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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.roots.root_finding_examples"></a><a class="link" href="root_finding_examples.html" title="Examples of Root-Finding (with and without derivatives)">Examples of
Root-Finding (with and without derivatives)</a>
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<div class="toc"><dl>
<dt><span class="section"><a href="root_finding_examples/cbrt_eg.html">Finding
the Cubed Root With and Without Derivatives</a></span></dt>
<dt><span class="section"><a href="root_finding_examples/lambda.html">Using
C++11 Lambda's</a></span></dt>
<dt><span class="section"><a href="root_finding_examples/5th_root_eg.html">Computing
the Fifth Root</a></span></dt>
<dt><span class="section"><a href="root_finding_examples/multiprecision_root.html">Root-finding
using Boost.Multiprecision</a></span></dt>
<dt><span class="section"><a href="root_finding_examples/nth_root.html">Generalizing
to Compute the nth root</a></span></dt>
<dt><span class="section"><a href="root_finding_examples/elliptic_eg.html">A
More complex example - Inverting the Elliptic Integrals</a></span></dt>
</dl></div>
<p>
The examples demonstrate how to use the various tools for <a href="http://en.wikipedia.org/wiki/Root-finding_algorithm" target="_top">root
finding</a>.
</p>
<p>
We start with the simple cube root function <code class="computeroutput"><span class="identifier">cbrt</span></code>
( C++ standard function name <a href="http://en.cppreference.com/w/cpp/numeric/math/cbrt" target="_top">cbrt</a>)
showing root finding <a class="link" href="root_finding_examples/cbrt_eg.html#math_toolkit.roots.root_finding_examples.cbrt_eg.cbrt_no_derivatives">without
derivatives</a>.
</p>
<p>
We then show how use of derivatives can improve the speed of convergence.
</p>
<p>
(But these examples are only a demonstration and do not try to make the ultimate
improvements of an 'industrial-strength' implementation, for example, of
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cbrt</span></code>, mainly by using a better computed
initial 'guess' at <a href="../../../../../../libs/math/include/boost/math/special_functions/cbrt.hpp" target="_top">cbrt.hpp</a>).
</p>
<p>
Then we show how a higher root (<a class="link" href="root_finding_examples/5th_root_eg.html" title="Computing the Fifth Root">fifth
root</a>) <sup>5</sup>√ can be computed, and in <a href="../../../../example/root_finding_n_example.cpp" target="_top">root_finding_n_example.cpp</a>
a generic method for the <a class="link" href="root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root">nth
root</a> that constructs the derivatives at compile-time.
</p>
<p>
These methods should be applicable to other functions that can be differentiated
easily.
</p>
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Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta,
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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