In this paper, we address the problem of approximating a function of bounded variation from its scattered data. Radial basis function(RBF) interpolation methods are known to approximate only functions in their native spaces, and to date, there has been no known proof that they can approximate functions outside the native space associated with the particular RBF being used. In this paper, we describe a scattered data interpolation method which can approximate any function of bounded variation from its scattered data as the data points grow dense. As the class of functions of bounded variation is a much wider class than the native spaces of the RBF, this method provides a crucial advantage over RBF interpolation methods.

翻译：在本文中,我们讨论了与分散数据相近的封闭变异功能问题,已知的辐射基函数(RBF)内插方法仅接近其本地空间的功能,而迄今为止,还没有已知的证据表明,它们能够接近与正在使用的特定RBF有关的本地空间以外的功能,我们在本文件中描述了一种分散的数据内插方法,随着数据点的密度增长,这种数据内插方法可以与其分散数据相近的封闭变异的任何功能。由于受约束变异功能的类别比RBF的本地空间大得多,这种方法比RBF的内插方法具有关键优势。