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Hermite Interpolation with Directed Sets

Title data

Baier, Robert ; Perria, Gilbert:
Hermite Interpolation with Directed Sets.
Hausdorff-Research-Institute
Bonn , 2008 . - 35 S.

Official URL: Volltext

Abstract in another language

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
Subject classification: Mathematics Subject Classification Code: 65D05 (28B20 52A20 41A05 54C60 49J53)
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 04 Mar 2021 10:02
Last Modified: 25 May 2021 12:51
URI: https://eref.uni-bayreuth.de/id/eprint/63669