What is the complexity of periodic weakly singular integral equations?
type: Item
instance of: scholarly article
title: What is the complexity of periodic weakly singular integral equations?
zbMATH Open document ID: 1152.65122
author: B. E. Eshmatov
published in: BIT
publication date: 2008-09-12T00:00:00Z
review text: The authors construct a method for the numerical solution of Fredholm integral equations with weak singularities in spaces of periodic functions. The method is based on collocation principles using trigonometric functions. Both the computational complexity and the approximation error are studied in a very detailed way. This leads to the conclusion that, depending on the precise assumptions, the method is either fast (in the sense that the relation between complexity and error is of optimal order as the number of collocation points grows) or quasifast (in the sense that this relation differs from the optimal value only by a logarithmic, and hence slowly growing, term). Thus the complexity of the problem is the same as that for corresponding equations without singularities.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 5343411
zbMATH Keywords: fast solver
zbMATH Keywords: weakly singular integral equation
zbMATH Keywords: Fredholm integral equation
zbMATH Keywords: periodicity
zbMATH Keywords: trigonometric collocation
MaRDI profile type: Publication
full work available at URL: s10543-008-0181-0
OpenAlex ID: W1995157000
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DOI: 10.1007/S10543-008-0181-0
description: scientific article; zbMATH DE number 5343411