A new stable basis for RBF approximation
Abstract
It's well know that Radial Basis Function approximants suffers of bad conditioning if the simple basis of translates is used. A recent work of M.Pazouki and R.Schaback gives a quite general way to build stable, orthonormal bases for the native space based on a factorization of the kernel matrix A. Starting from that setting we describe a particular orthonormal basis that arises from a weighted singular value decomposition of A. This basis is related to a discretization of the compact operator which leads to the so-called eigenbasis, and provides a connection with it. We give convergence estimates and stability bound for the interpolation and the discrete least-squares approximation based on this basis, which involves the eigenvalues of such an operator.
Cite
@article{arxiv.1210.1682,
title = {A new stable basis for RBF approximation},
author = {Gabriele Santin},
journal= {arXiv preprint arXiv:1210.1682},
year = {2018}
}