## 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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Author: Sergei V. Pereverzev, Eberhard Schock urn:nbn:de:hbz:386-kluedo-7975 Preprints (rote Reihe) des Fachbereich Mathematik (302) Preprint English 1999 1999 Technische Universität Kaiserslautern 2000/04/03 Complexity and performance of numerical algorithms; Improperly posed problems Journal of Complexity Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J20 Improperly posed problems; regularization 65-XX NUMERICAL ANALYSIS / 65Yxx Computer aspects of numerical algorithms / 65Y20 Complexity and performance of numerical algorithms [See also 68Q25] Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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