Module newton_raphson 

Newton-Raphson method for root finding

Implements Newton-Raphson method using numerical differentiation. Provides quadratic convergence near simple roots.

Algorithm

Given initial guess x0: x(n+1) = x(n) - f(x(n)) / f’(x(n))

Convergence

• Quadratic convergence near simple roots (error squares each iteration)
• Requires good initial guess
• May fail for multiple roots or if derivative is zero
• Uses finite differences for derivative: f’(x) ≈ (f(x+h) - f(x))/h

Structs

NewtonRaphson

Newton-Raphson method with numerical differentiation