Variable Transformation in Nonlinear Least Squares model Fitting

摘要

The numerical treatment of nonlinear model fitting problems often can be simplified by manipulating the model equations. Algebraic manipulations, including nonlinear transformations of model parameters, do not change the numerical result of the adjustment. Therefore, such manipulations can be a powerful method to improve the performance of solution algorithms. Nonlinear transformations of the observations, on the other hand, do change the numerical results unless the normal equations are transformed accordingly. The latter transformation has been neglected by previous authors and this article provides a complete set of formulas that are needed to implement transformations of observations. The transformations are, however, in general less useful than parameter transformations but may have applications in particular situations. (Author)