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.
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