I've seen that in Newton's method for interpolating polynomials, the coefficients can be found algorithmically using (in Python-ish): a = Y_DataPoints.copy()m = length(X_DataPoints)for k in range(1,m):       a[k: m] = (a[k:m] - a[k-1]) / (X_Data[k:m] - X_Data[k-1]) But I don't really understand the model is subtracting all points past $k_{i}$ by $k_{i-1}$. It seems like you would only subtract $k_{i}$  by $k_{i-1}$, not the entire vector. Can someone shed some light on this? EDIT: Spelling
Newton's method in interpolation
python;numerical analysis;interpolation;newton method