Convergence and Inclusion Isotonicity of the Tensorial Rational Bernstein Form

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2016
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NEHMEIER, Marco, ed., Jürgen Wolff VON GUDENBERG, ed., Warwick TUCKER, ed.. Scientific Computing, Computer Arithmetic, and Validated Numerics : 16th International Symposium, SCAN 2014. Cham: Springer, 2016, pp. 171-179. Lecture Notes in Computer Science. 9553. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-31768-7. Available under: doi: 10.1007/978-3-319-31769-4_14
Zusammenfassung

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.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
Bernstein polynomial, rational function, range bounding
Konferenz
SCAN 2014 : Scientific Computing, Computer Arithmetic, and Validated Numerics, 16th International Symposium, 21. Sept. 2014 - 26. Sept. 2014, Würzburg, Germany
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Zitieren
ISO 690GARLOFF, Jürgen, Tareq HAMADNEH, 2016. Convergence and Inclusion Isotonicity of the Tensorial Rational Bernstein Form. SCAN 2014 : Scientific Computing, Computer Arithmetic, and Validated Numerics, 16th International Symposium. Würzburg, Germany, 21. Sept. 2014 - 26. Sept. 2014. In: NEHMEIER, Marco, ed., Jürgen Wolff VON GUDENBERG, ed., Warwick TUCKER, ed.. Scientific Computing, Computer Arithmetic, and Validated Numerics : 16th International Symposium, SCAN 2014. Cham: Springer, 2016, pp. 171-179. Lecture Notes in Computer Science. 9553. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-31768-7. Available under: doi: 10.1007/978-3-319-31769-4_14
BibTex
@inproceedings{Garloff2016-04-09Conve-36705,
  year={2016},
  doi={10.1007/978-3-319-31769-4_14},
  title={Convergence and Inclusion Isotonicity of the Tensorial Rational Bernstein Form},
  number={9553},
  isbn={978-3-319-31768-7},
  issn={0302-9743},
  publisher={Springer},
  address={Cham},
  series={Lecture Notes in Computer Science},
  booktitle={Scientific Computing, Computer Arithmetic, and Validated Numerics : 16th International Symposium, SCAN 2014},
  pages={171--179},
  editor={Nehmeier, Marco and von Gudenberg, Jürgen Wolff and Tucker, Warwick},
  author={Garloff, Jürgen and Hamadneh, Tareq}
}
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