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Extended Interval Power Function

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.

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References

  1. C++ Interval Arithmetic Programming Reference, Sun Microsystems, 2000, http://wwws.sun.com//software/sundev/suncc/intervals.html.

  2. Hofschuster, W. et al.: The Interval Library fi lib++ 2.0, Design, Features and Sample Programs, Preprint 2001/4, Universität Wuppertal, 2001.

  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.

  4. Walster, G. W.: Closed Interval Systems, Sun Microsystems, white paper, 2002, http://wwws.sun.com/software/sundev/whitepapers/index.html.

  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.

  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.

  7. Wolff von Gudenberg, J.: Computing z y withMaximum Accuracy, Computing 31 (1983), pp. 185–189.

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Krämer, W., Von Gudenberg, J.W. Extended Interval Power Function. Reliable Computing 9, 339–347 (2003). https://doi.org/10.1023/A:1025175029490

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Keywords

  • Computational Mathematic
  • Industrial Mathematic
  • Power Function
  • Close Interval
  • White Paper