I've just updated my discussion from 2010 where I provided pictures and short commentars for the basic introduction into different interpolation proposals for the tetration. I included now also the comaprision with the Kneser-method, where I used one of the Pari/GP-scripts which Sheldon has kindly provided here.
Here is the link:
http://go.helms-net.de/math/tetdocs/Comp...ations.pdf
I'll attach it also here for the possibility that some website might drop down...
[updates]: included comparisions of the Kneser with the polynomial 32x32, polynomial 48x48 and polynomial 64x64 - interpolations.
Impression/conclusion:The bigger the matrix-size, the better the Kneser solution is approximated.
[/end update]
Ahh, ps: I would like it much to include more material of someone else, who has some other practical procedure and can provide data for the same environment (of base b=4, and the 1/20 to 1/40-step iterations with the given initial values) such that I can include them in my Excel-tables for plotting.
Have fun -
Gottfried
see for more material: http://go.helms-net.de/math/tetdocs/
Here is the link:
http://go.helms-net.de/math/tetdocs/Comp...ations.pdf
I'll attach it also here for the possibility that some website might drop down...
[updates]: included comparisions of the Kneser with the polynomial 32x32, polynomial 48x48 and polynomial 64x64 - interpolations.
Impression/conclusion:The bigger the matrix-size, the better the Kneser solution is approximated.
[/end update]
Ahh, ps: I would like it much to include more material of someone else, who has some other practical procedure and can provide data for the same environment (of base b=4, and the 1/20 to 1/40-step iterations with the given initial values) such that I can include them in my Excel-tables for plotting.
Have fun -
Gottfried
see for more material: http://go.helms-net.de/math/tetdocs/
Gottfried Helms, Kassel
