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Using Taylor Models in Exact Real Arithmetic

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Mathematical Aspects of Computer and Information Sciences (MACIS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9582))

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Abstract

Software libraries for Exact Real Arithmetic implement the theory of computability on non-denumerable sets. Usually they are based on interval arithmetic. We discuss enhancements where the interval arithmetic is augmented by versions of Taylor models. Although this has no effect on the abstract notion of computability, the efficiency of implementations can be improved dramatically.

The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA grant agreement no. PIRSES-GA-2011-294962-COMPUTAL and from the DFG/RFBR grant CAVER BE 1267/14-1 and 14-01-91334.

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Authors and Affiliations

  1. Abteilung Informatikwissenschaften, Universität Trier, Trier, Germany

    Franz Brauße & Norbert Müller

  2. A.P. Ershov Institute of Informatics Systems, Novosibirsk, Russia

    Margarita Korovina

Authors
  1. Franz Brauße
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  2. Margarita Korovina
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  3. Norbert Müller
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Corresponding author

Correspondence to Norbert Müller .

Editor information

Editors and Affiliations

  1. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  2. Hamburg University of Technology, Hamburg, Germany

    Siegfried M. Rump

  3. New York University, New York, New York, USA

    Chee K. Yap

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Brauße, F., Korovina, M., Müller, N. (2016). Using Taylor Models in Exact Real Arithmetic. In: Kotsireas, I., Rump, S., Yap, C. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2015. Lecture Notes in Computer Science(), vol 9582. Springer, Cham. https://doi.org/10.1007/978-3-319-32859-1_41

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  • DOI: https://doi.org/10.1007/978-3-319-32859-1_41

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32858-4

  • Online ISBN: 978-3-319-32859-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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