Set-valued Hermite interpolation

JOURNAL OF APPROXIMATION THEORY

卷:163

Article

Baier, Robert¹  Perria, Gilbert¹ 

[1] Univ Bayreuth, Chair Appl Math, D-95440 Bayreuth, Germany

关键词: Set-valued interpolation;    Hermite interpolation;    Embedding of convex;    compact sets;    Directed sets;    Derivatives of set-valued maps;   

DOI  :  10.1016/j.jat.2010.11.004

来源: Elsevier

【 摘 要 】

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 '' consisting of three parts together with its normal directions: the convex, the concave and the mixed-type part. In the Banach space of the directed sets, 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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free