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  On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition.

Werner, F. (2015). On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition. Journal of Inverse and III-posed Problems, 23(1), 75-84. doi:10.1515/jiip-2013-0074.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0018-EC16-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0027-F6F4-4
Genre: Journal Article

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2000345.pdf (Publisher version), 577KB
 
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 Creators:
Werner, F.1, Author              
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1Research Group of Statistical Inverse-Problems in Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_1113580              

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Free keywords: Regularization, nonlinear inverse problems, iteratively regularized Gauss–Newton method, non-Gaussian noise
 Abstract: We investigate a generalization of the well-known iteratively regularized Gauss–Newton method where the Newton equations are regularized variationally using general data delity and penalty terms. To obtain convergence rates, we use a general error assumption which has recently been shown to be useful for impulsive and Poisson noise. We restrict the nonlinearity of the forward operator only by a Lipschitztype condition and compare our results to other convergence rates results proven in the literature. Finally we explicitly state our convergence rates for the aforementioned case of Poisson noise to shed some light on the structure of the posed error assumption.

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Language(s): eng - English
 Dates: 2014-03-222015-02
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: DOI: 10.1515/jiip-2013-0074
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Title: Journal of Inverse and III-posed Problems
Source Genre: Journal
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Pages: - Volume / Issue: 23 (1) Sequence Number: - Start / End Page: 75 - 84 Identifier: -