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  27 <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
  28     (with and without derivatives)</a>
  29 </h2></div></div></div>
  30 <div class="toc"><dl class="toc">
  31 <dt><span class="section"><a href="root_finding_examples/cbrt_eg.html">Finding the
  32       Cubed Root With and Without Derivatives</a></span></dt>
  33 <dt><span class="section"><a href="root_finding_examples/lambda.html">Using C++11
  34       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 More
  42       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.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 <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
  60       by using a better computed initial 'guess' at <a href="../../../../../libs/math/include/boost/math/special_functions/cbrt.hpp" target="_top">cbrt.hpp</a>).
  61     </p>
  62 <p>
  63       Then we show how a higher root (<a class="link" href="root_finding_examples/5th_root_eg.html" title="Computing the Fifth Root">fifth
  64       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>
  65       a generic method for the <a class="link" href="root_finding_examples/nth_root.html" title="Generalizing to Compute the nth root">nth
  66       root</a> that constructs the derivatives at compile-time.
  67     </p>
  68 <p>
  69       These methods should be applicable to other functions that can be differentiated
  70       easily.
  71     </p>
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  75 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
  76       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
  77       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
  78       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
  79       Daryle Walker and Xiaogang Zhang<p>
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