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# Chapter 12. Tools: Root Finding & Minimization Algorithms, Polynomial Arithmetic & Evaluation

Table of Contents

Root finding
  Root Finding Without Derivatives
    Bisection
    Bracket and Solve Root
    Algorithm TOMS 748: Alefeld, Potra and Shi: Enclosing zeros of continuous functions
    Brent-Decker Algorithm
    Termination Condition Functors
    Implementation
  Root Finding With Derivatives: Newton-Raphson, Halley & Schröder
  Examples of Root-Finding (with and without derivatives)
    Finding the Cubed Root With and Without Derivatives
    Using C++11 Lambda's
    Computing the Fifth Root
    Root-finding using Boost.Multiprecision
    Generalizing to Compute the nth root
    A More complex example - Inverting the Elliptic Integrals
  The Effect of a Poor Initial Guess
  Examples Where Root Finding Goes Wrong
  Locating Function Minima using Brent's algorithm
  Comparison of Root Finding Algorithms
    Comparison of Cube Root Finding Algorithms
    Comparison of Nth-root Finding Algorithms
    Comparison of Elliptic Integral Root Finding Algoritghms
  Polynomials
  Polynomial and Rational Function Evaluation

| Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)