## 39 Nonlinear Least-Squares Fitting

This chapter describes functions for multidimensional nonlinear least-squares fitting. There are generally two classes of algorithms for solving nonlinear least squares problems, which fall under line search methods and trust region methods. GSL currently implements only trust region methods and provides the user with full access to intermediate steps of the iteration. The user also has the ability to tune a number of parameters which affect low-level aspects of the algorithm which can help to accelerate convergence for the specific problem at hand. GSL provides two separate interfaces for nonlinear least squares fitting. The first is designed for small to moderate sized problems, and the second is designed for very large problems, which may or may not have significant sparse structure.

The header file `gsl_multifit_nlinear.h` contains prototypes for the multidimensional nonlinear fitting functions and related declarations relating to the small to moderate sized systems.

The header file `gsl_multilarge_nlinear.h` contains prototypes for the multidimensional nonlinear fitting functions and related declarations relating to large systems.