On a minimal property of trigonometric interpolation at equidistant nodes
type: Item
instance of: scholarly article
title: On a minimal property of trigonometric interpolation at equidistant nodes
zbMATH Open document ID: 0545.42003
DOI: 10.1007/BF02277186
published in: Computing
publication date: 1981-01-01T00:00:00Z
review text: Let \(\ell_ i(x,a)\) be the trigonometric Lagrangian fundamental polynomials of degree n corresponding to the nodes \(a=(a_ 0,...,a_{2n})\). The author gives a very short proof of the following conjecture of Bitzer [\textit{G. Bitzer}, ibid. 21, 177-182 (1979; Zbl 0429.42004)]: Apart from rotations on the unit sphere, \(f(a):=\int^{2\pi}_{0}\sum^{2n}_{i=0}\ell^ 2_ i(x,a)dx\) attains its absolute minimum f(ā)\(=2\pi\) exactly for \(a=\bar a:=(2\pi k/2n+1)_{k=0,...,2n}\).
Mathematics Subject Classification ID: 42A15
zbMATH DE Number: 3867942
zbMATH Keywords: trigonometric Lagrangian fundamental polynomials
zbMATH Keywords: conjecture of Bitzer
author: Burkhard Suendermann
reviewed by: Bernd Dreseler
MaRDI profile type: Publication
cites work: Über eine Minimaleigenschaft der äquidistanten trigonometrischen Interpolation in 2n+1 Knoten
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description: scientific article; zbMATH DE number 3867942