Complexity of local solution of multivariate integral equations
type: Item
instance of: scholarly article
title: Complexity of local solution of multivariate integral equations
zbMATH Open document ID: 0846.65076
author: Karin Frank
published in: Journal of Complexity
publication date: 1996-09-04T00:00:00Z
review text: The complexity of a local solution of Fredholm integral equations of the second kind for a Sobolev class of multivariate periodic functions with dominating mixed derivative is discussed. To prove the lower bound, an \(s\)-number technique is used, which was applied earlier to two other special classes of functions. The upper bound is proved in a constructive way providing an implementable algorithm of optimal order based on Fourier coefficients and a hyperbolic cross approximation.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 45B05
zbMATH DE Number: 850549
zbMATH Keywords: complexity of a local solution
zbMATH Keywords: Fredholm integral equations
zbMATH Keywords: Sobolev class
zbMATH Keywords: multivariate periodic functions
zbMATH Keywords: algorithm
reviewed by: Lechoslaw Hącia
MaRDI profile type: Publication
OpenAlex ID: W2090048492
DOI: 10.1006/JCOM.1995.1021
description: scientific article; zbMATH DE number 850549