Umbral interpolation

Abstract

A general linear interpolation problem is posed and solved. This problem is called 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.

General Bivariate Appell Polynomials via Matrix Calculus and Related Interpolation Hints

“…Appell polynomials have many applications in various disciplines: probability theory [1][2][3][4][5], number theory [6], linear recurrence [7], general linear interpolation [8][9][10][11][12], operators approximation theory [13][14][15][16][17]. In [18], P. Appell introduced a class of polynomials by the following equivalent conditions: {A n } n∈IN is an Appell sequence (A n being a polynomial of degree n) if either…”