function [ x, it ] = fixed_point ( f, g, x, xtol, ftol, itmax )

  it <-- 0
  xold <-- 0
  old <-- 0
  new <-- 0
  alpha <-- 0

  Loop 

    it <-- it + 1
    xold <-- x
    x <-- g(x)
    old <-- new
    new <-- abs ( x - xold )

    alpha_old <-- alpha

    if old is not 0, THEN
      alpha <-- new / old
      if alpha_old is not 0 THEN
        r <-- log ( alpha ) / log ( alpha_old );
        print r

    if new <= xtol and |f(x)| <= ftol, break from loop with success
    if it > itmax, break from loop with failure
 
  End loop
  
  return
end