%
% In this example, we use the fixed-point iteration to solve
%   cos x = x
%

% Set the initial guess for x, TOL, N
x = pi/3;
TOL = 1e-8;
N = 100;

% Set the iteration index
i = 1;

% set the initial error
err = 1;

% start the iteration
while ( i<=N & err>TOL )
  i = i+1;
  x = cos(x);
  err = abs( cos(x)-x );
end

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

Found the root 0.7390851272 after 45 iterations.

Published with MATLAB® 7.6