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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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