Nonlinear Least Squares Minimization

[swartzism]

How should I go about solving this problem? This is only to get a better understanding of how NLLS works.

F(x;a) = (1+a1*x)/(a2+a3*x) (so n = 3)

I am choosing a1,a2,a3 to be 2,3,5 respectively. I am also picking 6 data points (so m = 6):

(0, 0), (-1/4, 1/4), (-1/2, 1/10), (1/4, 1/4), (1, 1), (1/2, 1/2).

I'm not even sure where to begin to attack this problem.

Any suggestions?

 

[AlephZero]

The Levenberg-Marquardt algorithm is a widely used method.

Alternatively, you can treat NLLSQ as a general nonlinear optimization problem, and use standard optimization methods like the BFGS algorithm if the problem is fairly well behaved, or the simplex search method (which can be very slow, but will find a local minimum of pretty much anything!) if it isn't.

IIRC all these are in "Numerical Recipes", or Google for other explanations of the algorithms and computer code.