% bisection.m --- a sample MATLAB code implementing the bisection 
% algorithm for solving the equation x*x-2 = 0. 

% a = the left end-point of the interval [a,b]
% b = the right end-point of the interval [a,b]
% N = maximum number of iterations
% epsilon = tolerance: the smallest absolute function value

  clear;

  a = 0; b = 2; N = 20; epsilon = 1.e-14;
  fa = a*a-2; fb = b*b-2; e = b-a;
  disp([a,b,fa,fb]); 
   
  if sign(fa) ~= sign(fb)
    for k = 1:N
      e = e/2; p = a+e; fp = p*p-2;
      disp(sprintf('%5.0f %12.8f %12.8f %12.8f %12.8f', k,p,abs(fp),e));
      if (abs(e) < epsilon)
        break;
      end
      if sign(fp) ~= sign(fa)
        b = p; fb = fp;
      else
                                % fill in this line to complete the code
      end
    end
  end