[Une stratégie dynamique pour les méthodes d'approximation]
Le résultat numérique fourni par une méthode d'approximation est entaché d'une erreur globale qui comprend à la fois une erreur de troncature et une erreur d'arrondi. Considérons la suite convergente générée en divisant par deux successivement le pas utilisé. Si les calculs sont effectués jusqu'à ce que, dans la zone de convergence, la différence entre deux approximations successives soit uniquement due aux erreurs d'arrondi, alors l'erreur globale sur le résultat obtenu est minimale. De plus, ses bits significatifs non entachés d'erreur d'arrondi sont en commun avec le résultat exact, à un près.
The numerical result provided by an approximation method is affected by a global error, which consists of both a truncation error and a round-off error. Let us consider the converging sequence generated by successively dividing by two the step size used. If computations are performed until, in the convergence zone, the difference between two successive approximations is only due to round-off errors, then the global error on the result obtained is minimal. Furthermore its significant bits which are not affected by round-off errors are in common with the exact result, up to one.
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Mots-clés : Informatique, Méthodes d'approximation, Validation numérique, Méthodes de quadrature, Méthodes de Newton–Cotes, Méthode de Gauss–Legendre, Méthode CESTAC, Arithmétique Stochastique Discrète
Fabienne Jézéquel 1
@article{CRMECA_2006__334_6_362_0,
author = {Fabienne J\'ez\'equel},
title = {A dynamical strategy for approximation methods},
journal = {Comptes Rendus. M\'ecanique},
pages = {362--367},
publisher = {Elsevier},
volume = {334},
number = {6},
year = {2006},
doi = {10.1016/j.crme.2006.04.005},
language = {en},
}
Fabienne Jézéquel. A dynamical strategy for approximation methods. Comptes Rendus. Mécanique, Volume 334 (2006) no. 6, pp. 362-367. doi : 10.1016/j.crme.2006.04.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.04.005/
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