Using rational functions to improve the results of approximating a function

Abstract

In this article, we use rational functions in order to improve the results obtained in the approximation of a function in an interval [a, b]. For this we will approximate the function chosen as an example in this study using a ratio of two polynomials. To determine the two polynomials, we use the Taylor series expansion about the point x = 0 of the function chosen and the Padé approximation. Also, to highlight the accuracy of the obtained approximation, we analyze the absolute error between the initial function and the Pade approximation respectively and the Taylor series in the considered interval. The analyzed data, in the chosen interval, highlights much better results obtained by the Padé approximation compared to the Taylor series.