The secant methode is a simplified version of the Newton method. The computation of x1 is done using the Newton method. The computation of f′(xn), n>1 is done approximatively. This method is used when the computation of the derivative is expensive:
|xi+1 = xi−|
|, f′est =|
The convergence for roots of multiplicity 1
is of order (1 + √5)/2 ≈ 1.62... .