Boost C++ Libraries

...one of the most highly regarded and expertly designed C++ library projects in the world. — Herb Sutter and Andrei Alexandrescu, C++ Coding Standards

Chapter 12. Tools: Root Finding and Minimization Algorithms

Chapter 12. Tools: Root Finding and Minimization Algorithms

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