Fitting an implicit nonlinear function

I am trying to fit a function whose xData depends on a parameter of the fit.

More in detail: my x axis is given by x=x0+a/(1+C*x^2) where x0 is an array, C2 is a constant and a is the parameter of my fitting function. My y axis, instead, is fixed. Is there a way to do that? What I need to derive from that is the value of a.

Thak you all for the help

Answer 1

[John D'Errico]

If everything is known except for a, then what is the problem? I'll rewrite it to make it more clear.

x - X0 = a*(1./(1+C*x.^2)

So here from your comments, I assume we have multiple points in the form of values for x and X0, as well as a known value for C.

Solve the general problem

v = a*u

where u and v are vectors or matrices of the same size as simply

a = u(:)\v(:);

Apply the same approach to your problem.

[Gian]

The problem is that I don't have x. I need to solve the equation (which depends on a) to find it.