Approximation theory

a.mlw.walker

Ok so for this one what method would you suggest. I know he does a trisection search (i have never used trisection, D H said it wasnt good, so I attempted using golden section search).
However I thjink I am running into what he is talking about. He said he solves for phi between 0 and 2pi using trisection then solved equation 43 using other methods ( i think by hand?). My values for nu and omega^2 always come out the same using this method, so I think this is why he did it his way, However if i want to get all parameters at once what method would you recommend. Can i use the downhill simplex for this, and just set it up as the modulus and the sum rather than squaring it?
D H mentioned an ant search which i have been reading about, however I dont think I understand what the algorithm is doing. A nice robust method like that though did sound appealing.

His data he uses for equation 42 is in the attached graph. its pretty dirty...
x axis is T0 (initial time) y axis is theta_f (fall angle)

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