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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 to cite this document: urn:nbn:de:bvb:703-epub-5602-1

Title data

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.

Further data

Item Type: Preprint, postprint
Keywords: Hermite interpolation; Derivatives of set-valued maps; Divided differences; Embedding of convex compact sets into a vector space
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5602-1
Date Deposited: 25 May 2021 12:50
Last Modified: 25 May 2021 12:51
URI: https://epub.uni-bayreuth.de/id/eprint/5602

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