(08/21/2022, 04:35 PM)bo198214 Wrote: I mean picture of the half-iterate! I thought all this Borel and whatever summation is to calculate values of the half-iterate?!
Aiihh, I see. Well - the best I could do then has been to get approximations to ten or twenty digits precision (using \( x \approx 1 \) ) and even that poor result needed manual finetuning of my hot-needle procedure - as the last 256-coefficients listing in my text showed. Just for review of my then selection of parameters I used today 1024 coefficients (which I didn't have then) to re-check that parameters and -
they were not good enough... phww... I knew that -with such need of manual finetuning of the parameters- it could not grow-out to more than a basic "proof-of-concept" (which was what I wanted basically anyway).
Well, on the other hand, using the functional relation, inserting integer iterates towards the fixpoint (near zero as far as wanted) and using the partial sums truncated where convergence seemed to occur ... you know the point, nothing better than that what is around in the forum and you fellows used happily from the beginning anyway
. So - no need for pictures or more pictures or tables. Just too expensive, and numerically inferior. Hope that explains ...
Gottfried
Gottfried Helms, Kassel
