Year: 2025
Type: article
Abstract: We provide improved error bounds for kernel-based numerical differentiation in terms of growth functions when kernels are of a finite smoothness, such as polyharmonic splines, thin plate splines or Wendland kernels. In contrast to existing literature, the new estimates take into account the Hölder class smoothness of kernel's derivatives, which helps to improve the order of the estimate. In addition, the new estimates apply to certain deficient point sets, relaxing a standard assumption that an approximation with conditionally positive definite kernels must rely on determining sets for polynomials.
Source: Researches in Mathematics
DOI: 10.15421/242514
Author: O.V. Davydov
Institution: Justus-Liebig-Universität Gießen
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $20
OpenAlex ID: W4417324152