The interpolation functional polynomial: the analogue of the Taylor formula

Ya. O. Baranetskij1, I. I. Demkiv2, M. I. Kopach3, A. F. Obshta4
1) Lviv Polytechnic National University, Lviv, Ukraine; 2) Lviv Polytechnic National University, Lviv, Ukraine; 3) Vasyl Stefanyk Precarpathian National University Ivano-Frankivsk, Ukraine; 4) Lviv Polytechnic National University, Lviv, Ukraine
The paper deals with a functional Newton type polynomial, which has two properties: the first one is that interpolation nodes are continual, that is, they depend on continuous parameters, and the second one is the invariance of the interpolation formulas with respect to polynomials of the corresponding degree. The first property is provided by the substitution rule, the fulfillment of which for a given functional is a sufficient condition for the possibility of the interpolation in the space of piecewise continuous functions on [0; 1] with a finite number of points of discontinuity of the first kind. On the basis of Newtons interpolation formulas, using the multiplicity of nodes by means of a passage to the limit, an interpolation functional Taylor type polynomial, which has the above-mentioned properties, is constructed.
Taylor formula; Newtons interpolation formula; interpolation node; functional polynomial
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Matematychni Studii
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