GCV for Tikhonov regularization via global Golub–Kahan decomposition
Copyright policy )GCV for Tikhonov regularization via global Golub–Kahan decomposition
SummaryGeneralized 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.
- University of Cagliari Italy
- Kent State University United States
- University System of Ohio United States
global Golub-Kahan decomposition, Numerical solutions to overdetermined systems, pseudoinverses, Gauss quadrature rule, Generalized cross validation; Tikhonov regularization; Parameter estimation; Global Golub–Kahan decomposition, Tikhonov regularization, singular value decomposition, large-scale least-squares problems, Numerical quadrature and cubature formulas, generalized cross validation, Ill-posedness and regularization problems in numerical linear algebra, standard Golub-Kahan bidiagonalization, Gauss-Radau quadrature rule, numerical experiments
global Golub-Kahan decomposition, Numerical solutions to overdetermined systems, pseudoinverses, Gauss quadrature rule, Generalized cross validation; Tikhonov regularization; Parameter estimation; Global Golub–Kahan decomposition, Tikhonov regularization, singular value decomposition, large-scale least-squares problems, Numerical quadrature and cubature formulas, generalized cross validation, Ill-posedness and regularization problems in numerical linear algebra, standard Golub-Kahan bidiagonalization, Gauss-Radau quadrature rule, numerical experiments
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