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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
- (with and without derivatives)</a>
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- <div class="toc"><dl class="toc">
- <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.root_finding_examples.cbrt_eg.cbrt_no_derivatives">without
- derivatives</a>.
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- <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.
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- Råde, 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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