Multidirectional Subspace Expansion for One-Parameter and Multiparameter Tikhonov Regularization

Tikhonov regularization is a popular method to approximate solutions of linear discrete ill-posed problems when the observed or measured data is contaminated by noise. Multiparameter Tikhonov regularization may improve the quality of the computed approximate solutions. We propose a new iterative met...

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Bibliographic Details
Published in:Journal of scientific computing 2017-03, Vol.70 (3), p.990-1009
Main Authors: Zwaan, Ian N., Hochstenbach, Michiel E.
Format: Article
Language:English
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Ill posed problems
Iterative methods
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Parameters
Regularization
Subspaces
Theoretical
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Summary:Tikhonov regularization is a popular method to approximate solutions of linear discrete ill-posed problems when the observed or measured data is contaminated by noise. Multiparameter Tikhonov regularization may improve the quality of the computed approximate solutions. We propose a new iterative method for large-scale multiparameter Tikhonov regularization with general regularization operators based on a multidirectional subspace expansion. The multidirectional subspace expansion may be combined with subspace truncation to avoid excessive growth of the search space. Furthermore, we introduce a simple and effective parameter selection strategy based on the discrepancy principle and related to perturbation results.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-016-0271-0