[Update] Comparision of 5 methods of interpolation to continuous tetration

[Gottfried]

Now I've got my matrices for base b=1.44, near eta. What a mess!
I don't have any idea - there is no obvious divergence in the power series with 64 terms. I also took z0=b^b ~ 1.69 as initial point; the curves originating from z0=1 were even more messed up.


This is the picture base b=1.44 z0=1+0î - I've no explanation so far for the messed curves.

Well, here is the same, but now taken with the "regular tetration" which uses the fixpoint-shift and works with power series without constant term.

   

At least, using the base b=1.3 the differences to the polynomial method are at order of 1e-7, so this picture might not be too distorted.
Gottfried