A fast surrogate cross validation algorithm for meshfree RBF collocation approaches

Cross-validation is an important tool in the Radial Basis Function (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 detail and then tested in various numerical experiments that confirm its efficiency and effectiveness.