Zobrazeno 1 - 10 of 64 pro vyhledávání: '"Discrete Stochastic Arithmetic"'
1
Akademický článek
Advantages of the Discrete Stochastic Arithmetic to Validate the Results of the Taylor Expansion Method to Solve the Generalized Abel’s Integral Equation
Autor: Eisa Zarei, Samad Noeiaghdam
Publikováno v: Symmetry, Vol 13, Iss 8, p 1370 (2021)
The aim of this paper is to apply the Taylor expansion method to solve the first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: the FPA and the DSA. In order to apply the DSA, we use the CES
Externí odkaz: https://doaj.org/article/5d733d6d7c864f7e8c99ebe298d8b585
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2
Akademický článek
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
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3
Akademický článek
Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection
Autor: Samad Noeiaghdam, Sanda Micula
Publikováno v: Mathematics, Vol 9, Iss 9, p 1031 (2021)
This study focuses on solving the nonlinear bio-mathematical model of malaria infection. For this aim, the HATM is applied since it performs better than other methods. The convergence theorem is proven to show the capabilities of this method. Instead
Externí odkaz: https://doaj.org/article/0c6f09afb5d24ba392e583db4f3aa2ec
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4
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
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5
Dynamical Strategy to Control the Accuracy of the Nonlinear Bio-Mathematical Model of Malaria Infection
Autor: Sanda Micula, Samad Noeiaghdam
Publikováno v: Mathematics
Volume 9
Issue 9
Mathematics, Vol 9, Iss 1031, p 1031 (2021)
This study focuses on solving the nonlinear bio-mathematical model of malaria infection. For this aim, the HATM is applied since it performs better than other methods. The convergence theorem is proven to show the capabilities of this method. Instead
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::733303a026f0d39e5b8404eacd99903e
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6
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
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7
Benefits of stochastic arithmetic in high performance simulations and arbitrary precision codes
Autor: Jézéquel, Fabienne
Publikováno v: 19th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2020)
19th international symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN 2020), Sep 2021, Szeged, Hungary
International audience
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::343d4cda1b2227811c45900e48533622
https://hal.archives-ouvertes.fr/hal-03346220
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8
Can we avoid rounding-error estimation in HPC codes and still get trustful results?
Autor: Jézéquel, Fabienne, Graillat, Stef, Mukunoki, Daichi, Imamura, Toshiyuki, Iakymchuk, Roman
Numerical validation enables one to improve the reliability of numerical computations that rely upon floating-point operations through obtaining trustful results. Discrete Stochastic Arithmetic (DSA) makes it possible to validate the accuracy of floa
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::b12d4cb0e3b3535c0075f3fe1de358e9
https://hal.archives-ouvertes.fr/hal-02486753
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9
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
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10
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
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