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2015 | OriginalPaper | Chapter

Iteratively Regularized Gauss-Newton Methods under Random Noise

Authors : Mikhail Yu. Kokurin, Anatoly B. Bakushinsky

Published in: Inverse Problems and Applications

Publisher: Springer International Publishing

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Abstract

We investigate a class of regularized Gauss–Newton type methods for solving irregular nonlinear equations with general smooth operators in a Hilbert space. Perturbations of right-hand sides of equations are modeled by Hilbert space valued random elements. We analyze two qualitatively different schemes of forming stochastic measurement data, establish approximation properties of the methods in the mean square sense and prove corresponding accuracy estimates The work is supported by the Russian Foundation for Basic Research (project no. 12–01–00239a).

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next chapter Methods of Quantitative Reconstruction of Shapes and Refractive Indices from Experimental data
Literature
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Bakushinsky, A.B., Kokurin, M.Yu.: Iterative Methods for Approximate Solution of Inverse Problems. Springer, Dordrecht (2004)MATH
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Vainikko, G.M., Veretennikov, A.Yu.: Iterative Procedures in Ill–Posed Problems. Nauka, Moscow (1986) (in Russian)
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Vakhania, N.N., Tarieladze, V.I., Chobanyan, S.A.: Probability Distributions on Banach Spaces. D. Reidel Publishing Co., Dordrecht (1987)CrossRefMATH
Metadata
Title
Iteratively Regularized Gauss-Newton Methods under Random Noise
Authors
Mikhail Yu. Kokurin
Anatoly B. Bakushinsky
Copyright Year
2015
Book
Inverse Problems and Applications

Print ISBN: 978-3-319-12498-8

Electronic ISBN: 978-3-319-12499-5

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-12499-5_1

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