### 4.4.5 `fsolve` or `nSolve` with the option `secant_solver`

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(xi)
f′est
| , f′est = |
f(xi) − f(xi−1)
(xi − xi−1)

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

`fsolve((cos(x))=x,x,-1..1,secant_solver)`

Output :

`[0.739085078239,0.739085137844]`

Input :

`fsolve((cos(x))=x,x,0,secant_solver)`

Output :

`0.739085133215`