A fast surrogate cross validation algorithm for meshfree RBF collocation approaches

TL;DR

This paper introduces a fast surrogate cross validation algorithm for meshfree RBF collocation methods, significantly reducing computational effort while maintaining accuracy in shape parameter tuning.

Contribution

The paper presents a novel surrogate cross validation algorithm that efficiently approximates validation error in RBF collocation, improving computational speed over traditional methods.

Findings

The proposed algorithm accurately approximates true validation error.

Numerical experiments confirm the efficiency and effectiveness of the method.

The approach reduces computational effort in shape parameter tuning.

Abstract

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.