A class of methods for tabular interpolation

Abstract

AbstractA generalization of the Neville–Aitken method is described which allows the construction of interpolating functions, other than polynomials, by means of simple recurrence relations. In particular, simple constructions are given for rational functions and trigonometric series which interpolate prescribed function values at non-equispaced positions of the independent variable.Restrictions imposed by requiring the interpolating functions to be invariant under linear transformations of the coordinates are discussed, and application of the technique to the problem of inverse interpolation is also considered.