The interpolation functional polynomial: the analogue of the Taylor formula 

Author 
kopachm2009@gmail.com^{3}
1) Lviv Polytechnic National University, Lviv, Ukraine; 2) Lviv Polytechnic National University, Lviv, Ukraine; 3) Vasyl Stefanyk Precarpathian National University
IvanoFrankivsk, Ukraine; 4) Lviv Polytechnic National University, Lviv, Ukraine

Abstract 
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 Newton’s interpolation formulas, using
the multiplicity of nodes by means of a passage to the limit, an interpolation functional Taylor
type polynomial, which has the abovementioned properties, is constructed.

Keywords 
Taylor formula; Newton’s interpolation formula; interpolation node; functional polynomial

DOI 
doi:10.15330/ms.50.2.198203

Reference 
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Pages 
198203

Volume 
50

Issue 
2

Year 
2018

Journal 
Matematychni Studii

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