863471c1d3
https://doi.org/10.3390/math9121321

Can We Avoid Rounding-Error Estimation in HPC Codes and Still Get Trustworthy Results?

Autor: Stef Graillat, Roman Iakymchuk, Fabienne Jézéquel, Daichi Mukunoki, Toshiyuki Imamura

Publikováno v: Lecture Notes in Computer Science ISBN: 9783030636173
VSTTE
Lecture Notes in Computer Science
Lecture Notes in Computer Science-Software Verification
NSV'20, 13th International Workshop on Numerical Software Verification
NSV'20, 13th International Workshop on Numerical Software Verification, Jul 2020, Los Angeles, CA, United States

International audience; 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 validate the accuracy of floating-point com

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2280c897afcdf19ec5edaeb3ecb3eaeb
https://doi.org/10.1007/978-3-030-63618-0_10