Nejlepší polynomiální aproximace

Abstract

For some mathematical problems we are not able to find solutions exactly, but only approximately by using methods of numerical mathematics. The key concept is then replacement or in other words approximation. One of the most used methods is, for example, polynomial interpolation, however at some points of the interval the error of this method might be significant. The approximation which minimizes the maximum error at every point of the interval is called the best approximation. Generally, there is a unique solution to the problem of finding the best polynomial approximation, but it is not possible to calculate it exactly. The approximate solution can be obtained, for example, by using the Remez algorithm. The interpolation at Chebyshev nodes also yields surprisingly good results, generally being near-best approximations. The goal of our thesis is namely to study and implement the Remez algorithm and test its functionality. Finally, we compare the Remez algorithm with Lagrange interpolation at Chebyshev nodes.