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<title>GNU Scientific Library &ndash; Reference Manual: One dimensional Root-Finding</title>

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<a name="One-dimensional-Root_002dFinding"></a>
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Next: <a href="One-dimensional-Minimization.html#One-dimensional-Minimization" accesskey="n" rel="next">One dimensional Minimization</a>, Previous: <a href="Discrete-Hankel-Transforms.html#Discrete-Hankel-Transforms" accesskey="p" rel="previous">Discrete Hankel Transforms</a>, Up: <a href="index.html#Top" accesskey="u" rel="up">Top</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="One-dimensional-Root_002dFinding-1"></a>
<h2 class="chapter">34 One dimensional Root-Finding</h2>
<a name="index-root-finding"></a>
<a name="index-zero-finding"></a>
<a name="index-finding-roots"></a>
<a name="index-finding-zeros"></a>
<a name="index-roots"></a>
<a name="index-solving-a-nonlinear-equation"></a>
<a name="index-nonlinear-equation_002c-solutions-of"></a>

<p>This chapter describes routines for finding roots of arbitrary
one-dimensional functions.  The library provides low level components
for a variety of iterative solvers and convergence tests.  These can be
combined by the user to achieve the desired solution, with full access
to the intermediate steps of the iteration.  Each class of methods uses
the same framework, so that you can switch between solvers at runtime
without needing to recompile your program.  Each instance of a solver
keeps track of its own state, allowing the solvers to be used in
multi-threaded programs.
</p>
<p>The header file <samp>gsl_roots.h</samp> contains prototypes for the root
finding functions and related declarations.
</p>
<table class="menu" border="0" cellspacing="0">
<tr><td align="left" valign="top">&bull; <a href="Root-Finding-Overview.html#Root-Finding-Overview" accesskey="1">Root Finding Overview</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Root-Finding-Caveats.html#Root-Finding-Caveats" accesskey="2">Root Finding Caveats</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Initializing-the-Solver.html#Initializing-the-Solver" accesskey="3">Initializing the Solver</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Providing-the-function-to-solve.html#Providing-the-function-to-solve" accesskey="4">Providing the function to solve</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Search-Bounds-and-Guesses.html#Search-Bounds-and-Guesses" accesskey="5">Search Bounds and Guesses</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Root-Finding-Iteration.html#Root-Finding-Iteration" accesskey="6">Root Finding Iteration</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Search-Stopping-Parameters.html#Search-Stopping-Parameters" accesskey="7">Search Stopping Parameters</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Root-Bracketing-Algorithms.html#Root-Bracketing-Algorithms" accesskey="8">Root Bracketing Algorithms</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Root-Finding-Algorithms-using-Derivatives.html#Root-Finding-Algorithms-using-Derivatives" accesskey="9">Root Finding Algorithms using Derivatives</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Root-Finding-Examples.html#Root-Finding-Examples">Root Finding Examples</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
</td></tr>
<tr><td align="left" valign="top">&bull; <a href="Root-Finding-References-and-Further-Reading.html#Root-Finding-References-and-Further-Reading">Root Finding References and Further Reading</a>:</td><td>&nbsp;&nbsp;</td><td align="left" valign="top">
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