User`s guide

Parametric Fitting
3-15
3 Adjust the coefficients and determine whether the fit improves. The
direction and magnitude of the adjustment depend on the fitting algorithm.
The toolbox provides these algorithms:
- Trust-region — This is the default algorithm and must be used if you
specify coefficient constraints. It can solve difficult nonlinear problems
more efficiently than the other algorithms and it represents an
improvement over the popular Levenberg-Marquardt algorithm.
- Levenberg-Marquardt — This algorithm has been used for many years
and has proved to work most of the time for a wide range of nonlinear
models and starting values. If the trust-region algorithm does not produce
a reasonable fit, and you do not have coefficient constraints, you should try
the Levenberg-Marquardt algorithm.
- Gauss-Newton — This algorithm is potentially faster than the other
algorithms, but it assumes that the residuals are close to zero. It’s included
with the toolbox for pedagogical reasons and should be the last choice for
most models and data sets.
For more information about the trust region algorithm, refer to [4] and to
“Trust Region Methods for Nonlinear Minimization” in the Optimization
Toolbox documentation. For more information about the
Levenberg-Marquardt and Gauss-Newton algorithms, refer to “Nonlinear
Least Squares Implementation” in the same guide. Additionally, the
Levenberg-Marquardt algorithm is described in [5] and [6].
4 Iterate the process by returning to step 2 until the fit reaches the specified
convergence criteria.
You can use weights and robust fitting for nonlinear models, and the fitting
process is modified accordingly.
Because of the nature of the approximation process, no algorithm is foolproof
for all nonlinear models, data sets, and starting points. Therefore, if you do not
achieve a reasonable fit using the default starting points, algorithm, and
convergence criteria, you should experiment with different options. Refer to
“Specifying Fit Options” on page 3-23 for a description of how to modify the
default options. Because nonlinear models can be particularly sensitive to the
starting points, this should be the first fit option you modify.