# Parameters to consider in non linear curve fitting

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Zine on 1 Mar 2014
Edited: Star Strider on 3 Mar 2014
I have a complex (sum and multiplication of several elementary functions) function to fit with experimental data, but I could not reach the desired fit, the program does his work but the parameters are far from what they should be, I noticed that if I change the lb or ub it changes the results also if I change Beta0 it also affects the results. I need help and advise on the factors that I should consider to have the best fit
note: the experimental data are about 6000 points, I have around 15 parameters to find

Star Strider on 1 Mar 2014
Without knowing more, I suggest you choose Beta0 to be close to what you expect the parameters to be as you can. I also suggest not restricting the parameters with lb and ub unless you know that, for instance, they must be positive or if you already know they should not exceed a specific value.
Fitting so many parameters will give any solver problems. Consider reducing them if you can.
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Star Strider on 3 Mar 2014
Edited: Star Strider on 3 Mar 2014
The only way I can think of to force real numbers is for the last lines of your objective function to return them as reals. For instance:
function (p,x) = fun(p,x)
(code)
p = abs(p);
end
That’s not recommended, but it is probably an experiment you can do to force the returned parameters to be real. If it fails to converge to what you consider a ‘correct’ solution, you can always remove the ’abs’ line and live with complex parameter estimates.

Image Analyst on 1 Mar 2014
Yeah, I don't know either from this description, so I'll just put in a plug for John's masterpiece: http://www.mathworks.com/matlabcentral/fileexchange/24443-slm-shape-language-modeling
Description
If you could only download one curve fitting tool to your laptop on a desert island, this should be it.
For many years.......
Star Strider on 1 Mar 2014
I’ll search on his name from the link you provided. Thanks again.

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