The Generalised Cross Validation (GCV) smoothing algorithm is a means by which to approximate the smoothing parameter associated to a regularised least-squares problem. A direct implementation of the GCV algorithm is, however, computationally and memory intensive, involving the minimisation of a function which requires repeated solution of a linear system and repeated computation of the trace of the inverse of a matrix, the dimension of which is approximately the number of data points being interpolated. For large data sets, in real-time or interactive mode, the direct implementation is impractical and even impossible. Thus efforts have been devoted in recent years toward producing faster iterative methods that are suited for sequential as well as parallel environments. These efforts were done in the context of a standard regularised least-squares problem. The Fast GCV technique is a Lanczos-based algorithm for fast evaluation of the GCV. In this work, we show how the fast GCV framework can be extended and applied to general regularised least-squares problems where the penalty term is a semi-norm. The study shows how the framework can be efficiently blended with data mining applications modelled by finite-element methods.

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