3.2 Half interval method
This algorithm is generally used when an analytical expression for the derivative of the function f(x) = 0 with respect to the x is not available.
In this case the algorithm is as follows:
 Choose 2 values for x in such a way that it is: f(a) f(b) < 0
 Calculate the new value for x_{new} = [a + b]/2
 Calculate the new value for f(x_{new})
 If f(x_{new}) is already almost zero (<e), x_{new} is the searched root
 If f(x_{new}) is >e, the procedure must be iterated from point 1 again until convergence. Of course, one of the new two values to choose in point 1 is x_{new}
Here below a scheme of the algorithm.
