  Cross validation is an important tool in the RBF collocation setting,
especially for the crucial tuning of the shape parameter related to the radial
basis function. In this paper, we define a new efficient surrogate cross
validation algorithm, which computes an accurate approximation of the true
validation error with much less computational effort with respect to a standard
implementation. The proposed scheme is first analyzed and described in details,
and then tested in various numerical experiments that confirm its efficiency
and effectiveness.
