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Type: Artigo de periódico
Title: On A Generalization Of Regińska's Parameter Choice Rule And Its Numerical Realization In Large-scale Multi-parameter Tikhonov Regularization
Author: Viloche Bazan F.S.
Borges L.S.
Francisco J.B.
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 Regińska (1996) [31], analyzed and algorithmically realized through a fast fixed-point method in Bazán (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. © 2012 Elsevier Inc. All rights reserved.
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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