MATLAB CURVE FITTING TOOLBOX - RELEASE NOTES Guide de l'utilisateur télécharger pdf (Page 91)

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.

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MATLAB CURVE FITTING TOOLBOX - RELEASE NOTES Guide de l'utilisateur Page 91