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

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-value...

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Bibliographic Details
Published in:arXiv.org 2020-05
Main Authors: Drake, Kathryn P, Wright, Grady B
Format: Article
Language:English
Subjects:
Algorithms
Divergence
Fields (mathematics)
Ill-conditioned problems (mathematics)
QR algorithms
Radial basis function
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2001.04557