Optimizing the shape parameter in rational RBF partition of unity interpolation

In this article we enhance the rational RBF partition of unity (RBF-PU) method presented in Farazandeh and Mirzaei (2021) for shape parameter free RBFs. Here, we propose a leave-one-out cross-validation technique to optimize the RBF shape parameter in the context of rational interpolation. This approach enables us to obtain remarkable results in the rational RBF-PU scheme for shape parameter dependent RBFs. Numerical experiments highlight performance of the rational RBF-PU interpolation, also in comparison to that of the standard method.