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International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics

SCAN 2015: Scientific Computing, Computer Arithmetic, and Validated Numerics pp 171–179Cite as

Convergence and Inclusion Isotonicity of the Tensorial Rational Bernstein Form

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9553))

Abstract

A method is investigated by which tight bounds on the range of a multivariate rational function over a box can be computed. The approach relies on the expansion of the numerator and denominator polynomials in Bernstein polynomials. Convergence of the bounds to the range with respect to degree elevation of the Bernstein expansion, to the width of the box and to subdivision are proven and the inclusion isotonicity of the related enclosure function is shown.

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Acknowledgements

The authors gratefully acknowledge support from the University of Applied Sciences/HTWG Konstanz through the SRP program.

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Authors and Affiliations

  1. University of Applied Sciences/HTWG Konstanz, Konstanz, Germany

    Jürgen Garloff

  2. University of Konstanz, Konstanz, Germany

    Tareq Hamadneh

Authors
  1. Jürgen Garloff
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  2. Tareq Hamadneh
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Correspondence to Jürgen Garloff .

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Editors and Affiliations

  1. Institute of Computer Science, University of Würzburg, Würzburg, Germany

    Marco Nehmeier

  2. Universität Würzburg, Würzburg, Germany

    Jürgen Wolff von Gudenberg

  3. Department of Mathematics, Uppsala University, Uppsala, Sweden

    Warwick Tucker

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Garloff, J., Hamadneh, T. (2016). Convergence and Inclusion Isotonicity of the Tensorial Rational Bernstein Form. In: Nehmeier, M., Wolff von Gudenberg, J., Tucker, W. (eds) Scientific Computing, Computer Arithmetic, and Validated Numerics. SCAN 2015. Lecture Notes in Computer Science(), vol 9553. Springer, Cham. https://doi.org/10.1007/978-3-319-31769-4_14

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  • DOI: https://doi.org/10.1007/978-3-319-31769-4_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31768-7

  • Online ISBN: 978-3-319-31769-4

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