Barycentric Interpolation

Abstract This survey focusses on the method of barycentric interpolation, which ties up to the ideas that August Ferdinand Möbius published in his seminal work “Der barycentrische Calcul ” in 1827. For univariate data, it leads to a special kind of rational interpolation which is guaranteed to have no poles and favourable ap-proximation properties. We further discuss how to extend this idea to bivariate data, both for scattered data and for data given at the vertices of a polygon.