Hermite-Fejér interpolation for rational systems
type: Item
instance of: scholarly article
title: Hermite-Fejér interpolation for rational systems
zbMATH Open document ID: 0932.41013
author: K. Appert
published in: Constructive Approximation
publication date: 1998-01-01T00:00:00Z
review text: Generalized Hermite-type interpolation based on the zeros of the Chebychev polynomial of the first kind for the real rational space \(P_n(a_1, a_2,\dots, a_n)\) was constructed. The non-real elements \(\{a_k\}^n_{k=1}\subset \mathbb{C}\setminus[-1, 1]\) may be paired by complex conjugation and repeated poles. The corresponding generalized Hermite-Fejér interpolation always converges uniformly for every continuous function on \([-1,1]\) provided that the poles stay outside a circle which contains the unit circle in its interior. The uniform approximation of the corresponding Günwald interpolation was characterized. The \(L^p\)-approximation of this Grünwald interpolation always holds for every continuous function on \([-1,1]\).
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 1268077
zbMATH Keywords: Hermite-type interpolation
zbMATH Keywords: Günwald interpolation
MaRDI profile type: Publication
full work available at URL: s003659900088
OpenAlex ID: W2060273936
DOI: 10.1007/S003659900088
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description: scientific article; zbMATH DE number 1268077