Error estimates for Tikhonov regularization with unbounded regularizing operators

  • It is shown that Tikhonov regularization for ill- posed operator equation \(Kx = y\) using a possibly unbounded regularizing operator \(L\) yields an orderoptimal algorithm with respect to certain stability set when the regularization parameter is chosen according to the Morozov's discrepancy principle. A more realistic error estimate is derived when the operators \(K\) and \(L\) are related to a Hilbert scale in a suitable manner. The result includes known error estimates for ordininary Tikhonov regularization and also the estimates available under the Hilbert scale approach.

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Author:M. Thamban Nair
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (279)
Document Type:Report
Language of publication:English
Publication Date:2017/11/09
Year of Publication:1996
Publishing Institute:Technische Universit├Ąt Kaiserslautern
Date of the Publication (Server):2017/11/09
Number of page:9
Faculties / Organisational entities:Kaiserslautern - Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)