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From Calculus to Algorithms without Errors

  • Norbert Müller
  • Martin Ziegler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

Abstract

Using mathematics within computer software almost always includes the necessity to compute with real (or complex) numbers. However, implementations often just use the 64-bit double precision data type. This may lead to serious stability problems even for mathematically correct algorithms. There are many ways to reduce these software-induced stability problems, for example quadruple or multiple-precision data types, interval arithmetic, or even symbolic computation. We propagate Exact Real Arithmetic (ERA) as a both convenient and practically efficient framework for rigorous numerical algorithms.

Keywords

Recursive Analysis Rigorous Numerics 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Norbert Müller
    • 1
  • Martin Ziegler
    • 2
  1. 1.Universität TrierGermany
  2. 2.TU DarmstadtGermany

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