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Set-valued Hermite interpolation

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005623
URN to cite this document: urn:nbn:de:bvb:703-epub-5623-7

Title data

Baier, Robert ; Perria, Gilbert:
Set-valued Hermite interpolation.
Bayreuth , 2011

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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 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.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erscheint in:
Journal of Approximation Theory. Bd. 163 (2011) Heft 10 . - S. 1349-1372
DOI: https://doi.org/10.1016/j.jat.2010.11.004
Keywords: set-valued interpolation; Hermite interpolation; embedding of convex, compact sets; directed sets; derivatives of set-valued maps
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-5623-7
Date Deposited: 26 May 2021 12:47
Last Modified: 08 Jun 2021 07:56
URI: https://epub.uni-bayreuth.de/id/eprint/5623

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