1Lytvyn, OM, 1Lytvyn, OO, 2Tkachenko, OV, 2Gritsay, OL 1Ukrainian Engineering Pedagogics Academy, Kharkiv 2Academician A.G. Ivchenko Zaporozhye Machine-Building Design Bureau Progress State Enterprise |
Dopov. Nac. akad. nauk Ukr. 2014, 7:53-59 |
https://doi.org/10.15407/dopovidi2014.07.053 |
Section: Information Science and Cybernetics |
Language: Ukrainian |
Abstract: Methods for constructing the operators of a Hermitian interlineation of the recovery of differentiable functions of two variables on the system of smooth disjoint curves that preserve the class of differentiability $C^{r}$ ($\mathbb{R}^{2})$ are studied. To construct these operators, the traces of the interpolated function and its partial derivatives with respect to one variable to a given order on the mentioned system of curves are used.
|
Keywords: functions, Hermitian interlineation, preservation of the class |
1. Sergienko I. V., Deineka V. S. System analysis of elastic and thermoelastic heterogeneous bodies. Kyiv: Nauk. dumka, 2012 (in Russian).
2. Sergienko I. V., Zadiraka V. K., Lytvyn O. M. Elements of the General theory of optimal algorithms and related matters. Kyiv: Nauk. dumka, 2012 (in Ukrainian).
3. Nikolskiy S. M. Approximation of functions of several variables and imbedding theorems. Moscow: Nauka, 1969 (in Russian).
4. Besov O. V., Ilin V. P., Nikolskiy S. M. Integral representations of functions and imbedding theorems. Moscow: Nauka, 1975 (in Russian).
5. Stein I. Singular integrals and differential properties of functions. Moscow: Mir, 1973 (in Russian).
6. Vladimirov V. S. C. Generalized functions in mathematical physics. Moscow: Nauka, 1979 (in Russian).
7. Hermander L. Differential operators with constant coefficients. Moscow: Mir, 1986 (in Russian).
8. Tikhonov A. N., Samarskiy A. A. Equations of mathematical physics. Moscow: Nauka, 1966 (in Russian).
9. Shylov G. E. Mathematical analysis. The second special course. Moscow: Nauka, 1965 (in Russian).
10. Kvasov B. I. The methods of iso-geometric approximation by splines. Moscow: Fizmatlit, 2006 (in Russian).
11. Vinogradova I. M. (Ed.). Mathematical encyclopedia. In 5th vols. Vol. 5.Moscow: Sov. entsyklopediia, 1984 (in Russian).
12. Lytvyn O. M. Dop. AN UkrRSR. Ser. A., 1984, No. 7: 15–19 (in Ukrainian).
13. Lytvyn O. M. Dop. AN UkrRSR. Ser. A., 1991, No. 3: 12–17 (in Ukrainian).
14. Lytvyn O. M. Dop. AN UkrRSR. Ser. A., 1987, No. 5: 13–17 (in Ukrainian).
15. Lytvyn O. M. Interlineation of the functions and some of its applications. Kharkiv: Osnova, 2002 (in Ukrainian).