I derive in detail the specific form of 2D Newton-Raphson for a simple root-finding problem on the complex plane. Try it out and create your own fractals!Video. Notes.
Category Archives: Numerical methods
Roots in 2D
Generalization of the Newton-Raphson method to 2D, i.e. two equations with two unknowns. Basic algebraic setup, schematics of the algorithm, potential pitfalls, and generalizations. Video. Notes.
Roots using the fixed-point method
A very brief introduction to the fixed-point method to calculate roots. I discuss the convergence criterion and its relation to the Newton-Raphson method. Video. Notes.
Roots via Newton-Raphson
This is a very brief explanation of the Newton-Raphson method, its geometry and derivation, and the schematics of the algorithm.Video. Notes.
Calculating roots: the bisection algorithm
A first look at numerical methods to calculate roots: the bisection algorithm. Steps, precision bounds, and an important caveat. Video. Notes.