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An Optimal Algorithm for the Local Solution of Integral Equations

  • The local solution problem of multivariate Fredholm integral equations is studied. Recent research proved that for several function classes the complexity of this problem is closely related to the Gelfand numbers of some characterizing operators. The generalization of this approach to the situation of arbitrary Banach spaces is the subject of the present paper. Furthermore, an iterative algorithm is described which - under some additional conditions - realizes the optimal error rate. The way these general theorems work is demonstrated by applying them to integral equations in a Sobolev space of periodic functions with dominating mixed derivative of various order.

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Author:Karin Frank
URN (permanent link):urn:nbn:de:hbz:386-kluedo-49231
Serie (Series number):Interner Bericht des Fachbereich Informatik (276)
Document Type:Report
Language of publication:English
Publication Date:2017/10/24
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/24
Number of page:26
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)