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Table of Contents
- Root Finding Without Derivatives
- Root Finding With Derivatives: Newton-Raphson, Halley & Schroeder
- Roots of Cubic Polynomials
- Roots of Quartic Polynomials
- Examples of Root-Finding (with and without derivatives)
- 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
Several tools are provided to aid finding minima and roots of functions.
Some root-finding without derivatives methods are bisection, bracket and solve, including use of TOMS 748 algorithm.
For root-finding with derivatives the methods of Newton-Raphson iteration, Halley, and Schröder are implemented.
For locating minima of a function, a Brent minima finding example is provided.
There are several fully-worked root-finding examples, including: