I have just written a newtinterp() method that implements newtons polynomial and horners formula.
How would i go about computing the interpolating polynomial p ∈ Pn, which interpolates the points (xi, f(xi)), i = 1, 2, . . . , n + 1 of a uniform partition of [−1, 1] for n = 5, 10, 20, 100. Let zi, i = 1, 2, . . . , 201, equi-distributed points of [−1, 1].