论文标题
从其散射数据中的多元变化的多元函数的近似
Approximation of a Multivariate Function of Bounded Variation from its Scattered Data
论文作者
论文摘要
本文解决了从其散射数据中近似有界变化的函数的问题。已知径向基函数（RBF）插值方法仅在其天然空间中仅近似函数，并且迄今为止，尚无已知证据表明它们可以在与所使用的特定RBF相关的天然空间之外近似函数。在本文中，我们描述了一种零散的数据插值方法，该方法可以随着数据点的稠密而近似其散射数据的任何函数。由于有界变化的函数类别比RBF的天然空间更宽，因此该方法比RBF插值方法具有至关重要的优势。
This paper addresses 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.
