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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

A convergence analysis of regularization by discretization in preimage space


Authors: Barbara Kaltenbacher and Jonas Offtermatt
Journal: Math. Comp. 81 (2012), 2049-2069
MSC (2010): Primary 65J20; Secondary 65M32
Published electronically: April 2, 2012
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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.


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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

DOI: http://dx.doi.org/10.1090/S0025-5718-2012-02596-8
PII: S 0025-5718(2012)02596-8
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
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.