Reviving an old idea with 2sinh.

[tommy1729]

Bad news.

I think this method fails huge !

It seems to overshoot ; give to high values.

This is based on interval arguments rather than precise computation.

So it is theoretical But Simple algebra/Geometry.

So im pretty convinced.

—-

It seems that Nice continu iterations or their asymptotics require

1) fixpoint derivative remains or converges to t > 0.

2) Fixpoint derivative > 1 has f ‘’(x) > 0 close to the fixpoint…

Or fixpoint derivative < 1 has f’’ (x) < 0 close to the fixpoint.

Minimum demands for single fixpoint methods  ! 

Ofcourse this is very general .. to general to prove or classify maybe.

But im getting convinced.

Btw the gaussian and 2sinh do not have this problem.
( and probably neither the similar ones )


regards 

tommy1729