Some Comments on the Non-Linear Model Fitting

Some tools are briefly presented which are useful at non-linear inverse problems. It is found that some parameters can be eliminated under some conditions from the minimization. If all parameters are eliminated except one, then the transformed merit-function is one-dimensional and can easily be minimized (and can easily be used for reliability testing, too). On the other hand, since each real-life merit function has a closest, noise-free merit-function in the Least Squares sense, this so called follower can be used in the minimization, and for reliability testing. The methods are illustrated by the evaluation of a laboratory and an in situ test. Both models are linear PDE-s resulting in `nice', convex shaped follower merit functions.