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I have some data samples and and my job is to find a curve that will fit these values.

The curve that i have gone for is in the form

y = k * sqrt(d1^x*d2^y)*d3^z

where kxyz are all unknowns that I need to find. I solve this with the MATLAB function fminsearch and the solution is just fine.

I did also try linearize the problem by log

log(y) = log(k) + xlog(d1)/2 + ylog(d2)/2 +zlog(n)

And this i solved with the function lsqnonlin

I should mention that i use the least square solution sum(Ymeasured-Yanalytical)

Anyways this brings me to my question. These two don't give the same solution!

According to wikipedia

"

In LLSQ the solution is unique, but in NLLSQ there may be multiple minima in the sum of squares.

"

Which means that either I'm doing something wrong or the solution after linearizing isn't necessarily the optimal solution.

So

Is the solution of a linear function the optimal solution or not?

The solution of a non-linear is not unique while it is for a linear function.

Shouldn't the linear function give the same or a better solution than the non linear?

Thanks