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.

翻译：交叉验证是径向基函数配点法中的重要工具，尤其适用于与径向基函数相关的形状参数的关键调优。本文定义了一种新的高效代理交叉验证算法，该算法能够在相比标准实现大幅降低计算开销的前提下，精确逼近真实验证误差。首先对所提出的方案进行了详细分析与描述，随后通过多种数值实验验证了其高效性与有效性。