Interpolation

Abstract

The problem of estimating the value of a function at a required point, given its values at some points, is called interpolation. One early application of this was prompted by research in astronomy in sixth-century China, where Liú Zhuó used interpolation at three equally spaced points. In the seventeenth century Isaac Newton completely solved the interpolation problem for a function of one variable. The “limiting form” of the interpolating polynomial as the interpolating points “collapse” to the same point gives the first terms of the Taylor series. In this chapter we also consider the interpolation problem for functions of several variables and discuss a method of evaluating the interpolating polynomial by the repeated use of linear (two-point) interpolation.

If I have seen further it is by standing on the shoulders of giants.