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Hermite Interpolation with Directed Sets

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005602
URN zum Zitieren der Version auf EPub Bayreuth: urn:nbn:de:bvb:703-epub-5602-1

Titelangaben

Baier, Robert ; Perria, Gilbert:
Hermite Interpolation with Directed Sets.
Hausdorff-Research-Institute
Bonn , 2008

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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 nonconvex set in |R^n consisting of three parts, the convex, the concave and the mixed-type part together with its normal directions. In this Banach space, a mapping resembling the Kergin map is established. The interpolating property and error estimates similar to the pointwise case are then shown based on the representation of the interpolant through means of divided differences. A comparison to other set-valued approaches is included. 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.

Weitere Angaben

Publikationsform: Preprint, Postprint
Keywords: Hermite interpolation; Derivatives of set-valued maps; Divided differences; Embedding of convex compact sets into a vector space
Themengebiete aus DDC: 500 Naturwissenschaften und Mathematik
500 Naturwissenschaften und Mathematik > 510 Mathematik
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
Sprache: Englisch
Titel an der UBT entstanden: Ja
URN: urn:nbn:de:bvb:703-epub-5602-1
Eingestellt am: 25 Mai 2021 12:50
Letzte Änderung: 25 Mai 2021 12:51
URI: https://epub.uni-bayreuth.de/id/eprint/5602

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