The Ivanov regularized Gauss–Newton method in Banach space with an a posteriori choice of the regularization radius
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Barbara Kaltenbacher
,
Andrej Klassen
Abstract
In this paper, we consider the iteratively regularized Gauss–Newton method, where regularization is achieved by Ivanov regularization, i.e., by imposing a priori constraints on the solution.
We propose an a posteriori choice of the regularization radius, based on an inexact Newton/discrepancy principle approach, prove convergence and convergence rates under a variational source condition as the noise level tends to zero and provide an analysis of the discretization error.
Our results are valid in general, possibly nonreflexive Banach spaces, including, e.g.,
Funding source: Austrian Science Fund
Award Identifier / Grant number: I2271
Award Identifier / Grant number: P30054
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: Cl 487/1-1
Funding statement: Supported by the FWF under grants I2271 and P30054 and by the DFG under grant Cl 487/1-1, as well as partially by the Karl Popper Kolleg “Modeling-Simulation-Optimization”, funded by the Alpen-Adria-Universität Klagenfurt and by the Carinthian Economic Promotion Fund (KWF).
Acknowledgements
The authors wish to thank Christian Clason, University of Duisburg-Essen for valuable discussions and support with the implementation. Moreover, the authors wish to thank all reviewers for their very careful reading of the manuscript and their detailed reports with valuable comments and suggestions that have led to an improved version of the paper.
References
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Numerical solution of a source identification problem: Almost coercivity
- Invertibility and stability for a generic class of radon transforms with application to dynamic operators
- A class of homotopy with regularization for nonlinear ill-posed problems in Hilbert space
- Inverse nodal problems for integro-differential operators with a constant delay
- Unique continuation for a reaction-diffusion system with cross diffusion
- On solenoidal-injective and injective ray transforms of tensor fields on surfaces
- The Ivanov regularized Gauss–Newton method in Banach space with an a posteriori choice of the regularization radius
- Identification of point sources in an elliptic equation from interior measurements: Application to a seawater intrusion problem
- Tikhonov regularization with ℓ0-term complementing a~convex penalty: ℓ1-convergence under sparsity constraints
- On the travel time tomography problem in 3D
Artikel in diesem Heft
- Frontmatter
- Numerical solution of a source identification problem: Almost coercivity
- Invertibility and stability for a generic class of radon transforms with application to dynamic operators
- A class of homotopy with regularization for nonlinear ill-posed problems in Hilbert space
- Inverse nodal problems for integro-differential operators with a constant delay
- Unique continuation for a reaction-diffusion system with cross diffusion
- On solenoidal-injective and injective ray transforms of tensor fields on surfaces
- The Ivanov regularized Gauss–Newton method in Banach space with an a posteriori choice of the regularization radius
- Identification of point sources in an elliptic equation from interior measurements: Application to a seawater intrusion problem
- Tikhonov regularization with ℓ0-term complementing a~convex penalty: ℓ1-convergence under sparsity constraints
- On the travel time tomography problem in 3D
