Оптимальне інтегрування швидкоосцилюючих функцій загального виду: Fìz.-mat. model. ìnf. tehnol. 2021, 33:68-72

• Дата: 2021
• Автори: Nechuiviter, Olesia, Ivanov, Serhii, Kovalchuk, Kyrylo
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Теми: кубатурна формула; інтеграл від швидкоосцилюючої функції; клас диференційовних функцій
• Онлайн доступ: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/204
• Назва журналу: Physico-mathematical modeling and informational technologies

The development of information technology contributes to the improvement of mathematical models of phenomena and processes in many scientific areas of the technical direction. In particular, modern methods of digital signal and image processing use algorithms with new information operators. Cubature formulas are constructed for the approximate calculation of integrals of highly oscillating functions of many variables for various types of data. The paper deals with the estimation of the error in the numerical integration of highly oscillating functions of a general form on the class of differentiable functions of three variables in the case when information about the functions is given to their traces on the corresponding planes. The results obtained make it possible to research the quality of cubature formulas for the approximate calculation of triple integrals of highly oscillating functions of a general form. References Sergienko, I. V., Zadiraka, V. K., Lytvyn, O. M., Nechuiviter, O. P. (2017). Optimal algorithms for calculating integrals from fast-oscillating functions with the use of new information operators. – Kyiv: Naukova dumka. (in Ukrainian). Lytvyn, O. M., Nechuiviter, O. P. (2014). Approximate Calculation of Triple Integrals of Rapidly Oscillating Functions with the Use of Lagrange Polynomial Interflatation, Cybernetics and Systems Analysis, 50(3), 410–418. DOI https://doi.org/10.1007/s10559-014-9629-1 Lytvyn, O. M, Nechuiviter, O., Pershyna, Y., Mezhuyev, V. (2019). Input Information in the Approximate Calculation of Two-Dimensional Integral from Highly Oscillating Functions (Irregular Case), Recent Developments in Data Science and Intelligent Analysis of Information, Proceedings of the XVIII International Conference on Data Science and Intelligent Analysis of Information. Kyiv, Ukraine. DOI https://doi.org/10.1007/978-3-319-97885-7_36 Mezhuyev, V., Lytvyn, O. M., Nechuiviter, O., Pershyna, Y, Keita, K., Lytvyn, O. O. (2018). Cubature formula for approximate calculation of integrals of two-dimensional irregular highly oscillating functions, U.P.B. Sci. Bull., Series A, 80(3), 169–182. DOI https://doi.org/10.1007/978-3-319-97885-7_36 Nechuiviter, O. P. (2020). Сubature formula for approximate calculation integral of highly oscillating function of tree variables (irregular case), Radio Electronics, Computer Science, Control, 4, 65–73. DOI https://doi.org/10.15588/1607-3274-2020-4-7