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arXiv · 2609.23833

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 $\ell_p$, 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 $\mathcal{S}^θ$ 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.

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S. G. Solodky, Y. A. Volynets. 2026-09-20. Numerical differentiation of functions on the half-line in a weighted uniform metric. https://arxiv.org/abs/2609.23833

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