Smoothing by, and eccentric smoothing of, compactly supported RBFs

Thomas Hangelbroek; Christian Rieger

Smoothing by, and eccentric smoothing of, compactly supported RBFs

Numerical Analysis 2026-07-05 v1

Authors: Thomas Hangelbroek , Christian Rieger

Abstract

We consider compactly supported RBFs having algebraically decaying Fourier transforms. Here we focus especially on generalized Wendland RBFs and their modification by making them smoother away from zero, a process we call eccentric smoothing. Specifically, we consider mapping properties of the integral operators (sometimes known as covariance operator) for these novel type RBFs. Moreover, we show that eccentric smoothing makes wavelet-inspired compression technique for the kernel matrix feasible.

Keywords

radial basis functions Wendland functions eccentric smoothing integral operators kernel compression Fourier transform

Cite

@article{arxiv.2607.04512,
  title  = {Smoothing by, and eccentric smoothing of, compactly supported RBFs},
  author = {Thomas Hangelbroek and Christian Rieger},
  journal= {arXiv preprint arXiv:2607.04512},
  year   = {2026}
}