Convergence-divergence of extended-Hermite-Fejér type interpolation of higher order
type: Item
instance of: scholarly article
title: Convergence-divergence of extended-Hermite-Fejér type interpolation of higher order
zbMATH Open document ID: 0662.41001
DOI: 10.1007/BF01848081
author: R. B. Saxena
author: S. R. Misra
published in: Periodica Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: Die Autoren stellen Konvergenzbetrachtungen zur Hermite-Fejér- Interpolation of Tschebyschev-Knoten \(x_{kn}=\cos (k-)\pi /n\), \(k=1,2,...,n\) an. Wenn \[ F_ n(f,T;x)=\frac{1}{n^ 4}\sum^{n}_{k=1}f(x_{kn})A_ n(x)B_ n(x),\quad A_ n(x):=(\frac{T_ n(x)}{x-x_{kn}})^ 4, \] \[ B_ n(x)=(1- xx_{kn})^ 2+(x-x_{kn})^ 2\{\frac{2}{3}(n^ 2-1)(1-xx_{kn})- xx_{kn}\} \] eine Darstellung des Interpolationspolynoms ist, wird die Konvergenzfrage für den Fall, daß an \(F_ n\) in den Punkten \(\pm 1\) Hermite-Bedingungen bzw. Birkhoff-Bedingungen gestellt werden, vollständig abgehandelt. Die Ergebnisse sind in einer vollständigen Tabelle zusammengestellt.
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 4082184
zbMATH Keywords: Hermite-Fejér type interpolation
zbMATH Keywords: Hermite-, Birkhoff-conditions
zbMATH Keywords: convergence
zbMATH Keywords: Chebyshev knots
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01848081
OpenAlex ID: W2046049940
description: scientific article; zbMATH DE number 4082184