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Interval Arithmetic

  • Jean-Michel Muller
  • Nicolas Brunie
  • Florent de Dinechin
  • Claude-Pierre Jeannerod
  • Mioara Joldes
  • Vincent Lefèvre
  • Guillaume Melquiond
  • Nathalie Revol
  • Serge Torres
Chapter

Abstract

The automation of the a posteriori analysis of floating-point error cannot be done in a perfect way (except possibly in straightforward or specific cases), yielding exactly the roundoff error. However, an approach based on interval arithmetic can provide results with a more or less satisfactory quality and with more or less efforts to obtain them. This is a historical reason for introducing interval arithmetic, as stated in the preface of R. Moore’s PhD dissertation [427]: “In a hour’s time a modern high-speed stored-program digital computer can perform arithmetic computations which would take a “hand-computer” equipped with a desk calculator five years to do. In setting out a five year computing project, a hand computer would be justifiably (and very likely gravely) concerned over the extent to which errors were going to accumulate—not mistakes, which he will catch by various checks on his work—but errors due to rounding” and discretization and truncation errors.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jean-Michel Muller
    • 1
  • Nicolas Brunie
    • 2
  • Florent de Dinechin
    • 3
  • Claude-Pierre Jeannerod
    • 4
  • Mioara Joldes
    • 5
  • Vincent Lefèvre
    • 4
  • Guillaume Melquiond
    • 6
  • Nathalie Revol
    • 4
  • Serge Torres
    • 7
  1. 1.CNRS - LIPLyonFrance
  2. 2.KalrayGrenobleFrance
  3. 3.INSA-Lyon - CITIVilleurbanneFrance
  4. 4.Inria - LIPLyonFrance
  5. 5.CNRS - LAASToulouseFrance
  6. 6.Inria - LRIOrsayFrance
  7. 7.ENS-Lyon - LIPLyonFrance

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