The "best" solver? Ii is the one you have access to, and the one you know how to use.
Fit is easy to use.
mdl = fittype('1/(a + b*x)','indep','x');
ab0 = [ ... ];
fittedmdl = fit(x,y,mdl,'start',ab0)
I've not supplied anything for ab0, since I don't have your data, or even a picture of it. But expect possibly bad results if you supply nothing, even though fit does not technically require starting estimates.
Oh, and fit needs the data to be in the form of COLUMN vectors, so x and y must both be column vectors.
Finally, you could probably obtain good starting values for the model:
1./y = a + b*x
using one line of code as:
ab0 = flip(polyfit(x(:),1./y(:),1));
While this would produce estimates of the parameters, I would point out that it does not properly deal with the error structure in the problem. But to then use those pre-estimates as starting values for fit, would probably be entirely reasonable. The flip in there is important, becausse polyfit will return the parameters in the wrong order for what fit will be expecting.
