Polynomial approximation

The basic idea underlying most interpolation schemes is to draw a polynomial through the data points. Polynomials are easy to evaluate and sufficient smooth functions to allow a theoretical analysis of the error. Moreover, if there is indeed a function underlying the data points, then the Weierstrass Approximation Theorem tells us there exist a good polynomial fit:

Theorem 8 (Weierstrass Approximation Theorem)

Taylor polynomials