  A neutral fixed point of a real iteration map $u$ becomes a super attracting
fixed point using a suitable double newtonisation. The map $u$ is so
transformed into a map $w$ which is here called the standard accelerator of
$u$. The map $w$ provides a unifying process to deal with a large set of fixed
point sequences which are not convergent or converge slowly. Several examples
illustrate the main results obtained.
