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