GCV for Tikhonov regularization via global Golub-Kahan decomposition

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 (C) 2016 John Wiley & Sons, Ltd.