Kernel-based interpolation at approximate Fekete points
Numerical Analysis
2020-06-23 v3 Numerical Analysis
Abstract
We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel interpolants at the resulting points. If the kernel is Gaussian we show that the approximate Fekete points in one dimension are the solution to a convex optimisation problem and that the interpolants converge with a super-exponential rate. Numerical examples are provided for the Gaussian kernel.
Cite
@article{arxiv.1912.07316,
title = {Kernel-based interpolation at approximate Fekete points},
author = {Toni Karvonen and Simo Särkkä and Ken'ichiro Tanaka},
journal= {arXiv preprint arXiv:1912.07316},
year = {2020}
}
Comments
Accepted for publication in Numerical Algorithms