Interpolation rational integral fraction of the Hermitian-type on a continual set of nodes

Ya. O.  Baranetskij; I. I. Demkiv; M. I. Kopach; A. V. Solomko

doi:10.30970/ms.56.2.185-192

Ya. O. Baranetskij Lviv Polytechnic National University, Lviv, Ukraine
I. I. Demkiv Lviv Polytechnic National University, Lviv, Ukraine
M. I. Kopach Vasyl Stefanyk Precarpathian National University, Ukraine
A. V. Solomko Vasyl Stefanyk Precarpathian National University, Ukraine

DOI: https://doi.org/10.30970/ms.56.2.185-192

Keywords: interpolation, double node, continual set of nodes, chain fraction, Hermitian formula

Abstract

Some approaches to the construction of interpolation rational integral approximations with arbitrary multiplicity of nodes are analyzed. An integral rational Hermitian-type interpolant of the third order on a continual set of nodes, which is the ratio of a functional polynomial of the first degree to a functional polynomial of the second degree, is constructed and investigated. The resulting interpolant is one that holds any rational functional of the resulting form.

Author Biography

A. V. Solomko, Vasyl Stefanyk Precarpathian National University, Ukraine

Department of Mathematics and Computer Science, Associate Professor

References

I.I. Demkiv, Interpolation functional polynomial of the fourth order which does not use substitution rule, J. Numer. Appl. Math., 100 (2010), No1, 40–59.

I.I. Demkiv, An interpolation functional third-degree polynomial that does not use substitution rules, Journal of Mathematical Sciences, 180 (2012), No1, 34–50.

Y.O. Baranetskij, I.I. Demkiv, M.I. Kopach, A.F. Obshta, The interpolation functional polynomial: the analogue of the Taylor formula, Mat. Stud., 50 (2018), No2, 198–203.

V.L. Makarov, I.I. Demkiv, Relation between interpolating integral continued fractions and interpolating branched continued fractions, Journal of Mathematical Sciences, 165 (2010), No2, 171–180.

V.L. Makarov, I.I. Demkiv, Interpolating integral continued fraction of the Thiele type, J. Math. Sci., 220 (2017), No1, 50–58.

V.L. Makarov, I.I. Demkiv, Abstract interpolation by continued Thiele-type fractions, Cybernetics and Systems Analysis, 54 (2018), No1, 122–129.

I. Demkiv, I. Ivasyuk, M. Kopach, Interpolation integral continued fraction with twofold node, Mathematical Modeling and Computing, 6 (2019), No1, 1–13.

W. Jones, V. Tron, Continued fractions. Analytical theory and applications, Moscow, 1985, 414 p. (in Russian)

I.P. Gavrylyuk, V.L. Makarov, Numerical methods, V.1, Kyiv, 1995, 368p. (in Ukrainian)

P.P. Zabreiko, A.I. Koshelev, M.A. Krasnoselsky, Integral equations, Nauka, Moscow, 1968, 448p. (in Russian)