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Function Interval Arithmetic

  • Jan Duracz
  • Amin Farjudian
  • Michal Konečný
  • Walid Taha
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

Abstract

We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1) Validated ordinary differential equation solving using the AERN library and within the Acumen hybrid system modeling tool. (2) Numerical theorem proving using the PolyPaver prover.

Keywords

Validated Numeric Computation ODEs Theorem Proving 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Jan Duracz
    • 1
  • Amin Farjudian
    • 2
  • Michal Konečný
    • 3
  • Walid Taha
    • 4
    • 5
  1. 1.No AffiliationPoland
  2. 2.School of Computer ScienceUniversity of Nottingham NingboChina
  3. 3.School of Engineering and Applied ScienceAston UniversityBirminghamUK
  4. 4.Halmstadt UniversitySweden
  5. 5.Rice UniversityHoustonUSA

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