Hi this is my first question here ;)
i'm struggling with some fitting of an exponential with offset.
To Fit an exponential with an offset: $y(x)= ae^{-\frac{x}{b}}+c$ where $a$, $b$ and $c$ are the parameters.
i wrote a LM-algorithm(LMA). Which works fine as long as the initial parameters are ok.
So now my problem is to get a good initial guess. There is a nice method by Yves Daoust (Here) if you can use 3 equally spaced points. My problem is that i don't have equally spaced point all the time. So i thought if i just take 3 points out of my Data i should be able to calculate the exponential curve through these Points(3 parameters = 3 points). This should give a initial guess close enough to run the LMA. You have to know the noise in my Data is quiet small. But cannot resolve the equation system. I don't know if i just miss something or if it isn't possible. I was taught that if you have an equation with n parameters, $n$ points are enough to solve the equation system.
It would be nice if someone can help me to solve the equation system or have a better idea to find a good initial guess for the parameters.
Without initial guess nor iteration, the method published p.17 in https://fr.scribd.com/doc/14674814/Regressions-et-equations-integrales :
The criteria of fitting isn't the usual least squares. If a specific criteria of fitting is required, one can use the above method and results as initial guess for a standard method of non-linear regression involving iterative process.