function [x,niter]=aitken(phi,x0,tol,nmax,varargin)
%AITKEN Aitken's method.
% [ALPHA,NITER]=AITKEN(PHI,X0) computes an
% approximation of a fixed point ALPHA of function PHI
% starting from the initial datum X0 using Aitken's
% extrapolation method. The method stops after 100
% iterations or after the absolute value of the
% difference between two consecutive iterates is
% smaller than 1.e-04. PHI can be defined either
% as an inline function or an anonymous function or
% by an M-file.
% [ALPHA,NITER]=AITKEN(PHI,X0,TOL,NMAX) allows to
% define the tolerance on the stopping criterion and
% the maximum number of iterations.
if nargin == 2
    tol = 1.e-04;
    nmax = 100;
elseif nargin == 3
    nmax = 100;
end
x = x0;
diff = tol + 1;
niter = 0;
while niter < nmax & diff >= tol
    gx = feval(phi,x,varargin{:});
    ggx = feval(phi,gx,varargin{:});
    xnew = (x*ggx-gx^2)/(ggx-2*gx+x);
    diff = abs(x-xnew);
    x = xnew;
    niter = niter  + 1;
end
if (niter==nmax & diff>tol)
    fprintf(['Fails to converge within maximum ',...
            'number of iterations\n']);
end
return