Hi -
the question which is the best method to interpolate to fractional/complex tetration is still open, so I thought it would be nice to see this visually at "just-another-example".
I used base b=4, which requires a nasty (complex) fixpoint for the regular tetration and also it is boring to always gamble in the interval of convergence of the infinite tower.
So here is a short text about regular tetration, linear interpolation, polynomial interpolation (just the empirical diagonalization of the truncated matrix using your favourite software) and a log-polar interpolation.
What I'm missing are the computations of that example interval for the Cauchy-integral-method (could someone do this for me?) and the method derived from the slog-ansatz of Walker and Andy Robbins.
Here is the link
]Comparision of interpolations(pdf)
(I'll upload that file to our forum here when the text-version is stable)
Gottfried
the question which is the best method to interpolate to fractional/complex tetration is still open, so I thought it would be nice to see this visually at "just-another-example".
I used base b=4, which requires a nasty (complex) fixpoint for the regular tetration and also it is boring to always gamble in the interval of convergence of the infinite tower.
So here is a short text about regular tetration, linear interpolation, polynomial interpolation (just the empirical diagonalization of the truncated matrix using your favourite software) and a log-polar interpolation.
What I'm missing are the computations of that example interval for the Cauchy-integral-method (could someone do this for me?) and the method derived from the slog-ansatz of Walker and Andy Robbins.
Here is the link
]Comparision of interpolations(pdf)
(I'll upload that file to our forum here when the text-version is stable)
Gottfried
Gottfried Helms, Kassel