Bounds of the error of Gauss-Turán-type quadratures. II.
type: Item
instance of: scholarly article
title: Bounds of the error of Gauss-Turán-type quadratures. II.
zbMATH Open document ID: 1200.41034
author: Gradimir V. Milovanović
author: Miodrag M. Spalević
author: Miroslav S. Pranić
published in: Applied Numerical Mathematics
publication date: 2010-05-06T00:00:00Z
review text: This paper is the continuation of the paper of \textit{G. V. Milovanović} and \textit{M. M. Spalević} [J. Comput. Appl. Math. 178, No. 1--2, 333--346 (2005; Zbl 1071.41028)] and is concerned with the remainder term in Gauss-Turán quadrature rule \[ \int^1_{-1} w(t) f(t)\,dt= \sum^n_{v=1} \sum^{2s}_{i=0} \lambda_{i,v}f^{(i)}(\tau_v) + R_{n,s}(f) \tag{1} \] with the weight functions \[ w_{n,\mu}(t) = (U_{n-1}(t)/n)^{2\mu+1}(1-t^2)^\mu, \] where \(\mu=l-1/2,\) \(l=1,2,\dots\) and \(U_n(\cos \Theta)=\frac{\sin(n+1)\Theta}{\sin \Theta} -\) is the Chebyshev polynomial of the second kind. An explicit representation of the remainder term in (1) on elliptic contours is obtained. Error bounds are found.
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 5704974
zbMATH Keywords: Gauss-Turán quadrature formula
zbMATH Keywords: error bound
zbMATH Keywords: remainder term for analytic functions
zbMATH Keywords: contour integral representation
Wikidata QID: Q115058731
MaRDI profile type: Publication
full work available at URL: j.apnum.2009.08.002
OpenAlex ID: W1989863738
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DOI: 10.1016/J.APNUM.2009.08.002
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description: scientific article; zbMATH DE number 5704974