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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Numerische Mathemati...arrow_drop_down
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Numerische Mathematik
Article . 1993 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1993
Data sources: zbMATH Open
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Convergence rates of iterated Tikhonov regularized solutions of nonlinear III ? posed problems

Convergence rates of iterated Tikhonov regularized solutions of nonlinear ill-posed problems
Authors: Scherzer, O.;

Convergence rates of iterated Tikhonov regularized solutions of nonlinear III ? posed problems

Abstract

Iterated Tikhonov regularization for the solution of nonlinear ill-posed problems is investigated. In the case of linear ill-posed problems it is well-known that (under appropriate assumptions) the \(n\)-th iterated regularized solutions can converge like \(O(\delta^{{2n \over 2n+1}})\), where \(\delta\) denotes the noise level of the data perturbation. Conditions are given that guarantee this convergence rate also for nonlinear ill-posed problems, and these conditions are motivated by the mapping degree. The results are derived by a comparison of the iterated regularized solutions of the nonlinear problem with the iterated regularized solutions of its linearization. Numerical examples are presented.

Keywords

numerical examples, parameter identification, convergence rate, 510.mathematics, Numerical solutions of ill-posed problems in abstract spaces; regularization, Iterative procedures involving nonlinear operators, inverse problems, Numerical solutions to equations with nonlinear operators, nonlinear ill-posed problems, Article, iterated Tikhonov regularization

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
17
Average
Top 10%
Average
Green