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GCV for Tikhonov regularization via global Golub–Kahan decomposition
Author(s) -
Fenu Caterina,
Reichel Lothar,
Rodriguez Giuseppe
Publication year - 2016
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.2034
Subject(s) - tikhonov regularization , regularization (linguistics) , backus–gilbert method , regularization perspectives on support vector machines , mathematics , mathematical optimization , gauss , algorithm , computer science , inverse problem , mathematical analysis , artificial intelligence , physics , quantum mechanics
Summary Generalized cross validation is a popular approach to determining the regularization parameter in Tikhonov regularization. The regularization parameter is chosen by minimizing an expression, which is easy to evaluate for small‐scale problems, but prohibitively expensive to compute for large‐scale ones. This paper describes a novel method, based on Gauss‐type quadrature, for determining upper and lower bounds for the desired expression. These bounds are used to determine the regularization parameter for large‐scale problems. Computed examples illustrate the performance of the proposed method and demonstrate its competitiveness. Copyright © 2016 John Wiley & Sons, Ltd.