% The program uses the bisection method to estimate a root of the equation 
% f(x)=0. The input parameters are x_1 and x_2 (which give an interval
% that contains a root) and the tolerance = epsilon with which the root will be
% estimated.


function [x] = Bisection(x_1,x_2,epsilon)

% With the next command ask for high accuracy (more decimals)

format long

% We give an initial value so that the while loop will get started

x = x_1 ; 

% n will count the number of repetitions needed to achieve the desired
% accuracy.

n=0;   

% The method 

while (abs(fcn(x)) > epsilon)

  x = (x_1 + x_2)/2          % Next estimate of the root.
  
  n=n+1                      % Number of repetitions.   
  
  test = fcn(x_1) * fcn(x);  % Perform product test. 

  if test < 0
    x_2 = x;                 % root is between x_1 and x.
  else                       % i.e. test > 0
    x_1 = x;                 % root is between x and x_2.
  end

end