УДК 519.65

П.С. МАЛАЧІВСЬКИЙ
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України, Львів, Україна,
 Petro.Malachivskyy@gmail.com

Л.С. МЕЛЬНИЧОК
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України, Львів, Україна
 levkom@gmail.com

Чебишовське наближення функцій багатьох змінних нелінійною
функцією від раціонального виразу

СПИСОК ЛІТЕРАТУРИ

• 1. Malachivskyi R.P., Bun R.A., Medynskyi I.P. Chebyshev approximation by the exponent from a rational expression. Mathematical Modeling and Computing. 2025. Vol. 12, N 1. P. 233–240. https://doi.org/10.23939/mmc2025.01.233 .


• 2. Malachivskyy P.S., Melnychok L.S. Chebyshev approximation by the logarithm from a rational expression. Cybernetics and Systems Analysis. 2025. Vol. 61, N 1. Р. 77–85. https://doi.org/10.1007/s10559-025-00745-3 .


• 3. Malachivskyy P.S., Melnychok L.S. Chebyshev approximation by the power from a rational expression. Cybernetics and Systems Analysis. 2025. Vol. 61, N. 3. Р. 434–442. https://doi.org/10.1007/s10559-025-00780-0.


• 4. Collatz L., Krabs W. Approximationstheorie. Tschebyscheffsche Approximation mit Anwendungen. Stuttgart: Vieweg+Teubner Verlag, 1973. 212 p.


• 5. Попов Б.А. Равномерное приближение сплайнами. Наук. думка, 1989. 272 с.


• 6. DeVore R.A. Nonlinear approximation and its applications. In: Multscale, nonlinear and adaptive approximation. DeVore R.A., Kunoth A. (Eds.). Berlin; Heidelberg: Springer, 2009. P. 169–201. https://doi.org/10.1007/978-3-642-03413-8 .


• 7. Trefethen L.N. Approximation theory and approximation practice. Philadelphia: SIAM, 2019. xii, 363 p. https://doi.org/10.1137/1.9781611975949 .


• 8. Tanash M., Riihonen T. Global minimax approximations and bounds for the Gaussian -function by sums of exponentials. IEEE Trans. Commun. 2020. Vol. 68, N 10. P. 6514–6524. https://doi.org/10.1109/TCOMM.2020.3006902 .


• 9. Wolfram MathWorld. Beta function. 2024. URL:  https://mathworld.wolfram.com/ .


• 10. Rodriguez A.C., Balicki L., Gugercin S. The p-AAA algorithm for datadriven modeling of parametric dynamical systems. SIAM Journal on Scientific Computing. 2023. Vol. 45, Iss. 3. P. A1332–A1358. https://doi.org/10.1137/20M1322698 .


• 11. Majewski J., Malaczіwskyj P., Yatsuk V., Stolyarczuk P., Michalewa M. Zastosowanie sensorow pojemnosciowych do szybkiej kontroli parametrow roztworow wieloskladnikowych. Przeglad Elektrotechniczny. 2010. N 10. P. 92–95.


• 12. Jamshidzadeh M., Ein-Mozaffari F., Lohi A. Experimental analysis of the mass transfer coefficient and interfacial area in an aerated coaxial mixing system comprising a non-Newtonian solution. Industrial & Engineering Chemistry Research. 2020. Vol. 59, Iss. 49. P. 21530–21547. https://doi.org/10.1021/acs.iecr.0c03641 .


• 13. Bani Shahabadi M., Huang Y. Logarithmic radiative effect of water vapor and spectral kernels. J. Geophys. Res. Atmos. 2014. Vol. 119, Iss. 10.  P. 6000– 6008. https://doi.org/10.1002/2014JD021623 .


• 14. Bubela T., Malachivskyy P., Pokhodylo Y., Mykyychuk M., Vorobets O. Mathematical modeling of soil acidity by the admittance parameters. Eastern-European Journal of Enterprise Technologies. 2016. Vol. 6, N 10(84). P. 4–9. https://doi.org/10.15587/1729-4061.2016.83972 .


• 15. Malachivskyy P.S., Pizyur Ya.V., Danchak N.V., Orazov E.B. Chebyshev approximation by exponential expression with relative error. Cybernetics and Systems Analysis. 2015. Vol. 51, N 2. P. 286–290. https://doi.org/10.1007/s10559-015-9720-2 .


• 16. Malachivskyy P.S., Melnychok L.S., Pizyur Ya.V. Chebyshev approximation of multivariable functions by the exponential expression. Cybernetics and Systems Analysis. 2021. Vol. 57, N 3. Р. 429–435. https://doi.org/10.1007/s10559-021-00367-5 .


• 17. Hughes-Riley T., Lugoda P., Dias T., Trabi C.L., Morris R.H. A study of thermistor performance within a textile structure. Sensors. 2017. Vol. 17, Iss. 8. Article number 1804. https://doi.org/10.3390/s17081804 .


• 18. Javaid A., Mohammed A., Ghaithan A. A regression-based model for prediction of flowmeters calibration cost in oil and gas industry. Flow Measurement and Instrumentation. 2022. Vol. 86. Article number 102191. https://doi.org/10.1016/j.flowmeasinst.2022.102191 .


• 19. Verlan A., Fedorchuk V., Ivaniuk V., Sterten J. Using non-linear integral models in automatic control and measurement systems for sensors’ input signals’ recovery. Proc. 11th World Conference “Intelligent System for Industrial Automation” (WCIS-2020) (27-28 October 2020, Tashkent, Uzbekistan). Tashkent, 2020. AISC. 2021. Vol. 1323. P. 18–25. https://doi.org/10.1007/978-3-030-68004-6_3.


• 20. Bomba A.Ya., Baranovsky S.V., Pasichnyk M.S., Pryshchepa O.V. Modeling small-scale spatial distributed influences on the development of infectious diseases. Mathematical Modeling and Computing. 2020. Vol. 7, N 2. Р. 310–321. https://doi.org/10.23939/mmc2020.02.310 .


• 21. Malachivskyy P.S., Pizyur Ya.V., Malachivsky R.P. Chebyshev approximation by a rational expression for functions of many variables. Cybernetics and Systems Analysis. 2020. Vol. 56, N 5. Р. 811–819. https://doi.org/10.1007/s10559-020-00302-0 .


• 22. Malachivskyy P.S., Melnychok L.S., Pizyur Ya.V. Chebyshev approximation of multivariable functions by a constrained rational expression. Cybernetics and Systems Analysis. 2023. Vol. 59, N 1. Р. 146–155. https://doi.org/10.1007/s10559-023-00552-8 .


• 23. Maple 2025 Now Available! URL: https://www.maplesoft.com/products/Maple/ .


• 24. Sergienko I.V., Zadiraka V.K., Lytvyn O.M. Elements of the general theory of optimal algorithms. SOIA. Springer Cham, 2021. Vol. 188. 377 p. https://doi.org/10.1007/978-3-030-90908-6 .