Estimating quadrature errors for analytic functions using kernel representations and biorthogonal systems
type: Item
instance of: scholarly article
title: Estimating quadrature errors for analytic functions using kernel representations and biorthogonal systems
zbMATH Open document ID: 0943.41014
author: Rudolf Scherer
author: Thomas Schira
published in: Numerische Mathematik
publication date: 2000-08-30T00:00:00Z
review text: A combination of two approaches to the derivative-free representation of the remainder term in quadrature formulas is proposed. One of these approaches is based on the contour integral representation with complex kernel function. Another one represents the remainder as a bounded linear functional in an appropriate Hilbert space. The kernel function is estimated by using the method of biorthogonal systems (namely, of Chebyshev type). This scheme is applied to the Clenshaw-Curtis, Pólya and Filippi quadrature formulas. The error bounds for the Gauss-Chebyshev and Lobatto-Chebyshev formulas are illustrated by the series of numerical results obtained within the framework of the discussed method.
reviewed by: Sergei V. Rogosin
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 65D30
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 1419745
zbMATH Keywords: quadrature formulas
zbMATH Keywords: remainder' estimation
zbMATH Keywords: analytic functions
zbMATH Keywords: polynomial biorthogonal systems
zbMATH Keywords: complex kernel function
MaRDI profile type: Publication
full work available at URL: s002110050007
OpenAlex ID: W2033748287
DOI: 10.1007/S002110050007
description: scientific article; zbMATH DE number 1419745