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PreprintCC0arXiv

Numerical differentiation of functions on the half-line in a weighted uniform metric

  • S. G. Solodky
  • Y. A. Volynets
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Abstract

We consider the problem of numerical differentiation of functions defined on the half-line: the derivative f(r), $ r=1,2,\ldots$, is recovered from a finite set of perturbed Fourier--Laguerre coefficients of a function f, whose error is measured in ℓp, while the accuracy of approximation is measured in the uniform metric with the weight tαe−t. It is established that the Wiener class Wμs admits such a setting for μ>r+1−1/s. A class of methods 𝒮θ is constructed that realize the optimal order of accuracy of numerical differentiation on Wμs and use the smallest amount of input information in order.

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Cite

BibTeXRIS
BibTeX
@misc{solodky2026numerical,
  title = {{Numerical differentiation of functions on the half-line in a weighted uniform metric}},
  author = {S. G. Solodky and Y. A. Volynets},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23833},
  eprint = {2609.23833},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23833},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Numerical differentiation of functions on the half-line in a weighted uniform metric
AU  - S. G. Solodky
AU  - Y. A. Volynets
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23833
UR  - https://arxiv.org/abs/2609.23833
AB  - We consider the problem of numerical differentiation of functions defined on the half-line: the derivative f^(r), $ r=1,2,\ldots$, is recovered from a finite set of perturbed Fourier--Laguerre coefficients of a function f, whose error is measured in ℓ_p, while the accuracy of approximation is measured in the uniform metric with the weight t^αe^−t. It is established that the Wiener class W^μ_s admits such a setting for μ>r+1−1/s. A class of methods 𝒮^θ is constructed that realize the optimal order of accuracy of numerical differentiation on W^μ_s and use the smallest amount of input information in order.
ER  -