| Autor: |
BARANETSKIJ, YA. O., DEMKIV, I. I., KOPACH, M. I., SOLOMKO, A. V. |
| Předmět: |
|
| Zdroj: |
Matematychni Studii; 2021, Vol. 56 Issue 2, p185-192, 8p |
| Abstrakt: |
The paper is devoted to approximation of functionals on a continual set of nodes. A frame of this set is arbitrary and we fix elements from the space of piecewise continuous functions on a segment [0; 1] with a finite number of jump discontinuity points. At first, a number of approaches to the construction of interpolation rational approximations with arbitrary multiplicity of interpolation nodes are analyzed. Such rational Hermitian interpolants are obtained by means of a limit transition from a suitable interpolation fraction. An integral rational Hermitian interpolant of the third order on a continual set of nodes is constructed and investigated. This interpolant is the ratio of a functional polynomial of the first degree to a functional polynomial of the second degree. An integral equation is obtained from interpolation conditions. This equation is reduced by elementary transformations to the standard form of integral Volterra equation of the second kind. The lemma on the existence of a unique continuous solution of this equation is proved. We also prove the theorem that the constructed rational fraction is interpolation. To obtain a functional interpolation rational interpolant with two double interpolation nodes, it is not possible to use the above technique through limit transition. Therefore, we use continual interpolation conditions of the Hermite type. The resulting interpolant is one that retains any rational functional of the resulting form. Therefore, this interpolant is the ratio of a functional polynomial of the first degree to a functional polynomial of the second degree. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
