Reliable Computing

, Volume 9, Issue 5, pp 339–347 | Cite as

Extended Interval Power Function

  • Walter Krämer
  • Jürgen Wolff Von Gudenberg
Article

Abstract

The containment set as an extension of the range of a function has been introduced in a series of white papers; see e.g. Walster, G. W.: Closed Interval Systems, Sun Microsystems, 2002, and Walster, G. W, et al.: Extended Real Intervals and the Topological Closure of Extended Real Relations, Sun Microsystems, 2002. The containment evaluation provides an exception free evaluation of functions over an arbitrary range.

In this paper we discuss alternative existing implementations (C++ Interval Arithmetic Programming Reference, Sun Microsystems, 2000, and Hofschuster, W. et al.: The Interval Library fi_lib++ 2.0, Design, Features and Sample Programs, Universität Wuppertal, 2001) of the power function, introduce a new version, develop containment sets and discuss algorithms for the implementation.

Keywords

Computational Mathematic Industrial Mathematic Power Function Close Interval White Paper 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. C++ Interval Arithmetic Programming Reference, Sun Microsystems, 2000, http://wwws.sun.com//software/sundev/suncc/intervals.html.Google Scholar
  2. Hofschuster, W. et al.: The Interval Library fi lib++ 2.0, Design, Features and Sample Programs, Preprint 2001/4, Universität Wuppertal, 2001.Google Scholar
  3. Krämer, W. et al.: Numerical Toolbox for Verified Computing II—Advanced Numerical Problems (Draft), chapter 9, http://www.uni-karlsruhe.de/~Rudolf.Lohner/papers/tb2.ps.gz.Google Scholar
  4. Walster, G. W.: Closed Interval Systems, Sun Microsystems, white paper, 2002, http://wwws.sun.com/software/sundev/whitepapers/index.html.Google Scholar
  5. Walster, G. W.: Moore's Single-Use-Expression Theorem on Extended Real Intervals, in: Kearfott, R. B. (ed.), Validated Computing, Toronto, May 2002, Extended Abstracts, http://cs.utep.edu/interval-comp/interval.02/wals.pdf.Google Scholar
  6. Walster, G. W. et al.: Extended Real Intervals and the Topological Closure of Extended Real Relations, Sun Microsystems, white paper, 2002, http://wwws.sun.com/software/sundev/whitepapers/index.html.Google Scholar
  7. Wolff von Gudenberg, J.: Computing z y withMaximum Accuracy, Computing 31 (1983), pp. 185–189.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Walter Krämer
    • 1
  • Jürgen Wolff Von Gudenberg
    • 2
  1. 1.Fachbereich 7 (Mathematik)Bergische Universität GH WuppertalWuppertalGermany
  2. 2.Lehrstuhl für Informatik 2, Am HublandWürzburgGermany

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