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2020 | OriginalPaper | Chapter

8. A Priori Parameter Choice in Tikhonov Regularization with Oversmoothing Penalty for Non-linear Ill-Posed Problems

Authors : Bernd Hofmann, Peter Mathé

Published in: Inverse Problems and Related Topics

Publisher: Springer Singapore

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Abstract

We study Tikhonov regularization for certain classes of non-linear ill-posed  operator equations in Hilbert spaces. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales. Inverse Problems 34(1), 2018, by the same authors. Optimal order convergence rates are established for the specific a priori parameter choice, as used for the corresponding linear equations.

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previous chapter Carleman Estimate for a General Second-Order Hyperbolic Equation
next chapter Case Studies and a Pitfall for Nonlinear Variational Regularization Under Conditional Stability
Literature
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B. Hofmann, P. Mathé, Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales. Inverse Probl. 34(1), 015007 (14 pp) (2018)
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T. Schuster, B. Kaltenbacher, B. Hofmann, K.S. Kazimierski, Regularization Methods in Banach Spaces, Radon Series on Computational and Applied Mathematics, vol. 10 (Walter de Gruyter, Berlin, 2012)CrossRef
Metadata
Title
A Priori Parameter Choice in Tikhonov Regularization with Oversmoothing Penalty for Non-linear Ill-Posed Problems
Authors
Bernd Hofmann
Peter Mathé
Copyright Year
2020
Publisher
Springer Singapore
Book
Inverse Problems and Related Topics

Print ISBN: 978-981-15-1591-0

Electronic ISBN: 978-981-15-1592-7

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-981-15-1592-7_8

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