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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <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
  28       Root-Finding (with and without derivatives)</a>
  29 </h3></div></div></div>
  30 <div class="toc"><dl>
  31 <dt><span class="section"><a href="root_finding_examples/cbrt_eg.html">Finding
  32         the Cubed Root With and Without Derivatives</a></span></dt>
  33 <dt><span class="section"><a href="root_finding_examples/lambda.html">Using
  34         C++11 Lambda's</a></span></dt>
  35 <dt><span class="section"><a href="root_finding_examples/5th_root_eg.html">Computing
  36         the Fifth Root</a></span></dt>
  37 <dt><span class="section"><a href="root_finding_examples/multiprecision_root.html">Root-finding
  38         using Boost.Multiprecision</a></span></dt>
  39 <dt><span class="section"><a href="root_finding_examples/nth_root.html">Generalizing
  40         to Compute the nth root</a></span></dt>
  41 <dt><span class="section"><a href="root_finding_examples/elliptic_eg.html">A
  42         More complex example - Inverting the Elliptic Integrals</a></span></dt>
  43 </dl></div>
  44 <p>
  45         The examples demonstrate how to use the various tools for <a href="http://en.wikipedia.org/wiki/Root-finding_algorithm" target="_top">root
  46         finding</a>.
  47       </p>
  48 <p>
  49         We start with the simple cube root function <code class="computeroutput"><span class="identifier">cbrt</span></code>
  50         ( C++ standard function name <a href="http://en.cppreference.com/w/cpp/numeric/math/cbrt" target="_top">cbrt</a>)
  51         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
  52         derivatives</a>.
  53       </p>
  54 <p>
  55         We then show how use of derivatives can improve the speed of convergence.
  56       </p>
  57 <p>
  58         (But these examples are only a demonstration and do not try to make the ultimate
  59         improvements of an 'industrial-strength' implementation, for example, of
  60         <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
  61         initial 'guess' at <a href="../../../../../../libs/math/include/boost/math/special_functions/cbrt.hpp" target="_top">cbrt.hpp</a>).
  62       </p>
  63 <p>
  64         Then we show how a higher root (<a class="link" href="root_finding_examples/5th_root_eg.html" title="Computing the Fifth Root">fifth
  65         root</a>) <sup>5</sup>&#8730; can be computed, and in <a href="../../../../example/root_finding_n_example.cpp" target="_top">root_finding_n_example.cpp</a>
  66         a generic method for the <a class="link" href="root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root">nth
  67         root</a> that constructs the derivatives at compile-time.
  68       </p>
  69 <p>
  70         These methods should be applicable to other functions that can be differentiated
  71         easily.
  72       </p>
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  76 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
  77       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
  78       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
  79       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
  80         Distributed under the Boost Software License, Version 1.0. (See accompanying
  81         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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