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Type: Artigo de periódico
Title: On a generalization of Reginska's parameter choice rule and its numerical realization in large-scale multi-parameter Tikhonov regularization
Author: Bazan, FSV
Borges, LS
Francisco, JB
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.
Subject: Parameter choice rules
Multi-parameter Tikhonov regularization
Large-scale discrete ill-posed problems
Country: EUA
Editor: Elsevier Science Inc
Citation: Applied Mathematics And Computation. Elsevier Science Inc, v. 219, n. 4, n. 2100, n. 2113, 2012.
Rights: fechado
Identifier DOI: 10.1016/j.amc.2012.08.054
Date Issue: 2012
Appears in Collections:Unicamp - Artigos e Outros Documentos

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