The use of interpolation polynomials in the approximation of functions: comparative study

Abstract

In this study, we present three methods for approximating functions using interpolation polynomials. In engineering, there are many situations where it is necessary to approximate the value of a function at a certain point, knowing only a finite set of experimental data or when the function itself is presented in a form that is not easily usable. We use specific methods in numerical analysis such as Lagrange interpolation, the method of dividing differences and Neville’s method. Given a function f defined on an interval [a,b], the purpose of this work is to construct a function that approximates the function f at a predetermined value. The expression of the approximation functions will be calculated and we will evaluate the obtained error for each approximation.