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

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

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

Interpolation Functions

Cubic B-spline interpolation
Barycentric Rational Interpolation

Adaptive Trapezoidal Quadrature