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Extension of GKB‐FP algorithm to large‐scale general‐form Tikhonov regularization
Author(s) -
Viloche Bazán Fermín S.,
Cunha Maria C.C.,
Borges Leonardo S.
Publication year - 2014
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1874
Subject(s) - tikhonov regularization , regularization (linguistics) , mathematics , regularization perspectives on support vector machines , backus–gilbert method , smoothing , algorithm , mathematical optimization , mathematical analysis , computer science , inverse problem , statistics , artificial intelligence
SUMMARY In a recent paper an algorithm for large‐scale Tikhonov regularization in standard form called GKB‐FP was proposed and numerically illustrated. In this paper, further insight into the convergence properties of this method is provided, and extensions to general‐form Tikhonov regularization are introduced. In addition, as alternative to Tikhonov regularization, a preconditioned LSQR method coupled with an automatic stopping rule is proposed. Preconditioning seeks to incorporate smoothing properties of the regularization matrix into the computed solution. Numerical results are reported to illustrate the methods on large‐scale problems. Copyright © 2013 John Wiley & Sons, Ltd.