An efficient raster evaluation method for univariate polynomials (Q1094080)

An evaluation algorithm for univariate polynomials is presented which yields the function values for a sequence of equidistant points. The method is based on a formula which relates the forward differences with step size \(\lambda\) h (\(\lambda\) a positive integer) to forward differences with step size h. The new method needs about half as many essential operations as Horner's applied to each point separately. It is also compared with a third method from literature which is faster yet less accurate.