Newton's interpolation Note

Note also that Newton interpolation can be done incrementally; i.e., the interpolant can be created as

points are being added.

It may be important to be able to do this depending on the application.
So we t a straight line to two points, then add a point and t a quadratic to three points, then add a point

and t a cubic to four points, etc.

With the other two methods, if more data points are added, the computation of the interpolants has to be
started from scratch.