will fsolve/lsqnonlin and excel solver give the same solution to non linear least squares estimation?

hi, i hope someone can clear my doubt.

I have a function S(x)= a1 exp(-exp[(x/b1)^g1]) + a2 exp(-cosh[(x/b2)^g2]). There is one constraint where a1<a2. I only have x values and S(x) values. Hence i have 6 unknown parameters to solve via non linear least squares estimation, minimising [S(x)-S(x_hat)]^2. I used Excel Solver to find an answer that converge when it is less than 1E-6. But in Matlab, what is the default where the iteration produces convergence? 1E-6? 1E-8? or something else? I have different values for the estimated parameters in both Excel and Matlab.

Thanks in advance for replying.;)

Answer 1

[Matthias Walle]

You can use optimoptions function to set the step size tolerance and other performance characteristics to fsolve

For instance, your code might change to:

opts = optimoptions('fsolve', 'TolFun', 1E-8, 'TolX', 1E-8);
[B,fval] = fsolve(@(b) myfun(b,x,y), b0, opts);

you can use this to compare your results.

Hope this helped you,

Matthias