%
function [x] = fpoint(g, x0, tolerance, maxiter, printflag)
% fpoint  fixed point iteration
% g = function to iterate
% x0 = initial guess
% tolerance = maximum error desired
% maxiter = maximum iterations
% printflag = true, display intermediate results
% printflag = false, display only the final result

   x = x0;
   
   if printflag
      fprintf('%3s%19s%19s\n', 'n','x','err');
   end

   n = 1;
   while n <= maxiter
      gx = g(x);
      err = abs(x - gx);
      x = gx;
      
      if err < tolerance
         break; % exit loop
      end 
      
      if printflag
         fprintf('%3d%19.10e%19.10e\n', n,x,err);
      end
      
      n = n + 1;
   end
   if (n > maxiter)
      fprintf('Failure to converge in %d iterations\n', maxiter);
   end
   % x is automatically returned here
end