Local theory of the collocation method for the approximate solution of singular integral equations. I
type: Item
instance of: scholarly article
title: Local theory of the collocation method for the approximate solution of singular integral equations. I
zbMATH Open document ID: 0558.65095
DOI: 10.1007/BF01195867
author: Peter Junghanns
author: B. Silbermann
published in: Integral Equations and Operator Theory
publication date: 1984-01-01T00:00:00Z
review text: First, the authors describe an elegant abstract setting for analyzing projection methods for solving linear operator equations: The convergence of a projection method turns out to be equivalent to the invertibility of the coset of the sequence of projected operators in a certain factor algebra of a Banach algebra formed in a natural way from the projectional scheme; this invertibility in turn can be characterized by a local principle. The authors use these results to prove convergence of collocation methods for solving systems of singular integral equations with piecewise continuous coefficients.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45F15
Mathematics Subject Classification ID: 46H10
zbMATH DE Number: 3890687
zbMATH Keywords: projection methods
zbMATH Keywords: convergence
zbMATH Keywords: factor algebra
zbMATH Keywords: Banach algebra
zbMATH Keywords: local principle
zbMATH Keywords: collocation methods
zbMATH Keywords: piecewise continuous coefficients
reviewed by: Heinz W. Engl
MaRDI profile type: Publication
cites work: Kollokationsverfahren zur näherungsweisen Lösung singulärer Integralgleichungen mit unstetigen Koeffizienten
cites work: Notwendige und hinreichende Bedingungen für die Konvergenz des Kollokationsverfahrens bei singulären Integralgleichungen
cites work: Lokale Theorie des Reduktionsverfahrens für Toeplitzoperatoren
cites work: Lokale Theorie des Reduktionsverfahrens für singuläre Integralgleichungen
description: scientific article; zbMATH DE number 3890687