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 Mat. Zametki, 2020, Volume 108, Issue 5, Pages 771–781 (Mi mz12508)

Local approximation by parabolic splines in the mean with large averaging intervals

V. T. Shevaldin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: In the paper, local parabolic splines on the whole real line $\mathbb R$ with equidistant nodes are considered. These splines realize the simplest local approximation scheme, but instead of the function values at the nodes, their average values in symmetric neighborhoods of the nodes are approximated. For an arbitrary averaging step $H$, which more than twice is more than the spline grid step $h$, the approximation errors in the uniform metric for functions and their derivatives are precisely calculated on the class $W_{\infty}^2$. For small steps of averaging $H\leq 2h$, these values were found by E.V.Strelkova in 2007.

Keywords: local approximation, parabolic splines, interpolation in the mean

 Funding Agency Grant Number Ural Mathematical Center This work is part of the research carried out at the Ural Mathematical Center.

DOI: https://doi.org/10.4213/mzm12508

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English version:
Mathematical Notes, 2020, 108:5, 733–742

Bibliographic databases:

UDC: 519.65
Revised: 24.04.2020

Citation: V. T. Shevaldin, “Local approximation by parabolic splines in the mean with large averaging intervals”, Mat. Zametki, 108:5 (2020), 771–781; Math. Notes, 108:5 (2020), 733–742

Citation in format AMSBIB
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