Newton's Divided Differences and its associated Polynomial

Computes Newton's table for Divided Differences and the coefficients of the associated polynomial function for a given dataset (X,Y).

This function solves the following formula:

Pn(x) = f(x0) + f[x0,x1](x-x0) + f[x0,x1,x2](x-x0)(x-x1) + ... + f[x0,x1,..,xn](x-x0)(x-x1)..(x-x[n-1]),

where:

f[x0,x1] = (f(x1-f(x0))/(x1-x0),

f[x0,x1,..,xn] = (f[x1,..,xn]-f[x0,..,x_[n-1]])/(xn-x0), .... ,

i.e. the divided differences.

This function was inspired by the function by the Divided Differences function of T.R.

Here, I simply added the capability of directly outputting the coefficients of the associated polynomial. So that the polynomial can be evaluated to produce interpolations/extrapolations directly with Matlab's 'polyval' function.

Happy coding ; )