PHYSICS AND MATHEMATICS

Simple solution of Hermit interpolation problem

V. V. Shustov

State Research Institute of Aviation Systems

Abstract: The Hermite interpolation problem on the construction of a polynomial taking given values of a function and its derivatives at the nodal points is considered. A new way of solving this problem is proposed. Using the Taylor formula, we simplified the derivation of the Hermite interpolation polynomial formula. An interpretation of this polynomial in the representations of the Taylor polynomial is proposed. An algorithm is given for obtaining finite formulas for the Hermite polynomial in cases when the maximal orders of the derivatives given at the node points are the same.

Keywords: Hermite problem, Taylor polynomial, the formula for the Hermite interpolation polynomial, interpretation of the Hermite polynomial.

DOI: 10.23670/IRJ.2018.70.028