%
% In this example, we use the bisection method to solve
%   cos x - x = 0
%

% Set a, b, TOL, N
a = 0;
b = pi/2;
TOL = 1e-8;
N = 100;

% Set the iteration index
i = 1;

% Start the iteration
while ( i<=N & b-a>2*TOL )
  i = i+1;
  p = (a+b)/2;
  if  (cos(a)-a)*(cos(p)-p)>0
    a = p;
  else
    b = p;
  end
end

% Print the result
if  ( b-a<2*TOL )
  fprintf('Found the root %12.10f after %d iterations.\n', p, i-1);
else
  fprintf('Method failed after %d iterations', i);
end

Found the root 0.7390851380 after 27 iterations.

Published with MATLAB® 7.6