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<title>Examples of Root-Finding (with and without derivatives)</title>
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.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
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(with and without derivatives)</a>
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</h2></div></div></div>
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<div class="toc"><dl class="toc">
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<dt><span class="section"><a href="root_finding_examples/cbrt_eg.html">Finding the
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Cubed Root With and Without Derivatives</a></span></dt>
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<dt><span class="section"><a href="root_finding_examples/lambda.html">Using C++11
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Lambda's</a></span></dt>
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<dt><span class="section"><a href="root_finding_examples/5th_root_eg.html">Computing
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the Fifth Root</a></span></dt>
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<dt><span class="section"><a href="root_finding_examples/multiprecision_root.html">Root-finding
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using Boost.Multiprecision</a></span></dt>
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<dt><span class="section"><a href="root_finding_examples/nth_root.html">Generalizing
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to Compute the nth root</a></span></dt>
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<dt><span class="section"><a href="root_finding_examples/elliptic_eg.html">A More
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complex example - Inverting the Elliptic Integrals</a></span></dt>
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</dl></div>
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<p>
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The examples demonstrate how to use the various tools for <a href="http://en.wikipedia.org/wiki/Root-finding_algorithm" target="_top">root
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finding</a>.
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</p>
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<p>
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We start with the simple cube root function <code class="computeroutput"><span class="identifier">cbrt</span></code>
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( C++ standard function name <a href="http://en.cppreference.com/w/cpp/numeric/math/cbrt" target="_top">cbrt</a>)
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showing root finding <a class="link" href="root_finding_examples/cbrt_eg.html#math_toolkit.root_finding_examples.cbrt_eg.cbrt_no_derivatives">without
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derivatives</a>.
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</p>
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<p>
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We then show how use of derivatives can improve the speed of convergence.
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</p>
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<p>
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(But these examples are only a demonstration and do not try to make the ultimate
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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
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by using a better computed initial 'guess' at <a href="../../../../../libs/math/include/boost/math/special_functions/cbrt.hpp" target="_top">cbrt.hpp</a>).
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</p>
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<p>
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Then we show how a higher root (<a class="link" href="root_finding_examples/5th_root_eg.html" title="Computing the Fifth Root">fifth
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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>
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a generic method for the <a class="link" href="root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root">nth
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root</a> that constructs the derivatives at compile-time.
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</p>
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<p>
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These methods should be applicable to other functions that can be differentiated
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easily.
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</p>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
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Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
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Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
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Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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Daryle Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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</p>
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