English

A stable algorithm for divergence-free radial basis functions in the flat limit

Numerical Analysis 2020-07-15 v2 Numerical Analysis

Abstract

The direct method used for calculating smooth radial basis function (RBF) interpolants in the flat limit becomes numerically unstable. The RBF-QR algorithm bypasses this ill-conditioning using a clever change of basis technique. We extend this method for computing interpolants involving matrix-valued kernels, specifically surface divergence-free RBFs on the sphere, in the flat limit. Results illustrating the effectiveness of this algorithm are presented for a divergence-free vector field on the sphere from samples at scattered points.

Keywords

Cite

@article{arxiv.2001.04557,
  title  = {A stable algorithm for divergence-free radial basis functions in the flat limit},
  author = {Kathryn P. Drake and Grady B. Wright},
  journal= {arXiv preprint arXiv:2001.04557},
  year   = {2020}
}

Comments

11 pages, 3 figures

R2 v1 2026-06-23T13:10:19.361Z