Approximation with Conditionally Positive Definite Kernels on Deficient Sets
Numerical Analysis
2025-08-26 v1 Numerical Analysis
Abstract
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define kernel-based numerical approximation of the functional with usual properties of optimal recovery. Application examples include generation of sparse kernel-based numerical differentiation formulas for the Laplacian on a grid and accurate approximation of a function on an ellipse.
Cite
@article{arxiv.2006.13543,
title = {Approximation with Conditionally Positive Definite Kernels on Deficient Sets},
author = {Oleg Davydov},
journal= {arXiv preprint arXiv:2006.13543},
year = {2025}
}