The secant methode is a simplified version of the Newton method. The computation of x_{1} is done using the Newton method. The computation of f′(x_{n}), n>1 is done approximatively. This method is used when the computation of the derivative is expensive:
x_{i+1} = x_{i}− 
 , f′_{est} = 

The convergence for roots of multiplicity 1
is of order (1 + √5)/2 ≈ 1.62... .
Input :
Output :
Input :
Output :