Modifications of some first kind integral equations with logarithmic kernel to improve numerical conditioning
type: Item
instance of: scholarly article
title: Modifications of some first kind integral equations with logarithmic kernel to improve numerical conditioning
zbMATH Open document ID: 0551.65093
DOI: 10.1007/BF02253319
published in: Computing
publication date: 1985-01-01T00:00:00Z
review text: We consider a pair of integral equations derived by \textit{G. T. Symm} [Numer. Math. 10, 437-445 (1967; Zbl 0155.215)] and by \textit{G. Hsiao} and \textit{R. C. MacCamy} [SIAM Rev. 15, 687-705 (1973; Zbl 0235.45006)] for use in various boundary value problems. We investigate the matrix which results when some collocation methods are applied to these equations. We find that the \(\ell_ 2\)-condition number of the matrix can be reduced by performing three minor modifications of the integral equations.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 45F15
zbMATH DE Number: 3878311
zbMATH Keywords: pair of integral equations
zbMATH Keywords: collocation methods
zbMATH Keywords: matrix norms
zbMATH Keywords: singular values
zbMATH Keywords: condition number
zbMATH Keywords: scaling
author: Søren Christiansen
describes a project that uses: IMSL Numerical Libraries
MaRDI profile type: Publication
cites work: Q3867123
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full work available at URL: https://doi.org/10.1007/bf02253319
OpenAlex ID: W73160570
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description: scientific article; zbMATH DE number 3878311