Наближення розривних функцій трьох змінних розривними інтерпояційними сплайнами: Fìz.-mat. model. ìnf. tehnol. 2021, 33:99-104

• Дата: 2021
• Автор: Pershyna, Iuliia
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Теми: розривна функція трьох змінних; 3D інтерполяція; розривні сплайни; розрив першого роду
• Онлайн доступ: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/210
• Назва журналу: Physico-mathematical modeling and informational technologies

In this paper, discontinuous interpolation splines of three variables are constructed and a method for reconstructing of the discontinuous internal structure of a three-dimensional body by constructed splines is proposed. It is believed that a three-dimensional object, which is described by a function of three variables with discontinuities of the first kind on a given grid of nodes, is completely covered by a system of parallelepipeds. The experimental data are the one-sided value of the discontinuous function in a given grid of nodes. In the article, theorems on interpolation properties and the error of the constructed discontinuous structures are formulated and proved. Moreover, the constructed discontinuous interpolation splines include, as a special case, classical continuous splines. The developed approximation method can be applied in three-dimensional mathematical modeling of discontinuous processes, including in computed tomography. References Lytvyn, O., Pershina, Yu. (2005). Reconstruction of 3 – D objects with use interflation of functions. Signal and image processing: Proceeding of the Second IASTED International Multi – Conference on Automation, Control, and Information Technology (June 20 – 24 2005). Novosibirsk. Lytvyn, O. M., Pershina, I. I. (2011). Approximation of discontinuous functions of two variables by discontinuous spline interlination by trapezoidal elements. Taurian Bulletin of Informatics and Mathematics. Simferopol, 2, 59 - 70. DOI https://doi.org/10.24874/jsscm.2020.14.01.07 Lytvyn, O. N., Pershina, I. I., Sergienko, I. V. (2014). Restoration of discontinuousg functions of two variables when discontinuity lines are unknown (rectangular elements). Cybernetics and systems analysis, 4, 126–134. DOI https://doi.org/10.1007/s10559-014-9647-z Sergienko, I. V., Zadiraka, V. K., Lytvyn, O. M., Pershina, I. I. (2017). Theory of discontinuous splines and its application in computed tomography: Monograph K . Nauk. opinion. Lytvyn, O. M. (2002). Interlination of functions and some of its applications. N.: Osnova.