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

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.