Adaptive residual subsampling algorithms for kernel interpolation based on cross validation techniques

In this article, we present an adaptive residual subsampling scheme designed for kernel based interpolation. For an optimal choice of the kernel shape parameter we consider some cross validation (CV) criteria, using efficient algorithms of k-fold CV and leave-one-out CV (LOOCV) as a special case. In this framework, the selection of the shape parameter within the residual subsampling method is totally automatic, provides highly reliable and accurate results for any kind of kernel, and guarantees existence and uniqueness of the kernel based interpolant. Numerical results show the performance of this new adaptive scheme, also giving a comparison with other computational techniques.