Set-valued Hermite interpolation

Titelangaben

Baier, Robert ; Perria, Gilbert:
Set-valued Hermite interpolation.
In: Journal of Approximation Theory. Bd. 163 (2011) Heft 10 . - S. 1349-1372.
ISSN 1096-0430
DOI: https://doi.org/10.1016/j.jat.2010.11.004

Weitere URLs

Angaben zu Projekten

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.