A convergence analysis of regularization by discretization in preimage space
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- by Barbara Kaltenbacher and Jonas Offtermatt PDF
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Abstract:
In this paper we investigate the regularizing properties of discretization in preimage space for linear and nonlinear ill-posed operator equations with noisy data. We propose to choose the discretization level, that acts as a regularization parameter in this context, by a discrepancy principle. While general convergence has been shown not to hold, we provide convergence results under appropriate conditions on the exact solution.References
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Additional Information
- Barbara Kaltenbacher
- Affiliation: Institute for Mathematics, University of Klagenfurt, Universitätsstraße 65-67, A-9020 Klagenfurt, Austria
- Email: barbara.kaltenbacher@aau.at
- Jonas Offtermatt
- Affiliation: Institute for Stochastics and Applications, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Email: jonas.offtermatt@mathematik.uni-stuttgart.de
- Received by editor(s): April 10, 2011
- Received by editor(s) in revised form: June 26, 2011
- Published electronically: April 2, 2012
- Additional Notes: Support by the German Science Foundation (DFG) within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart is gratefully acknowledged
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 81 (2012), 2049-2069
- MSC (2010): Primary 65J20; Secondary 65M32
- DOI: https://doi.org/10.1090/S0025-5718-2012-02596-8
- MathSciNet review: 2945147