Information complexity of multivariate Fredholm integral equations in Sobolev classes
type: Item
instance of: scholarly article
title: Information complexity of multivariate Fredholm integral equations in Sobolev classes
zbMATH Open document ID: 0858.65131
author: Karin Frank
author: Stefan Heinrich
author: Sergei V. Pereverzyev
published in: Journal of Complexity
publication date: 1997-04-02T00:00:00Z
review text: Information-based complexity theory studies the difficulty of the approximate solution of numerical problems for which the information is partial, contaminated, and priced. Determining the information complexity of the basic problems of mathematical physics is a principal goal of information-based complexity theory. One of these basic problems is the solution of Fredholm integral equations of the second kind. The authors determine the exact order information complexity for Fredholm equations with kernels from Sobolev classes using a Gelfand number technique. An algorithm of optimal order, based on Fourier coefficients and a hyperbolic cross approximation of the kernel function is derived. Numerical examples are given.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 884755
zbMATH Keywords: information-based complexity
zbMATH Keywords: numerical examples
zbMATH Keywords: Fredholm integral equations of the second kind
zbMATH Keywords: exact order information complexity
zbMATH Keywords: Gelfand number technique
zbMATH Keywords: algorithm
reviewed by: Florica Luban
MaRDI profile type: Publication
OpenAlex ID: W1999228658
DOI: 10.1006/JCOM.1996.0004
description: scientific article; zbMATH DE number 884755