UDC 519.6
1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine
 incyb@incyb.kiev.ua
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4 Ivchenko-Progress ZMKB, Zaporizhzhia, Ukraine
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OPTIMIZATION OF THE ERROR IN THE OPERATORS OF INTERLINEATION
OF A FUNCTION ON PARALLEL LINES
Abstract. This article discusses the issue of estimating the error and optimizing the choice of parameters
in Hermitian-type operators of interlineation of functions on a system of M parallel lines.
For this, the formulas of generalized Hermitian-type interlineation are used, which, unlike the formulas
of ordinary Hermitian-type interlineation, allow automatically preserving the same class of differentiability
to which the approximate function belongs. When constructing
these operators, an arbitrary system of unequal each other
numbers β 0, β 1,..., β N is used.
The article proposes a method for the optimal choice of these parameters and an estimation of error of the remainder.
Keywords: interlineation, operator, remainder, optimization.
FULL TEXT
REFERENCES
- Lytvyn O.M. Interlination of functions and its applications [in Ukrainian]. Kharkiv: Osnova, 2002. 544p.
- Sergienko I.V., Lytvyn O.M., Lytvyn O.O., Tkachenko O.V., Hrytsai O.L. Construction and analysis of the approximation operator of functions of two variables with preservation of a class of differentiation on traces of their derivatives to the fixed order on the given line. Problemy mashynobuduvannya. 2016. Vol. 19, N 2. P. 50–57.
- Lytvyn O.M., Lytvyn O.O., Tkachenko O.V., Biloborodov A.A. Optimization of parameter selection in the generalized D'Alembert formula for the function of two variables. Modern problems of mathematical modeling, forecasting and optimization: abstracts of the 9th International Scientific Conference. Kamianets-Podilskyi: Ivan Ogienko National University of Kamianets-Podilskyi, 2020. P. 96–99. URL: https://inf.kpnu.edu.ua/wp-content/uploads/2020/05/optima_2020_tezy.pdf.
- Sergienko I.V., Lytvyn O.M., Lytvyn O.O., Tkachenko O.V., Hrytsai O.L. Restoration of functions of two variables with preservation of a class by means of their traces and traces of their derivatives to the fixed order on the given line. Dop. NAN Ukrayiny. 2014. N 2. P. 50–55.
- Lytvyn O.M. Interpolation of functions and their normal derivatives on smooth lines in Rn. Dop. AN URSR. 1984. N 7. P. 15–19.
- Lytvyn O.N. Interpolation of Cauchy data on several parallel lines in R2 while preserving the class of differentiability. Ukrainian Mathematical Journal. 1985. N 5. P. 509–514.
