I'm new to this community and my first question probably reflect my lack of confidence with Mathematica.
My problem is the following: I find the roots of a transcendental equation dependent on a parameter, let's say $x = \cos(\alpha x)$, And compare these roots with a set of assigned values via an error function (e.g. sum of the absolute value of the difference between each root and the corresponding fixed value). I want to minimize the outcome of the error function varying the parameter $\alpha$, in order to get a value for $\alpha$ such that the transcendental roots lie the closest possible to the assigned values.
I'm basically trying to fit data (the assigned values) with the roots of an equation depending on a parameter. I think that it should work in this way:
- Find roots of transcendental equation
- Error function outputs an error given by confronting the calculated roots with data
- Some minimization, varying the parameter until you get to a value for it that minimize the error function.
The minimization function should than be able to repeat the process from point number 1 at every change of the parameter, but I couldn't find any simple function doing that. I'm not sure if you can do that with the fitting function I've already seen, like FindFit
, and I'm not sure I'm looking at the problem the right way.
Is there an easy way to do that with Mathematica's function?