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<title>Chapter 10. Root Finding & Minimization Algorithms</title>
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<div class="chapter">
<div class="titlepage"><div><div><h1 class="title">
<a name="root_finding"></a>Chapter 10. Root Finding & Minimization Algorithms</h1></div></div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dt><span class="section"><a href="math_toolkit/roots_noderiv.html">Root Finding Without Derivatives</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/roots_noderiv/bisect.html">Bisection</a></span></dt>
<dt><span class="section"><a href="math_toolkit/roots_noderiv/bracket_solve.html">Bracket and
Solve Root</a></span></dt>
<dt><span class="section"><a href="math_toolkit/roots_noderiv/TOMS748.html">Algorithm TOMS 748:
Alefeld, Potra and Shi: Enclosing zeros of continuous functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/roots_noderiv/brent.html">Brent-Decker Algorithm</a></span></dt>
<dt><span class="section"><a href="math_toolkit/roots_noderiv/root_termination.html">Termination
Condition Functors</a></span></dt>
<dt><span class="section"><a href="math_toolkit/roots_noderiv/implementation.html">Implementation</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/roots_deriv.html">Root Finding With Derivatives:
Newton-Raphson, Halley & Schröder</a></span></dt>
<dt><span class="section"><a href="math_toolkit/root_finding_examples.html">Examples of Root-Finding
(with and without derivatives)</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/root_finding_examples/cbrt_eg.html">Finding the
Cubed Root With and Without Derivatives</a></span></dt>
<dt><span class="section"><a href="math_toolkit/root_finding_examples/lambda.html">Using C++11
Lambda's</a></span></dt>
<dt><span class="section"><a href="math_toolkit/root_finding_examples/5th_root_eg.html">Computing
the Fifth Root</a></span></dt>
<dt><span class="section"><a href="math_toolkit/root_finding_examples/multiprecision_root.html">Root-finding
using Boost.Multiprecision</a></span></dt>
<dt><span class="section"><a href="math_toolkit/root_finding_examples/nth_root.html">Generalizing
to Compute the nth root</a></span></dt>
<dt><span class="section"><a href="math_toolkit/root_finding_examples/elliptic_eg.html">A More
complex example - Inverting the Elliptic Integrals</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/bad_guess.html">The Effect of a Poor Initial Guess</a></span></dt>
<dt><span class="section"><a href="math_toolkit/bad_roots.html">Examples Where Root Finding Goes
Wrong</a></span></dt>
<dt><span class="section"><a href="math_toolkit/brent_minima.html">Locating Function Minima using
Brent's algorithm</a></span></dt>
<dt><span class="section"><a href="math_toolkit/root_comparison.html">Comparison of Root Finding
Algorithms</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/root_comparison/cbrt_comparison.html">Comparison
of Cube Root Finding Algorithms</a></span></dt>
<dt><span class="section"><a href="math_toolkit/root_comparison/root_n_comparison.html">Comparison
of Nth-root Finding Algorithms</a></span></dt>
<dt><span class="section"><a href="math_toolkit/root_comparison/elliptic_comparison.html">Comparison
of Elliptic Integral Root Finding Algorithms</a></span></dt>
</dl></dd>
</dl>
</div>
<p>
Several tools are provided to aid finding minima and roots of functions.
</p>
<p>
Some <a class="link" href="math_toolkit/roots_noderiv.html" title="Root Finding Without Derivatives">root-finding without derivatives</a>
methods are <a class="link" href="math_toolkit/roots_noderiv/bisect.html" title="Bisection">bisection</a>,
<a class="link" href="math_toolkit/roots_noderiv/bracket_solve.html" title="Bracket and Solve Root">bracket and solve</a>,
including use of <a class="link" href="math_toolkit/roots_noderiv/TOMS748.html" title="Algorithm TOMS 748: Alefeld, Potra and Shi: Enclosing zeros of continuous functions">TOMS 748
algorithm</a>.
</p>
<p>
For <a class="link" href="math_toolkit/roots_deriv.html" title="Root Finding With Derivatives: Newton-Raphson, Halley & Schröder">root-finding with derivatives</a>
the methods of <a class="link" href="math_toolkit/roots_deriv.html#math_toolkit.roots_deriv.newton">Newton-Raphson
iteration</a>, <a class="link" href="math_toolkit/roots_deriv.html#math_toolkit.roots_deriv.halley">Halley</a>,
and <a class="link" href="math_toolkit/roots_deriv.html#math_toolkit.roots_deriv.schroder">Schröder</a> are implemented.
</p>
<p>
For locating minima of a function, a <a class="link" href="math_toolkit/brent_minima.html#math_toolkit.brent_minima.example">Brent
minima finding example</a> is provided.
</p>
<p>
There are several fully-worked <a class="link" href="math_toolkit/root_finding_examples.html" title="Examples of Root-Finding (with and without derivatives)">root-finding
examples</a>, including:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<a class="link" href="math_toolkit/root_finding_examples/cbrt_eg.html#math_toolkit.root_finding_examples.cbrt_eg.cbrt_no_derivatives">root-finding
without derivatives</a>
</li>
<li class="listitem">
<a class="link" href="math_toolkit/root_finding_examples/cbrt_eg.html#math_toolkit.root_finding_examples.cbrt_eg.cbrt_1st_derivative">root-finding
with 1st derivatives</a>
</li>
<li class="listitem">
<a class="link" href="math_toolkit/root_finding_examples/cbrt_eg.html#math_toolkit.root_finding_examples.cbrt_eg.cbrt_2_derivatives">root-finding
with 1st and 2nd derivatives</a>
</li>
</ul></div>
</div>
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Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
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RÃ¥de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
Daryle Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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