Hermite-Fejér interpolation with boundary conditions for \(\rho\)-normal sets
type: Item
instance of: scholarly article
title: Hermite-Fejér interpolation with boundary conditions for \(\rho\)-normal sets
zbMATH Open document ID: 0734.41001
DOI: 10.1016/0021-9045(90)90117-9
author: Péter Vértesi
author: Philip Rabinowitz
published in: Journal of Approximation Theory
publication date: 1990-01-01T00:00:00Z
review text: In his Habilitationsschrift [Universität, Duisburg (1981] \textit{H. B. Knoop} introduced the polynomials \(H_{n,p,q}f\) which are extensions of the Hermite-Fejer interpolating polynomials. These are based on a triangular set of points \(T\subset [-1,1]\) and include boundary conditions at the end points -1,1 and values and first derivatives at all the points. The boundary conditions at -1 and 1 require all derivatives up to order p-1 and q-1 respectively. Following Fejer and Grunwald, the authors introduce an appropriate generalization of normality and call it (p,q) normality and the corresponding notion of (p,q)-\(\rho\) normality for some \(\rho\), \(0<\rho \leq 1\). They show that when the nodes form a (p,q)-\(\rho\) normal set, the polynomials \(H_{n,p,q}f\) have nice convergence behaviour.
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 4214624
zbMATH Keywords: Hermite-Fejer interpolating polynomials
zbMATH Keywords: normality
reviewed by: A. Sharma
MaRDI profile type: Publication
full work available at URL: 0021-9045(90)90117-9
OpenAlex ID: W1976512402
cites work: On the theory of interpolation
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cites work: Q4093885
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cites work: ϱ-normal point systems
cites work: Hermite-Fejér type interpolations. IV (Convergence criteria for Jacobi abscissas)
description: scientific article; zbMATH DE number 4214624