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Interval Arithmetic and Standardization

Authors: Jürgen Wolff von Gudenberg

Published in: Dagstuhl Seminar Proceedings, Volume 8021, Numerical Validation in Current Hardware Architectures (2008)

Abstract

Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of real numbers with floating-point bounds. Operations for intervals can be efficiently implemented. There is an unanimous agreement, how to define the basic operations, if we exclude division by an interval containing zero. Hence, it should be standardized. For division by zero, two options are possible, the clean exception free interval arithmetic or the containment arithmetic. They can be standardized as options. Elementary functions for intervals can be defined. In some application areas loose evaluation of functions, i.e. evaluation over an interval which is not completely contained in the function domain, is recommended, In this case, however, a discontinuity flag has to be set to inform that Brouwer's fixed point theorem is no longer applicable in that case.

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Jürgen Wolff von Gudenberg. Interval Arithmetic and Standardization. In Numerical Validation in Current Hardware Architectures. Dagstuhl Seminar Proceedings, Volume 8021, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{wolffvongudenberg:DagSemProc.08021.14,
  author =	{Wolff von Gudenberg, J\"{u}rgen},
  title =	{{Interval Arithmetic and Standardization}},
  booktitle =	{Numerical Validation in Current Hardware Architectures},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8021},
  editor =	{Annie Cuyt and Walter Kr\"{a}mer and Wolfram Luther and Peter Markstein},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08021.14},
  URN =		{urn:nbn:de:0030-drops-14342},
  doi =		{10.4230/DagSemProc.08021.14},
  annote =	{Keywords: Intervals, containment sets, IEEE754r}
}

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Documents authored by Wolff von Gudenberg, Jürgen

Interval Arithmetic and Standardization

Abstract

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