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Chapitres

Wrapping in exact real arithmetic

De Norbert Müller

Apparaît dans la collection : Effective analysis: foundations, implementations, certification / Analyse effective: fondations, programmation, certification

A serious problem common to all interval algorithms is that they suffer from wrapping effects, i.e. unnecessary growth of approximations during a computation. This is essentially connected to functional dependencies inside vectors of data computed from the same inputs. Reducing these effects is an important issue in interval arithmetic, where the most successful approach uses Taylor models. In TTE Taylor models have not been considered explicitly, as they use would not change the induced computability, already established using ordinary interval computations. However for the viewpoint of efficiency, they lead to significant improvements. In the talk we report on recent improvements on the iRRAM software for exact real arithmetic (ERA) based on Taylor models. The techniques discussed should also easily be applicable to other software for exact real computations as long as they also are based on interval arithmetic. As instructive examples we consider the one-dimensional logistic map and a few further discrete dynamical systems of higher dimensions Joint work with Franz Brauße, Trier, and Margarita Korovina, Novosibirsk.

Informations sur la vidéo

Date de captation 12/01/2016
Date de publication 03/02/2016
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.18914503
Citer cette vidéo Müller, Norbert (12/01/2016). Wrapping in exact real arithmetic. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18914503
URL https://dx.doi.org/10.24350/CIRM.V.18914503

Domaine(s)

Bibliographie

iRRAM homepage - http://irram.uni-trier.de/
GitHub - Norbert Müller/iRRAM: Exact real arithmetic in C++ - https://github.com/norbert-mueller/iRRAM

Codes MSC

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