A note on the alternate trapezoidal quadrature method for Fredholm integral eigenvalue problems
type: Item
instance of: scholarly article
title: A note on the alternate trapezoidal quadrature method for Fredholm integral eigenvalue problems
zbMATH Open document ID: 1337.65178
author: A. C. da Rocha
author: Saulo P. Oliveira
author: Ailín Ruiz de Zárate
author: Daniel G. Alfaro Vigo
published in: Numerical Algorithms
publication date: 2013-04-12T00:00:00Z
review text: The authors study the alternate trapezoidal quadrature method, introduced by \textit{A. Sidi} and \textit{M. Israeli} [J. Sci. Comput. 3, No. 2, 201--231 (1988; Zbl 0662.65122)], for the eigenvalue problem of periodic, convolution-type singular integrals. Since the discrete eigenvalues exhibit some symmetry properties that are not observed for the eigenvalues of the continuous problem, it can be shown that the method always yields eigenvalues with enlarged multiplicity. This leads to error estimates that are valid only for a subset of the discrete spectrum. To loosen this constraint the authors introduce an improved method and establish error estimates valid for the whole discrete spectrum. Numerical examples illustrate the results.
reviewed by: Gunther Schmidt
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 6153512
zbMATH Keywords: alternate trapezoidale quadrature
zbMATH Keywords: singular integrals of convolution type
zbMATH Keywords: eigenvalue problems
MaRDI profile type: Publication
full work available at URL: s11075-012-9681-8
OpenAlex ID: W2090514524
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DOI: 10.1007/S11075-012-9681-8
description: scientific article; zbMATH DE number 6153512