An alternative procedure for selecting a good value for the parameter \(c\) in RBF-interpolation (Q618779)

When a real \(d\)-valued function \(f:\Omega\to\mathbb{R}^d\) has to be reconstructed from its values at a finite number of points by interpolation schemes using radial basis functions, the choice of the value of the scaling parameter has a great influence on the accuracy of the interpolation. In this paper the author in the case of a cost function based on the Euclidean norm proposes a method for selecting a good parameter value which is a modification of an algorithm due to Rippa based on a variant of the cross validation. He compares the performance of the method with that of Rippa and discuss its limitations and some computational aspects of the algorithm.