Інтерполяційний раціональний інтегральний дріб n - го порядку на континуальній множині вузлів: Fìz.-mat. model. ìnf. tehnol. 2021, 32:101-105

• Date: 2021
• Main Authors: Demkiv, Ihor, Baranetskyi, Yaroslav, Berehova, Halyna
• Format: Article
• Language: Ukrainian
• Published: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2021
• Subjects: інтерполяція; вузли інтерполяції; раціональний дріб; континуальна множина вузлів; ланцюговий дріб; поліноміальна інтерполяція функціоналів
• Online Access: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/168
• Journal Title: Physico-mathematical modeling and informational technologies

The paper constructs and investigates an integral rational interpolant of the nth order on a continuum set of nodes, which is the ratio of a functional polynomial of the first degree to a functional polynomial of the (n-1)th degree. Subintegral kernels are determined from the corresponding continuum conditions. Additionally, we obtain an integral equation to determine the kernel of the numerator integral. This integral equation, using elementary transformations, is reduced to the standard form of the integral Volterra equation of the second kind. Substituting the obtained solution into expressions for the rest of the kernels, we obtain expressions for all kernels included in the integral rational interpolant. Then, in order for a rational functional of the nth order to be interpolation on continuous nodes, it is sufficient for this functional to satisfy the substitution rule. Note that the resulting interpolant preserves any rational functional of the obtained form. References Demkiv, I. I. (2010). Interpolation funktional polynomial of the fourth order which does not use substitution rule.J. Numer. Appl. Math., 1(100), 40–59. Demkiv, I. I. (2012). An interpolation functional third-degree polynomial that does not use substitution rules. Journal of Mathematical Sciences, 180 (1), 34–50. DOI doi.org/10.1007/s10958-011-0627-9 ] Baranetskij, Y. O., Demkiv, I. I., Kopach, M. I., Obshta, A. F. (2018). The interpolation functional polynomial: the analogue of the Taylor formula, 50(2), 198–203. DOI doi.org/10.15330/ms.50.2.198-203 Makarov, V. L., Demkiv, I. I. (2010). Relation between interpolating integral continued fractions and interpolating branched continued fractions. Journal of Mathematical Sciences, 165(2), 171–180. DOI doi.org/10.1007/s10958-010-9787-2 Makarov, V. L., Demkiv, I. I. (2017). Interpolating integral continued fraction of the Thiele type. J. Math. Sci., 220(1), 50–58. DOI doi.org/10.1007/s10958-016-3167-5 Makarov, V., Demkiv, I. I. (2018). Abstract interpolating fraction of the thiele type. Ukrainskyi matematychnyi visnyk, 231(4), 536–546. DOI doi.org/10.1007/s10958-018-3832-y Makarov, V., Demkiv, I. (2018). Abstract interpolation by continued thiele-type fractions. Cybernetics and Systems Analysis, 54(1), 122–129. DOI doi.org/10.1007/s10559-018-0013-4 Demkiv, I., Ivasyuk, I., Kopach, M. I. (2019). Interpolation integral continued fraction with twofold node. Mathematical Modeling and Computing, 6(1), 1–13. Zabreiko, P. P., Koshelev, A. I., Krasnoselsky, M. A. (1968). Integral equations. Moscow: Nauka.