In this paper is given a description of Neville’s algorithm which is generated from Lagrange interpolation polynomials. Given a summary of the properties of these polynomials with some applications. Then, using the Lagrange polynomials of lower degrees, Neville algorithm allows recursive computation of those of the larger degrees, including the adaption of Neville’s method to trigonometric interpolation. Furthermore, using a software application, such as in our case, Matlab, we will show the numerical experiments comparisons between the Lagrange interpolation and Neville`s interpolation methods and conclude for their advantages or disadvantages
