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

 

Heuristic parameter selection based on functional minimization: Optimality and model function approach


Authors: Shuai Lu and Peter Mathé
Journal: Math. Comp. 82 (2013), 1609-1630
MSC (2010): Primary 65J20; Secondary 47A52
Published electronically: February 21, 2013
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Abstract: We analyze some parameter choice strategies in regularization of inverse problems, in particular, the (modified) L-curve method and a variant of the Hanke-Raus type rule. These are heuristic rules, free of the noise level, and they are based on minimization of some functional. We analyze these functionals, and we prove some optimality results under general smoothness conditions. We also devise some numerical approach for finding the minimizers, which uses model functions. Numerical experiments indicate that this is an efficient numerical procedure.


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Additional Information

Shuai Lu
Affiliation: School of Mathematical Sciences, Fudan University, Shanghai 200433, China
Email: slu@fudan.edu.cn

Peter Mathé
Affiliation: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany
Email: mathe@wias-berlin.de

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02674-9
PII: S 0025-5718(2013)02674-9
Keywords: Parameter choice, L-curve, model function
Received by editor(s): March 15, 2010
Received by editor(s) in revised form: October 7, 2011
Published electronically: February 21, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.