12.5.5. - Convergence and statistical parameters
Finally, you are asked if you wish to change the statistical criteria. These variables are concerned with certain details of the fitting algorithm and don't normally need to be altered.
The first variable you can change is the starting value of the Marquardt algorithm compromise parameter, λ. This parameter controls how much of the gradient search versus how much of parabolic expansion is used to determine the direction of the search. The larger λ is, the more the algorithm uses the gradient search.
The next variable is the minimum value allowed for λ. It won't be permitted to go lower than the value selected here.
When the program calculates the derivative of the fitting function numerically with respect to a fitted parameter bi, it uses values of the function at bi and at (1 + δ)bi. You can enter here a value to use for δ. The default value is 0.00001.
The next two values, ε and τ, are important in deciding at what point the fit has converged. They are used in a convergence test that is satisfied if for each parameter bi and parameter increment δbi,
|δbi|/(τ + |bi|) < ε .The parameter increments are the changes in the value of each parameter from the prior iteration. τ mostly functions to prevent division by zero. The default value for both is 0.001.
The parameter γ measures the angle between the direction of steepest descent of the χ2 hypersurface and the direction of the current iteration. When γ falls below the critical value set here, the course of the fitting algorithm changes as described below under
fi. The value of the matrix singularity variable lets you adjust how small the determinant of the parameter correlation matrix can be before giving up on the fit.
The last two variables, ff and tt, are concerned only with the quantities on the final printout obtained with the
fp command.