(08/20/2022, 04:09 PM)bo198214 Wrote: But Gottfried, with doubling to 2048 you get only a tenth more in x values, you go from 10=log2(1024) to 11=log2(2048\), you will not see much more - thats what I mean - its exponential.
Yesss, I'm aware of that - that wil give a very small progress. But reduces the "space of possible patterns" . Let's see...
(08/20/2022, 04:09 PM)bo198214 Wrote:(08/20/2022, 03:31 PM)Gottfried Wrote: I'm moreover curious, whether a stretch of the x-axis should be an option, to capture the periodicity better. Say log(2.1) instead or so ... and see whether there would be a meaningful value there - yet I did not collect exampledata so far...you mean that the zeros go to integers?
Yes, I had several times tried to find an idea for this; it seems that the periodicities/wave length on the log of the index k are not really constant but might at least go to a limit. I've overlapped the sinusoidal curves, after rescaling the amplitude to maximum height with real sinus curves and saw this non-matching...
But this all needs so many coefficients that one needs a supercomputer or some abo on R.P.(?) Brent for better matrix-modules... Except you hit a nugget by chance, as it seems to be with the exp(x)-1-curve...
update: attached three articles of R.P.Brent on (computability) efficiency of composition of powerseries.
Brent: Complexity of Composition Of Powerseries 1980 (rpb050i.pdf)
Brent/Kung: Fast Algorithms for Manipulating FormalPowerseries 1978 (rpb045.pdf)
Brent/Traub: Complexity Of Composition ... 1991 (abstract) (rpb050a)
(didn't save the links from where I downloaded them, sorry, likely has/had a personal or university homepage)
Also don't know at the moment, whether he is the Brent known for the superior fast matrix operations modules...
Gottfried Helms, Kassel
