Divided Difference Interpolating Polynomials

Suppose that is the -th interpolating polynomial that agrees with the function at the distinct numbers . has the form:

for appropriate constants . The constants can be found by setting to the known data points .

Divided-difference notation

Divided differences are defined with respect to a set of distinct numbers.

Zeroth divided difference

First divided difference

Second divided difference

k-th divided difference

Note

Now can be rewritten in a form called Newton’s Divided Difference: