Weighted integration of periodic functions on the real line.
type: Item
instance of: scholarly article
title: Weighted integration of periodic functions on the real line.
zbMATH Open document ID: 1072.65033
DOI: 10.1016/S0096-3003(01)00080-7
author: Giuseppe Mastroianni
author: Gradimir V. Milovanović
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Integration of periodic functions on the real line with an even rational weight function is considered. A transformation method of such integrals to the integrals on \((-1,1)\) with respect to the Szegő-Bernstein weights and a construction of the corresponding Gaussian quadrature formulas are given. The recursion coefficients in the three-term recurrence relation for the corresponding orthogonal polynomials are obtained in an analytic form. Numerical examples are also included.
reviewed by: Feng Qi
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 1861077
zbMATH Keywords: Gauss type quadratures
zbMATH Keywords: error term
zbMATH Keywords: convergence
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: nonnegative measure
zbMATH Keywords: weights
zbMATH Keywords: Chebyshev weight
zbMATH Keywords: Szegő-Bernstein weights
zbMATH Keywords: nodes
zbMATH Keywords: modified moments
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: periodic functions
zbMATH Keywords: three-term recurrence relation
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
cites work: How to generate unknown orthogonal polynomials out of known orthogonal polynomials
cites work: Q3938409
cites work: Q5690368
cites work: Calculation of Gauss Quadrature Rules
cites work: Generalized Christoffel functions and error of positive quadrature
cites work: Q4749793
full work available at URL: s0096-3003(01)00080-7
OpenAlex ID: W1967681672
description: scientific article; zbMATH DE number 1861077