Umbral Interpolation

Francesco Aldo Costabile, Elisabetta Longo

A general linear interpolation problem is posed and solved. This problem is called \emph{umbral interpolation problem} because its solution can be expressed by a basis of Sheffer polynomials. The truncation error and its bounds are considered. Some examples are discussed, in particular generalizations of Abel--Gontscharoff and central interpolation are studied. Numerical examples are given too.