On Polynomial Interpolation in the Points of a Geometric Progression, Stirling, Schellbach, Runge and Romberg

摘要

It is very well known Newton's interpolation series with divided differences simplifies considerably in the case that we interpolate in the points of an arithmetic progression. It seems much less known that a similar simplification occurs in the case when the points of interpolation form a geometric progression. We describe here the practically forgotten work of Stirling (1730), Schellbach) (1864), and Runge (1981), and its connection with the elegant and more recent algorithm of Romberg (1955). (Author)