Approximation of Bivariate Functions by Generalized Wendland Radial Basis Functions

Abstract

In this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the theory of the presented method is justified by proving the corresponding convergence result. Likewise, to illustrate this method, some graphical and numerical examples are presented in R2, and a comparison with another work is analyzed.

Keywords

• radial basis functions
• generalized Wendland radial basis functions
• interpolation
• smoothing
• variational methods