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Information Complexity of Multivariate Fredholm Equations in Sobolev Classes

  • In this paper, the complexity of full solution of Fredholm integral equations of the second kind with data from the Sobolev class \(W^r_2\) is studied. The exact order of information complexity is derived. The lower bound is proved using a Gelfand number technique. The upper bound is shown by providing a concrete algorithm of optimal order, based on a specific hyperbolic cross approximation of the kernel function. Numerical experiments are included, comparing the optimal algorithm with the standard Galerkin method.

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Author:Karin Frank, Stefan Heinrich, Sergei Pereverzev
URN (permanent link):urn:nbn:de:hbz:386-kluedo-50629
Serie (Series number):Interner Bericht des Fachbereich Informatik (263)
Document Type:Report
Language of publication:English
Publication Date:2017/11/10
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/11/10
Number of page:17
Faculties / Organisational entities:Fachbereich Informatik
DDC-Cassification:0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)