Probabilistic analysis of numerical methods for integral equations
type: Item
instance of: scholarly article
title: Probabilistic analysis of numerical methods for integral equations
zbMATH Open document ID: 0732.65119
author: Stefan Heinrich
published in: Journal of Integral Equations and Applications
publication date: 1991-01-01T00:00:00Z
review text: Numerical problems and algorithms for solving Fredholm integral equations are analyzed from a probabilistic point of view. The probability measures on the set of right-hand sides and on the set of kernels are fixed. The author uses Wiener type measures which are naturally related to the scale of Sobolev spaces. This allows to extend the comparison between worst and probabilistic cases. Statistical features of the approximation process - the most likely rate of convergence and the dominating individual behaviour are determined. Two typical numerical methods are studied - the Galerkin and the iterated Galerkin method.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 65C99
zbMATH DE Number: 4211457
zbMATH Keywords: Wiener measure
zbMATH Keywords: algorithms
zbMATH Keywords: Fredholm integral equations
zbMATH Keywords: probability measures
zbMATH Keywords: scale of Sobolev spaces
zbMATH Keywords: rate of convergence
zbMATH Keywords: iterated Galerkin method
reviewed by: I. Dimov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/jiea/1181075619
OpenAlex ID: W1976513899
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DOI: 10.1216/JIEA/1181075619
description: scientific article; zbMATH DE number 4211457