Constructing totally positive piecewise Chebyshevian B-spline bases
| Autor: | Marie-Laurence Mazure |
|---|---|
| Přispěvatelé: | Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]) |
| Rok vydání: | 2018 |
| Předmět: |
blossoms
Class (set theory) Pure mathematics Extended Chebyshev spaces geometric design Context (language use) 010103 numerical & computational mathematics AMS subject classification: 65D17 65D07 01 natural sciences Chebyshev filter Mathematics::Numerical Analysis Total positivity generalised derivatives B-spline bases Quartic function [MATH]Mathematics [math] 0101 mathematics Mathematics Applied Mathematics B-spline Bernstein-type bases Connection (mathematics) 010101 applied mathematics Computational Mathematics shape parameters Computer Science::Graphics Piecewise Variety (universal algebra) |
| Zdroj: | Journal of Computational and Applied Mathematics Journal of Computational and Applied Mathematics, Elsevier, 2018, 342, pp.550-586. ⟨10.1016/j.cam.2018.03.032⟩ Journal of Computational and Applied Mathematics, 2018, 342, pp.550-586. ⟨10.1016/j.cam.2018.03.032⟩ |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2018.03.032 |
| Popis: | We consider piecewise Chebyshevian splines, in the sense of splines with pieces taken from any different five-dimensional Extended Chebyshev spaces, and with connection matrices at the knots. In this large context we establish necessary and sufficient conditions for the existence of totally positive refinable B-spline bases. These conditions are applied in many important special cases, e.g. symmetric cardinal geometrically continuous quartic B-spline, parametrically continuous mixed L-splines. The great variety of illustrations provided proves the richness of this class of splines for design. This richness can be exploited in various other fields as well. |
| Databáze: | OpenAIRE |
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