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

 

Regularization of some linear ill-posed problems with discretized random noisy data


Authors: Peter Mathé and Sergei V. Pereverzev
Journal: Math. Comp. 75 (2006), 1913-1929
MSC (2000): Primary 62G05; Secondary 62G20, 65J20
Published electronically: June 28, 2006
MathSciNet review: 2240642
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Abstract: For linear statistical ill-posed problems in Hilbert spaces we introduce an adaptive procedure to recover the unknown solution from indirect discrete and noisy data. This procedure is shown to be order optimal for a large class of problems. Smoothness of the solution is measured in terms of general source conditions. The concept of operator monotone functions turns out to be an important tool for the analysis.


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Additional Information

Peter Mathé
Affiliation: Weierstraß Institute for Applied Analysis and Stochastics, Mohrenstraße 39, D–10117 Berlin, Germany
Email: mathe@wias-berlin.de

Sergei V. Pereverzev
Affiliation: Johann-Radon-Institute (RICAM), Altenberger Strasse 69, A-4040 Linz, Austria
Email: sergei.pereverzyev@oeaw.ac.at

DOI: http://dx.doi.org/10.1090/S0025-5718-06-01873-4
PII: S 0025-5718(06)01873-4
Keywords: Statistical ill-posed problem, general source condition, operator monotone function
Received by editor(s): February 2, 2005
Received by editor(s) in revised form: August 26, 2005
Published electronically: June 28, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.