Methods of interpolations illustrated on the interpolation of the German income tax tariff

Increasing complexity of economic models evolve optimization problems that are not differentiable any more. To solve that problems heuristic optimization or approximation methods have to be used. In this article three methods of polynomial interpolations are summarized and explained. The three methods are in detail the Lagrange interpolation method, the Newton interpolation method and the interpolation using the monomial basis. The advantages and disadvantages of approximation methods such as the polynomial interpolation are illustrated by approximating the German income tariff function