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
Львів, Україна,  levkom@gmail.com

ЧЕБИШОВСЬКЕ НАБЛИЖЕННЯ ЛОГАРИФМОМ
ВІД РАЦІОНАЛЬНОГО ВИРАЗУ

СПИСОК ЛІТЕРАТУРИ

• 1. Malachivskyy P.S., Melnychok L.S., Pizyur Y.V. Chebyshev approximation of multivariable functions by a logarithmic expression. Cybernetics and Systems Analysis. 2023. Vol. 59, N 2. Р. 317–324. https://doi.org/10.1007/s10559-023-00565-3. .


• 2. Gutierrez R., Valls J. Low cost hardware implementation of logarithm approximation. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 2011. Vol. 19, Iss. 12. P. 2326–2330. https://doi.org/10.1109/TVLSI.2010.2081387. .


• 3. Hajjar A.F., Awedh M.H. Efficient logarithmic function approximation. International Journal of Scientific Engineering and Technology. 2015. Vol. 4, Iss. 7. P. 387–391.


• 4. Yudell L. Luke mathematical functions and their approximations, 1st ed. Academic Press, 1975. 568 p.


• 5. Попов Б.А., Теслер Г.С. Приближение функций для технических приложений. Киев: Наук. думка, 1980. 352 с.


• 6. Skopetskii V.V., Malachivskii P.S. Chebyshev approximation of functions by the sum of a polynomial and an expression with a nonlinear parameter and endpoint interpolation. Cybernetics and Systems Analysis. 2009. Vol. 45, N 1. P. 58–68. https://doi.org/10.1007/s10559-009-9078-4. .


• 7. 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. .


• 8. 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. Advances in Intelligent Systems and Computing. 2021. Vol. 1323. P. 18–25. https://doi.org/10.1007/ .


• 9. Majewski J. Low humidity characteristics of polymer-based capacitive humidity sensors. Metrology and Measurement Systems. 2017. Vol. 24, N 4. P. 607–616. https://doi.org/10.1515/mms-2017-0048. .


• 10. Khudayarov B.A., Turaev F., Vishesh R.K., Verlan A.A. A study on dynamic characteristics of the flutter for three-layer plates and shells flown around by a gas flow. International Journal of Computational Materials Science and Engineering. 2023. https://doi.org/10.1142/ S2047684123500392. .


• 11. Bomba A., Baranovsky S., Blavatska O., Bachyshyna L. Infectious disease model generalization based on diffuse perturbations under conditions of body’s temperature reaction. Computers in Biology and Medicine. 2022. Vol. 146. Article number 105561. https://doi.org/10.1016/j.compbiomed.2022.105561. .


• 12. Baranovsky S.V., Bomba A.Ya. Generalizing the infectious disease model taking into account diffusion perturbations, logistic dynamics, and biostimulation. Cybernetics and Systems Analysis. 2023. Vol. 59, N 1. Р. 134–145. https://doi.org/10.1007/s10559-023-00549-3. .


• 13. Ремез Е.Я. Основы численных методов чебышевского приближения. Киев: Наук. думка, 1969. 623 с.


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


• 15. DeVore R.A. Nonlinear approximation and its applications. In: Multscale, Nonlinear and Adaptive Approximation. DeVore R.A., Kunoth A. (Eds.). Berlin; Heidelberg: Springer–Verlag, 2009. P. 169–201. https://doi.org/10.1007/978-3-642-03413-8_6. .


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


• 17. 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. .


• 18. Malachivskyy P.S., Melnychok L.S., Pizyur Ya.V. Chebyshev approximation of multivariable functions by a power expression. Cybernetics and Systems Analysis. 2024. Vol. 60, N 4. Р. 571–578. https://doi.org/10.1007/s10559-024-00697-0. .


• 19. Попов Б.А. Равномерное приближение сплайнами. Киев: Наук. думка, 1989. 272 с.


• 20. Malachivskyy P.S., Pizyur Ya.V., Malachivskyi 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. .


• 21. 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. .


• 22. S. Hyperpower least squares progressive iterative approximation. J. Comput. Appl. Math. 2023. Vol. 422. Article number 114888. https://doi.org/10.1016/j.cam.2022.114888. .


• 23. Hofreither C. An algorithm for best rational approximation based on barycentric rational interpolation. Numer Algor. 2021. Vol. 88, N 1. Р. 365–388. https://doi.org/10.1007/ s11075-020-01042-0. .


• 24. Austin A.P., Krishnamoorthy M., Leyffer S., Mrenna S., Mller J., Schulz H. Practical algorithms for multivariate rational approximation. Comput. Phys. Commun. 2021. Vol. 261. Article number 107663. https://doi.org/10.1016/j.cpc.2020.107663. .


• 25. Gonnet P., Pachon R., Trefethen L.N. Robust rational interpolation and least-squares. Electron. Trans. 2011. N 38. P. 146–167. URL: https://people.maths.ox.ac.uk/ .


• 26. Maple — The Essential Tool for Mathematics. URL: https://www.maplesoft.com/products/Maple/. .


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