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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.

ariadnus
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1 Answers1

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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).

user
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  • Thanks. Any idea on how $f(x_{min})$ is calculated using parabolic interpolation? – ariadnus Oct 31 '19 at 04:41
  • Given the three points around the minimum(maximum) we approximate the function by $q(x)$ and then we find the miimum(maximum) by the condition on the derivative $q'(x)=0$. – user Oct 31 '19 at 06:23