Convergence of the Simplicial Rational Bernstein Form

Titi, Jihad; Hamadneh, Tareq; Garloff, Jürgen

Convergence of the Simplicial Rational Bernstein Form

Dateien

Zu diesem Dokument gibt es keine Dateien.

Datum

2015

Publikationstyp

Beitrag zu einem Konferenzband

Publikationsstatus

Published

Erschienen in

Modelling, Computation and Optimization in Information Systems and Management Sciences : Proceedings of the 3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences - MCO 2015 - Part I. Cham: Springer International Publishing, 2015, pp. 433-441. Advances in Intelligent Systems and Computing. 359. ISBN 978-3-319-18160-8. Available under: doi: 10.1007/978-3-319-18161-5_37

Zusammenfassung

Bernstein polynomials on a simplex V are considered. The expansion of a given polynomial p into these polynomials provides bounds for range of p over V. Bounds for the range of a rational function over V can easily be obtained from the Bernstein expansions of the numerator and denominator polynomials of this function. In this paper it is shown that these bounds converge monotonically and linearly to the range of the rational function if the degree of the Bernstein expansion is elevated. If V is subdivided then the convergence is quadratic with respect to the maximum of the diameters of the subsimplices.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Bernstein polynomial, simplex, range bounds, rational function, degree elevation, subdivision

Konferenz

Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2015), 11. Mai 2015 - 13. Mai 2015, Metz, France

Zitieren

ISO 690

TITI, Jihad, Tareq HAMADNEH, Jürgen GARLOFF, 2015. Convergence of the Simplicial Rational Bernstein Form. Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2015). Metz, France, 11. Mai 2015 - 13. Mai 2015. In: Modelling, Computation and Optimization in Information Systems and Management Sciences : Proceedings of the 3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences - MCO 2015 - Part I. Cham: Springer International Publishing, 2015, pp. 433-441. Advances in Intelligent Systems and Computing. 359. ISBN 978-3-319-18160-8. Available under: doi: 10.1007/978-3-319-18161-5_37

BibTex

@inproceedings{Titi2015Conve-33224,
  year={2015},
  doi={10.1007/978-3-319-18161-5_37},
  title={Convergence of the Simplicial Rational Bernstein Form},
  number={359},
  isbn={978-3-319-18160-8},
  publisher={Springer International Publishing},
  address={Cham},
  series={Advances in Intelligent Systems and Computing},
  booktitle={Modelling, Computation and Optimization in Information Systems and Management Sciences : Proceedings of the 3rd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences - MCO 2015 - Part I},
  pages={433--441},
  author={Titi, Jihad and Hamadneh, Tareq and Garloff, Jürgen}
}

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