Clustering Effect for Stationary Points of Discrepancy Functionals Associated with Conditionally Well-Posed Inverse Problems

In a Hilbert space we consider a class of conditionally well-posed inverse problems for which a Hölder-type estimate of conditional stability on a closed convex bounded subset holds. We investigate the Ivanov quasi-solution method and its finite-dimensional version associated with minimization of a...

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Bibliographic Details
Published in:Numerical analysis and applications 2018-10, Vol.11 (4), p.311-322
Main Author: Kokurin, M. Yu
Format: Article
Language:English
Subjects:
Clustering
Dimensional stability
Hilbert space
Inverse problems
Mathematics
Mathematics and Statistics
Numerical Analysis
Well posed problems
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Summary:In a Hilbert space we consider a class of conditionally well-posed inverse problems for which a Hölder-type estimate of conditional stability on a closed convex bounded subset holds. We investigate the Ivanov quasi-solution method and its finite-dimensional version associated with minimization of a multi-extremal discrepancy functional over a conditional stability set or over a finite-dimensional section of this set, respectively. For these optimization problems, we prove that each of their stationary points that is located not too far from the desired solution of the original inverse problem belongs to a small neighborhood of the solution. Estimates for the diameter of this neighborhood in terms of error levels in input data are also given.
ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423918040043