Convergence and inclusion isotonicity of the tensorial rational Bernstein form

  • 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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Metadaten
Author:Jürgen GarloffGND, Tareq Hamadneh
DOI:https://doi.org/10.1007/978-3-319-31769-4
ISBN:978-3-319-31768-7
Parent Title (German):Scientific Computing, Computer Arithmetic, and Validated Numerics, 16th International Symposium, SCAN 2014, Würzburg, Germany, September 21-26, 2014, (Lecture Notes in Computer Science ; 9553)
Publisher:Springer
Place of publication:Cham
Document Type:Conference Proceeding
Language:English
Year of Publication:2016
Release Date:2018/11/23
Tag:Bernstein polynomial; Range bounding; Rational function
First Page:171
Last Page:179
Note:
Volltextzugriff für Angehörige der Hochschule Konstanz möglich.
DDC functional group:500 Naturwissenschaften und Mathematik / 510 Mathematik
Open Access?:Nein
Licence (English):License LogoLizenzbedingungen Springer