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<title>GNU Scientific Library – Reference Manual: Nonlinear Least-Squares Fitting</title>
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Next: <a href="Basis-Splines.html#Basis-Splines" accesskey="n" rel="next">Basis Splines</a>, Previous: <a href="Least_002dSquares-Fitting.html#Least_002dSquares-Fitting" accesskey="p" rel="previous">Least-Squares Fitting</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Nonlinear-Least_002dSquares-Fitting-1"></a>
<h2 class="chapter">39 Nonlinear Least-Squares Fitting</h2>
<a name="index-nonlinear-least-squares"></a>
<a name="index-least-squares_002c-nonlinear"></a>
<p>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.
</p>
<p>The header file <samp>gsl_multifit_nlinear.h</samp> contains prototypes for the
multidimensional nonlinear fitting functions and related declarations
relating to the small to moderate sized systems.
</p>
<p>The header file <samp>gsl_multilarge_nlinear.h</samp> contains prototypes for the
multidimensional nonlinear fitting functions and related declarations
relating to large systems.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Overview.html#Nonlinear-Least_002dSquares-Overview" accesskey="1">Nonlinear Least-Squares Overview</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-TRS-Overview.html#Nonlinear-Least_002dSquares-TRS-Overview" accesskey="2">Nonlinear Least-Squares TRS Overview</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Weighted-Overview.html#Nonlinear-Least_002dSquares-Weighted-Overview" accesskey="3">Nonlinear Least-Squares Weighted Overview</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Tunable-Parameters.html#Nonlinear-Least_002dSquares-Tunable-Parameters" accesskey="4">Nonlinear Least-Squares Tunable Parameters</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Initialization.html#Nonlinear-Least_002dSquares-Initialization" accesskey="5">Nonlinear Least-Squares Initialization</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Function-Definition.html#Nonlinear-Least_002dSquares-Function-Definition" accesskey="6">Nonlinear Least-Squares Function Definition</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Iteration.html#Nonlinear-Least_002dSquares-Iteration" accesskey="7">Nonlinear Least-Squares Iteration</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Testing-for-Convergence.html#Nonlinear-Least_002dSquares-Testing-for-Convergence" accesskey="8">Nonlinear Least-Squares Testing for Convergence</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-High-Level-Driver.html#Nonlinear-Least_002dSquares-High-Level-Driver" accesskey="9">Nonlinear Least-Squares High Level Driver</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Covariance-Matrix.html#Nonlinear-Least_002dSquares-Covariance-Matrix">Nonlinear Least-Squares Covariance Matrix</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Troubleshooting.html#Nonlinear-Least_002dSquares-Troubleshooting">Nonlinear Least-Squares Troubleshooting</a>:</td><td> </td><td align="left" valign="top">
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<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-Examples.html#Nonlinear-Least_002dSquares-Examples">Nonlinear Least-Squares Examples</a>:</td><td> </td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">• <a href="Nonlinear-Least_002dSquares-References-and-Further-Reading.html#Nonlinear-Least_002dSquares-References-and-Further-Reading">Nonlinear Least-Squares References and Further Reading</a>:</td><td> </td><td align="left" valign="top">
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Next: <a href="Basis-Splines.html#Basis-Splines" accesskey="n" rel="next">Basis Splines</a>, Previous: <a href="Least_002dSquares-Fitting.html#Least_002dSquares-Fitting" accesskey="p" rel="previous">Least-Squares Fitting</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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