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   4 <title>Chapter&#160;12.&#160;Tools: Root Finding &amp; Minimization Algorithms, Polynomial Arithmetic &amp; Evaluation</title>
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  26 <div class="titlepage"><div><div><h1 class="title">
  27 <a name="rooting"></a>Chapter&#160;12.&#160;Tools: Root Finding &amp; Minimization Algorithms, Polynomial Arithmetic
  28   &amp; Evaluation</h1></div></div></div>
  29 <div class="toc">
  30 <p><b>Table of Contents</b></p>
  31 <dl>
  32 <dt><span class="section"><a href="math_toolkit/roots.html">Root finding</a></span></dt>
  33 <dd><dl>
  34 <dt><span class="section"><a href="math_toolkit/roots/roots_noderiv.html">Root Finding Without
  35       Derivatives</a></span></dt>
  36 <dd><dl>
  37 <dt><span class="section"><a href="math_toolkit/roots/roots_noderiv/bisect.html">Bisection</a></span></dt>
  38 <dt><span class="section"><a href="math_toolkit/roots/roots_noderiv/bracket_solve.html">Bracket
  39         and Solve Root</a></span></dt>
  40 <dt><span class="section"><a href="math_toolkit/roots/roots_noderiv/TOMS748.html">Algorithm
  41         TOMS 748: Alefeld, Potra and Shi: Enclosing zeros of continuous functions</a></span></dt>
  42 <dt><span class="section"><a href="math_toolkit/roots/roots_noderiv/brent.html">Brent-Decker
  43         Algorithm</a></span></dt>
  44 <dt><span class="section"><a href="math_toolkit/roots/roots_noderiv/root_termination.html">Termination
  45         Condition Functors</a></span></dt>
  46 <dt><span class="section"><a href="math_toolkit/roots/roots_noderiv/implementation.html">Implementation</a></span></dt>
  47 </dl></dd>
  48 <dt><span class="section"><a href="math_toolkit/roots/roots_deriv.html">Root Finding With Derivatives:
  49       Newton-Raphson, Halley &amp; Schr&#246;der</a></span></dt>
  50 <dt><span class="section"><a href="math_toolkit/roots/root_finding_examples.html">Examples of
  51       Root-Finding (with and without derivatives)</a></span></dt>
  52 <dd><dl>
  53 <dt><span class="section"><a href="math_toolkit/roots/root_finding_examples/cbrt_eg.html">Finding
  54         the Cubed Root With and Without Derivatives</a></span></dt>
  55 <dt><span class="section"><a href="math_toolkit/roots/root_finding_examples/lambda.html">Using
  56         C++11 Lambda's</a></span></dt>
  57 <dt><span class="section"><a href="math_toolkit/roots/root_finding_examples/5th_root_eg.html">Computing
  58         the Fifth Root</a></span></dt>
  59 <dt><span class="section"><a href="math_toolkit/roots/root_finding_examples/multiprecision_root.html">Root-finding
  60         using Boost.Multiprecision</a></span></dt>
  61 <dt><span class="section"><a href="math_toolkit/roots/root_finding_examples/nth_root.html">Generalizing
  62         to Compute the nth root</a></span></dt>
  63 <dt><span class="section"><a href="math_toolkit/roots/root_finding_examples/elliptic_eg.html">A
  64         More complex example - Inverting the Elliptic Integrals</a></span></dt>
  65 </dl></dd>
  66 <dt><span class="section"><a href="math_toolkit/roots/bad_guess.html">The Effect of a Poor Initial
  67       Guess</a></span></dt>
  68 <dt><span class="section"><a href="math_toolkit/roots/bad_roots.html">Examples Where Root Finding
  69       Goes Wrong</a></span></dt>
  70 <dt><span class="section"><a href="math_toolkit/roots/brent_minima.html">Locating Function Minima
  71       using Brent's algorithm</a></span></dt>
  72 <dt><span class="section"><a href="math_toolkit/roots/root_comparison.html">Comparison of Root
  73       Finding Algorithms</a></span></dt>
  74 <dd><dl>
  75 <dt><span class="section"><a href="math_toolkit/roots/root_comparison/cbrt_comparison.html">Comparison
  76         of Cube Root Finding Algorithms</a></span></dt>
  77 <dt><span class="section"><a href="math_toolkit/roots/root_comparison/root_n_comparison.html">Comparison
  78         of Nth-root Finding Algorithms</a></span></dt>
  79 <dt><span class="section"><a href="math_toolkit/roots/root_comparison/elliptic_comparison.html">Comparison
  80         of Elliptic Integral Root Finding Algoritghms</a></span></dt>
  81 </dl></dd>
  82 <dt><span class="section"><a href="math_toolkit/roots/polynomials.html">Polynomials</a></span></dt>
  83 <dt><span class="section"><a href="math_toolkit/roots/rational.html">Polynomial and Rational
  84       Function Evaluation</a></span></dt>
  85 </dl></dd>
  86 </dl>
  87 </div>
  88 </div>
  89 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
  90 <td align="left"></td>
  91 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
  92       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
  93       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
  94       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
  95         Distributed under the Boost Software License, Version 1.0. (See accompanying
  96         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>)
  97       </p>
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