Divided Differences

Neville's method calculated iteratively the interpolating polynomial or its value at a given point. Divided Difference Methods are used to determine the explicit representation of an interpolating polynomial. They also have some relevance for the approximation of derivatives or integrals of functions. We will restrict our discussion to forward differences .

Definition of Divided Differences

Newton's forward divided difference formula

Theorem 12

Proof

Equidistant data points