Error bounds for numerical differentiation using kernels of finite smoothness
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909974299410432 |
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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 |