Double newtonisation of fixed point sequences
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.
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