Increase free parameters accuracy for fits with 20 parameters

Newbie
1

I am trying to use a fitting function that consists of a sum of 20 cosine functions of the form [0]*exp(-x/[1])*( 1.0+[2]*cos([3]*x-[j])). The order of magnitude for the parameters are 10^5 for p0, 10^1 for p1, 10^-1 for p2, 10^0 for p3, and 10^-3 for p[i]. The fit converges, but it strongly depends on the initial values for p[i] parameters.
If my initial guess is 0 for all of the parameters p[i] the result is:

FCN=4750.84 FROM MIGRAD    STATUS=CONVERGED    2101 CALLS        2102 TOTAL
                     EDM=5.58924e-08    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   0.9 per cent

But if my initial guess is closer to the real values, the result is

FCN=4712.66 FROM MIGRAD    STATUS=CONVERGED    1835 CALLS        1836 TOTAL
                     EDM=9.18336e-07    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   0.1 per cent

Is there a way to make MIGRAD get closer to the real values of p[i] without stopping the minimizer algorithm?

2

Try to modify your function so that all parameters are of the order of 1, e.g.:
([0]/1.e5)*exp(-x/([1]/1.e1))*(1.+([2]/1.e-1)*cos(([3])*x-([j]/1.e-3)))

3

It does converge, but the values are wrong again:

 FCN=7.20178e+15 FROM MIGRAD    STATUS=CONVERGED    1272 CALLS        1273 TOTAL
                     EDM=2.83846e-11    STRATEGY= 1  ERROR MATRIX UNCERTAINTY   0.4 per cent