CONSTRUCTION AND RESEARCH INTO THE OPERATOR OF INTERLINEATION OF THE FUNCTIONS OF TWO VARIABLES WITH THE PRESERVATION OF THE CLASS OF DIFFERENTIABILITY USING THE TRACES OF THEIR DERIVATIVES TO A FIXED ORDER ON THE LINE SPECIFIED

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DOI https://doi.org/10.15407/pmach2016.02.050
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 19, no. 2, 2016 (June)
Pages 50-57
Cited by J. of Mech. Eng., 2016, vol. 19, no. 2, pp. 50-57

 

Authors

I. V. Serhiienko, V. M. Glushkov Institute of Cybernetics of the NASU (40, Academician Glushkov Ave., Kyiv, 03187, Ukraine)

O. M. Lytvyn, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine), e-mail: academ_mail@ukr.net

O. O. Lytvyn, Ukrainian Engineering Pedagogics Academy (16, Universitetskaya St., Kharkiv, 61003, Ukraine)

O. V. Tkachenko, Zaporozhye Machine-Building Design Bureau Progress State Enterprise named after Academician A. G. Ivchenko (2, Ivanova Str., 69068, Zaporozhye, Ukraine), e-mail: avt2007@outlook.com

O. L. Hrytsai, Zaporozhye Machine-Building Design Bureau Progress State Enterprise named after Academician A. G. Ivchenko (2, Ivanova Str., 69068, Zaporozhye, Ukraine), e-mail: avt2007@outlook.com

 

Abstract

This article proposes and investigates methods of constructing operators for restoring the differentiable functions of two variables in the neighborhood of a smooth line G: w(x, y) = 0 w Î Cr(R2) that preserve the class of differentiability Cr (R2). To construct the specified operators, these methods use the traces of the function being restored and its partial derivatives with respect to one variable to a specified order on the line specified.

 

Keywords: preservation of the class of differentiability, traces of a function, traces of derivatives on a line, Taylor polynomial with respect to one variable

 

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Received 03 March 2016

Published 30 June 2016