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

Table of Contents

Root finding
Root Finding Without Derivatives
Bracket and Solve Root
Algorithm TOMS 748: Alefeld, Potra and Shi: Enclosing zeros of continuous functions
Brent-Decker Algorithm
Termination Condition Functors
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
Polynomial and Rational Function Evaluation