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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On a generalization of Reginska's parameter choice rule and its numerical realization in large-scale multi-parameter Tikhonov regularization

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Author(s):
Viloche Bazan, Fermin S. [1] ; Borges, Leonardo S. [2] ; Francisco, Juliano B. [1]
Total Authors: 3
Affiliation:
[1] Univ Fed Santa Catarina, Dept Math, BR-88040900 Florianopolis, SC - Brazil
[2] Univ Estadual Campinas, Dept Appl Math, IMECC UNICAMP, BR-13081970 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Applied Mathematics and Computation; v. 219, n. 4, p. 2100-2113, NOV 1 2012.
Web of Science Citations: 3
Abstract

A crucial problem concerning Tikhonov regularization is the proper choice of the regularization parameter. This paper deals with a generalization of a parameter choice rule due to Reginska (1996) {[}31], analyzed and algorithmically realized through a fast fixed-point method in Bazan (2008) {[}3], which results in a fixed-point method for multi-parameter Tikhonov regularization called MFP. Like the single-parameter case, the algorithm does not require any information on the noise level. Further, combining projection over the Krylov subspace generated by the Golub-Kahan bidiagonalization (GKB) algorithm and the MFP method at each iteration, we derive a new algorithm for large-scale multi-parameter Tikhonov regularization problems. The performance of MFP when applied to well known discrete ill-posed problems is evaluated and compared with results obtained by the discrepancy principle. The results indicate that MFP is efficient and competitive. The efficiency of the new algorithm on a super-resolution problem is also illustrated. (C) 2012 Elsevier Inc. All rights reserved. (AU)