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.
| Author: | Jürgen GarloffORCiDGND, 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; Rational function; Range bounding |
| First Page: | 171 |
| Last Page: | 179 |
| Note: | Volltextzugriff für Angehörige der Hochschule Konstanz möglich. |
| DDC functional group: | 510 Mathematik |
| Open Access?: | Nein |
| Licence (German): |  Urheberrechtlich geschützt |
