Module secant 

Secant method for root finding

Implements the secant method which approximates the derivative using two function evaluations. No analytical or numerical derivative required.

Algorithm

Given two initial guesses x0 and x1: x(n+1) = x(n) - f(x(n)) * (x(n) - x(n-1)) / (f(x(n)) - f(x(n-1)))

Convergence

• Superlinear convergence rate: ≈ 1.618 (golden ratio)
• Faster than bisection, slower than Newton-Raphson
• No derivative calculation required
• Requires two initial guesses (not necessarily a bracket)

Structs

SecantMethod

Secant method for root finding