Parabolic Interpolation

Question

I'm reading this lecture page: http://fourier.eng.hmc.edu/e176/lectures/NM/node25.html and towards the end of the discussion, it says that upon finding $x_{min}$, the process can be repeated using a new set of points by eliminating one of the old ones. Is this essentially what successive parabolic interpolation is? Or is there a subtlety involved? Also, how do I generate $f(x_{min})$? Thanks.

Answer 1

Yes it is a kind dichotomy method by successive parabolic interpolation.

At each step we find a new set of three points which gives a better approximation for the minimum (or maximum).