Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness
type: Item
instance of: scholarly article
title: Quadrature formulae with multiple nodes and a maximal trigonometric degree of exactness
zbMATH Open document ID: 1173.65017
author: Gradimir V. Milovanović
author: Aleksandar S. Cvetković
author: Marija P. Stanić
published in: Numerische Mathematik
publication date: 2009-06-30T00:00:00Z
review text: The authors construct for the integral \(\int_{-\pi}^{\pi} w(x)f(x)dx\) an interpolatory quadrature formulae with multiple nodes, which have the maximal trigonometric degree of exactness. For that purpose they introduce and consider the so-called \(\sigma\)-orthogonal trigonometric polynomials of semi-integer degree and give a numerical method for their construction. Some numerical examples are given. For the weight function \(w(x)=1\) a thus study was considered by \textit{D. P. Dryanov} [Numer. Math. 67, No. 4, 441--464 (1994; Zbl 0798.41023)].
reviewed by: Dumitru Acu
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 42A05
zbMATH DE Number: 5571605
zbMATH Keywords: numerical integration
zbMATH Keywords: quadrature and cubature formulas
zbMATH Keywords: trigonometric polynomials, inequalities, extremal problems
Wikidata QID: Q115058739
describes a project that uses: OrthogonalPolynomials
MaRDI profile type: Publication
full work available at URL: s00211-009-0219-5
OpenAlex ID: W2001134214
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DOI: 10.1007/S00211-009-0219-5
description: scientific article; zbMATH DE number 5571605