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Set-valued Hermite interpolation

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Baier, Robert ; Perria, Gilbert:
Set-valued Hermite interpolation.
In: Journal of Approximation Theory. Bd. 163 (2011) Heft 10 . - S. 1349-1372.
ISSN 1096-0430
DOI: https://doi.org/10.1016/j.jat.2010.11.004

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Projektfinanzierung: Bundesministerium für Bildung und Forschung

Abstract

The problem of interpolating a set-valued function with convex images is addressed by means of directed sets. A directed set will be visualised as a usually non-convex set in |R^n consisting of three parts together with its normal directions: the convex, the concave and the mixed-type part. In this Banach space, a mapping resembling the Kergin map is established. The interpolating property and error estimates similar to the point-wise case are then shown; the representation of the interpolant through means of divided differences is given. A comparison to other set-valued approaches is presented. The method developed within the article is extended to the scope of the Hermite interpolation by using the derivative notion in the Banach space of directed sets. Finally, a numerical analysis of the explained technique corroborates the theoretical results.

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Publikationsform: Artikel in einer Zeitschrift
Begutachteter Beitrag: Ja
Zusätzliche Informationen: Zentralblattnummer: 1252.41002
Contents:
1. Introduction
2. Directed Sets
2.1 Preliminaries
2.2 Definition
2.3 Properties of Directed Sets
3. Set-Valued Derivatives and Divided Differences
4. The (Kergin) Interpolating Map
5. Connections to Other Approaches
6. Numerical Tests
7. Conclusions
Keywords: set-valued interpolation; Hermite interpolation; embedding of convex, compact sets; directed sets; derivatives of set-valued maps
Fachklassifikationen: Mathematics Subject Classification Code: 65D05 (41A05 54C60 26E25 46G05)
Institutionen der Universität: Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik)
Fakultäten
Fakultäten > Fakultät für Mathematik, Physik und Informatik
Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut
Titel an der UBT entstanden: Ja
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Eingestellt am: 03 Mär 2021 13:26
Letzte Änderung: 26 Mai 2021 12:47
URI: https://eref.uni-bayreuth.de/id/eprint/63651