gsl-ref.info: Nonlinear Least-Squares Fitting

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41 Nonlinear Least-Squares Fitting
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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.

Overview

Overview<6>.

Solving the Trust Region Subproblem (TRS)

Solving the Trust Region Subproblem TRS.

Weighted Nonlinear Least-Squares

Tunable Parameters

Initializing the Solver

Initializing the Solver<3>.

Providing the Function to be Minimized

Iteration

Iteration<5>.

Testing for Convergence

High Level Driver

Covariance matrix of best fit parameters

Troubleshooting

Troubleshooting<2>.

Examples

Examples<32>.

References and Further Reading

References and Further Reading<34>.