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H 2 Wrapping in exact real arithmetic

Auteurs : Müller, Norbert (Auteur de la Conférence)
CIRM (Editeur )

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computability on real numbers exact real arithmetic wrapping effects Taylor models example 1 : logistic map example 2 : Van der Pol oscillator

Résumé : 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.

Codes MSC :
03D60 - Computability and recursion theory on ordinals, admissible sets, etc.
65Y15 - Packaged methods in numerical analysis
68Q25 - Analysis of algorithms and problem complexity

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 03/02/16
    Date de captation : 12/01/16
    Collection : Research talks
    Format : MP4 (.mp4) - HD
    Durée : 00:59:51
    Domaine : Computer Science ; Logic and Foundations
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2016-01-12_Muller.mp4

Informations sur la rencontre

Nom du congrès : Effective analysis: foundations, implementations, certification / Analyse effective: fondations, programmation, certification
Organisteurs Congrès : Mahboubi, Assia ; Schuster, Peter ; Spitters, Bas
Dates : 11/01/16 - 15/01/16
Année de la rencontre : 2016
URL Congrès : http://conferences.cirm-math.fr/1508.html

Citation Data

DOI : 10.24350/CIRM.V.18914503
Cite this video as: Müller, Norbert (2016). Wrapping in exact real arithmetic. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18914503
URI : http://dx.doi.org/10.24350/CIRM.V.18914503

Voir aussi


  1. iRRAM homepage - http://irram.uni-trier.de/

  2. GitHub - Norbert Müller/iRRAM: Exact real arithmetic in C++ - https://github.com/norbert-mueller/iRRAM

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