Because of the high approximation power and simplicity of computation of smooth radial basis functions (RBFs), in recent decades they have received much attention for function approximation. These RBFs contain a shape parameter that regulates the relation between their accuracy and stability. A difficulty in approximation via smooth RBFs is optimal selection of shape parameter. The aim of this paper is to introduce an alternative for smooth RBFs, which in addition to overcoming this difficulty, its approximation power is almost equal to RBFs....

翻译：由于光滑径向基函数具有高逼近能力和计算简便性，近几十年来它们在函数逼近领域备受关注。这类径向基函数包含一个形状参数，用于调节其精度与稳定性之间的关系。光滑径向基函数逼近的难点在于形状参数的最优选取。本文旨在引入一种光滑径向基函数的替代方案，该方案不仅克服了这一难题，其逼近能力也几乎与径向基函数相当...