On Approximation of Smooth Functions by <i>L</i>-Splines at a Point

Zhanna V. Khudaya

doi:10.1615/JAutomatInfScien.v40.i7.70

Journal of Automation and Information Sciences

Éditeur en chef: Arkadiy A. Chikriy (open in a new tab)

Éditeur associés: Vyacheslav F. Gubarev (open in a new tab) Yuriy P. Kondratenko (open in a new tab) Nonna V. Turovyerova (open in a new tab)

Publication de 12 numéros par an

ISSN Imprimer: 1064-2315

ISSN En ligne: 2163-9337

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On Approximation of Smooth Functions by L-Splines at a Point

Volume 40, Numéro 7, 2008, pp. 73-80

DOI: 10.1615/JAutomatInfScien.v40.i7.70

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Zhanna V. Khudaya
Dneprodzerzhinsk State Technical University, Dneprodzerzhinsk, Ukraine

RÉSUMÉ

We constructed "almost interpolation" generalized L-splines based on the basis functions, composed of parts of solutions of the differential equation, which coefficients change from segment to segment. Estimate of error for approximation by these splines of smooth functions at arbitrary point were obtained and we proved superconvergence in nodes of spline, which approximates functions holding the same differential equation as the built splines.

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