标题： 径向多项式作为平滑径向基函数的替代及其应用 显示英文标题

标题： Radial polynomials as alternatives to smooth radial basis functions and their applications

摘要： 由于平滑径向基函数（RBFs）具有高逼近能力和计算简便性，近年来它们在函数逼近中受到了广泛关注。这些RBFs包含一个形状参数，该参数调节其准确性和稳定性的关系。通过平滑RBF进行逼近的一个困难是形状参数的最优选择。本文的目的是引入一种平滑RBF的替代方法，该方法除了克服这一困难外，其逼近能力几乎与RBFs相当。 显示英文摘要

摘要： 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....