Please can people advise me on this

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In summary, the conversation is about a paper discussing equations for least squares minimization based on empirical data. The first equation (eqn 40) uses levenberg marquardt to minimize a, b, and c0, where k is a constant and t_k represents stored times. The second equation (eqn 41) freezes beta and uses the golden section method to refine a and b. The author also provides sub equations for c0. The third equation (eqn 42) uses the same method as the first two, but for nu, phi, and omega^2. The conversation also touches on the use of levenberg marquardt and the author's desire for discussion and understanding rather than just the answer
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a.mlw.walker
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Hi I have attached an image of part of a freely available paper I was reading. It shows the equations for least squares minimization of some equations based on empirical data.

I am not completely confident I understand the required steps, and therefore just wanted to talk it through with others, see what you say and see if it sparks any ideas to solve these.

As I understand it, the first equation (eqn 40) is minimizes using levenberg marquardt for a, b and c0. k is 1,2,3,4... t_k is times stored, the rest of the equation is trying to model the time it will take (whatever that time may be).

Ok so using levenberg marquardt estimate a, b and c0.
But the the next equation (eqn 41) says that he freezes beta to be ab^2, and uses golden section method to 'refine' a and b?

Did the leveneberg marquardt not do a good enough job because I thought we found and ab that way?

the author also give the sub equations for c0. Why? I thought we estimated c0?

Ok so however it has been done, we have a good estimate for a, b and c0.
Eqn 42. Same thing again except now for nu, phi, omega^2.

How is it explaining to solve this?
"robus linear estimation"? "Directly minimizing"? Is that how? Why can't we use levenberg marquardt again?

I just would like discussion, I am not after just the answer, I would like to understand when to use what, and why...

Thanks guys

By the way, that is the whole chapter I haven't left anything out except the chapter title
 

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Is this in the wrong forum?
 

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