Error bounds for numerical differentiation using kernels of finite smoothness

Fuente: arXiv
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Autore principale: Davydov, Oleg
Natura: Preprint
Pubblicazione: 2025
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author Davydov, Oleg
author_facet Davydov, Oleg
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_12776
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Error bounds for numerical differentiation using kernels of finite smoothness
Davydov, Oleg
Numerical Analysis
65D25, 65D12, 41A30, 41A80, 41A63
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.
title Error bounds for numerical differentiation using kernels of finite smoothness
topic Numerical Analysis
65D25, 65D12, 41A30, 41A80, 41A63
url https://arxiv.org/abs/2511.12776