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I'm studying for an exam, and in some past papers they ask to provide 'a mathematical derivation of the iteration scheme'. Now, I understand successive parabolic interpolation, I can do it (or I certainly hope I can!) but I can't find any mathematical derivation for it.

I understand if people are a little bit prickly on providing help for exams, but if i could simply be pointed in the right direction, like somewhere to study how it is derived, that would be of great help. I don't know where to go right now, and I have certainly looked!

Thanks a lot!

Squimmy
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1 Answers1

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The iteration scheme of Successive Parabolic Interpolation is the repeated use of the quadratic polynomial to find the value of the next function variable, and the interpolation scheme for interpolating the new value within the last two, i.e. if X(k+1) > X(k) and f(X(K+1))> f(X(K)) then (X(K-1), X(K), X(K+1) brackets the minimum. To derive this iteration scheme mathematically, you would need to derive the quadratic polynomial for calculating the next value of X, given the previous 3 values, and also explain why the interpolation scheme works for interpolating the next value of X in the correct place.

See http://itee.uq.edu.au/~engg7302/material/lectureNotes/OP/Engg7302_OPT_lecture3_s2_2013_online.pdf slide 18 for a derivation of the iteration scheme.

Tom Bell
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