Чебишовське наближення функцій двох змінних раціональним виразом з інтерполюванням: Fìz.-mat. model. ìnf. tehnol. 2021, 33:33-39

• Date: 2021
• Main Author: Melnychok, Lev
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: чебишовське наближення; раціональний вираз; функції двох змінних; середньостепеневе наближення; метод найменших квадратів
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/198
• Journal Title: Physico-mathematical modeling and informational technologies

A method for constructing a Chebyshev approximation by a rational expression with interpolation for functions of two variables is proposed The idea of the method is based on the construction of the ultimate mean-power approximation in the norm of space Lp at p¬∞ . An iterative scheme based on the least squares method with two variable weight functions was used to construct such a Chebyshev approximation. The results of test examples confirm the effectiveness of the proposed method for constructing the Chebyshev approximation by a rational expression with interpolation. References Collatz, L., Krabs, W. (1973). Approximationstheorie: Tschebyscheffsche Approximation mit Anwendungen (Teubner Studienbücher Mathematik). Stuttgart: Teubner Verlag. Popov, B. A., Tesler, G. S. (1980). Approximation of Functions for Engineering Applications [in Russian], Naukova Dumka, Kyiv. Verlan, A. F., Adbusadarov, B. B., Ignatenko, A. A., Maksimovich, N. N. (1993). Methods and devices for interpreting experimental dependencies in the study and control of energy processes [in Russian], Naukova Dumka, Kyiv. Gerashchenko, O. A., Gordov, A. I., Eremina, A. K. (1989). Temperature measurements [in Russian], Naukova Dumka, Kyiv. Lenovenko, A., Malachivckyj, P., Vasyluk, V. (2002). Linearization of Sensor Characteristic Dependent on Two Variables. Materialy "VII Konferencja Naukowa Czujniki optoelektroniczne i elektroniczne" (COE 2002) Rzeszów, 5-8 zerwca 2002. Tom II. Melnychok, L. S., Popov, B. A. (1977). Best approximation of table functions with a condition, in: Algorithms and programs for calculating functions on a digital computer [in Russian], Institute of Cybernetics, 4, 95-102. Malachivskyy, P. S., Melnychok, L. S., Pizyur, Y. V. (2020). "Chebyshev Approximation of the Functions of Many Variables with the Condition," 2020 IEEE 15th International Conference on Computer Sciences and Information Technologies (CSIT), Zbarazh, Ukraine. doi: 10.1109/CSIT49958.2020.9322026. Kalenchuk-Porkhanova, A. A., Vakal, L. P. (2007). Construction of the best uniform approximations of functions of many variables. Computer tools, networks and systems, 6, 141–148. [in Ukrainian]. Malachivskyy, P. S., Pizyur, Y. V., Malachivskyi, R. P., Ukhanska, O. M. (2020). Chebyshev approximation of functions of several variables. Cybernetics and Systems Analysis, 56(1), 118-125. DOI https://doi.org/10.1007/s10559-020-00227-8 Filip, S.-I., Nakatsukasa, Y., Trefethen, L. N., Beckermann, B. (2017). Rational minimax approximation via adaptive barycentric representations. DOI https://doi.org/10.1137/17m1132409 Nakatsukasa, Y., Sete, `O., Trefethen, L. N. (2018). The AAA algorithm for rational approximation. SIAM J. SCI. COMPUT. 2018, 40(3), A1494–A1522. DOI https://doi.org/10.1137/16m1106122 Malachivskyy, P. S., Montsibovych, B. R., Pizyur, Y. V., Malachivskyi, R. P. (2019). “Chebyshev approximation of functions of two variables by a rational expression,” [in Ukrainian] Matematychne ta Komp. Modelyuvannya, Ser. Tekhnichni Nauky, 19, 75–81. DOI:10.32626/2308-5916.2019-19.75-81. DOI https://doi.org/10.32626/2308-5916.2019-19.75-81 Malachivskyy, P. S., Pizyur, Y. V., Malachivskyi, R. P. (2020). Chebyshev approximation by the rational expression of functions of many variables. Cybernetics and Systems Analysis, 56(5), 118-125. DOI https://doi.org/10.1007/s10559-020-00227-8 Malachivskyy, P. S., Pizyur, Y. V. (2016). Solving Problems in the Maple Environment [in Ukrainian], RASTR-7. Malachivskyy, P. S., Skopetsky, V. V. (2013). Continuous and Smooth Minimax Spline Approximation [in Ukrainian], Naukova Dumka, Kyiv.