Brakhage's implicit iteration method and Information Complexity of equations with operators having closed range

  • An a posteriori stopping rule connected with monitoringthe norm of second residual is introduced forBrakhage's implicit nonstationary iteration method, applied to ill-posed problems involving linear operatorswith closed range. It is also shown that for someclasses of equations with such operators the algorithmconsisting in combination of Brakhage's method withsome new discretization scheme is order optimal in the sense of Information Complexity.

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Metadaten
Author:Sergei V. Pereverzev, Eberhard Schock
URN (permanent link):urn:nbn:de:hbz:386-kluedo-7975
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (302)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Tag:Complexity and performance of numerical algorithms; Improperly posed problems
Source:Journal of Complexity
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):65J20 Improperly posed problems; regularization
65Y20 Complexity and performance of numerical algorithms [See also 68Q25]

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