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Re: Re: Re: Optimized structure of an equation

Lai Ngoc Anh wrote:
> Dear Kuska, Dear all,
> 
> yes, it is minimization of the function. 
> 
> For example, I have experimental data set {x,Zexp}={{x1,Zexp1},{x2,Zexp2},...{xn,Zexpn}}, with n is total experimental data points.
> 
> I need to find parameters of the function
> Zcal(x)=a*x^(i/6)+b*x^(j/6)+c*x^(k/6)+d*x^(m/6)+g*x^(n/6)
> by minimize the sum of ((Zexp-Zcal)/Zexp)^2. 
> 
> The problem for me is how to choose the best set of i, j, k, m, n for given data Z(x) and then parameters a, b, c, d, g.
> 
> May be the parameters can be found by using evolution strategies. I really don't know how to do and not sure whether these strategies or other strategies would be helpful.
>   
> Thank you very much in advance!
> 
> N.A
> [...]

What you are asking for is a hard computation. And it seems the maximum 
exponent, 100, is chosen arbitrarily. Also it is not obvious why you 
allow at most 5 terms. What I wonder is this: Might there might be a 
better type of function to fit to your data? As stated, you have 
something of a mixed-integer programming problem, and this brings in 
computational complexity well beyond that of the usual curve-fitting 
problem.

To get some idea of what is involved, you  might have a look at the 
computational sections of the paper at
http://arxiv.org/abs/0808.0284
Your problem is similar but probably harder insofar as you do not have 
an exact fit, and do not have (or at least have not stated) "nice" 
restrictions on the coefficients.


Daniel Lichtblau
Wolfram Research
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