ANALYSIS OF GAUSSIAN INTERPOLATION FUNCTION ALGORITHM ON ELEMENTARY ALGEBRAIC FUNCTIONS

Abstract

The paper deals with an analysis of Gaussian interpolation function algorithm on elementary algebraic functions, the results have been compared with the Lagrange polynomial and the algorithm is improved by changing the variational coefficient α, that lead to decreasing interpolation error.

         Set of mathematical tools with different functional content are used with working mathematical model. Interpolation is one of the types of work with experimental data. Set of tools of mathematical models has many different interpolation methods, but Lagrange polynomial is used most often on practice as classic method of polynomial interpolation.

         The results of some interpolation algorithms are presented in the article. Results of interpolation of elementary algebraic functions by classical Lagrange method and three types of Gaussian interpolation functions with a small number of interpolation nodes and a steady step have been considered and analyzed. These methods have been tested with variable interpolation step. In addition, the results of interpolation with different variable parameter α are presented. It has been concluded that it is appropriate to change this parameter for different functions.

         For the arbitrary function analysis, also consider the interpolation of experimental data using the Gauss interpolation function on the example of COVID-19 distribution in Ukraine. It has been concluded about the use of different values of the variable parameter for the interpolation of experimental data with minimal error.

         Based on using Gauss interpolation function, computer system for analyzing a working principle of the Gauss function by the example of elementary mathematical functions with constant and variable steps and with ability to control the value of the variable parameter, which reduced the interpolation error has been created.

         Keywords: interpolation, Gaussian interpolation function, interpolation error, variable coefficient.