(09/13/2009, 07:24 AM)mike3 Wrote: Why do you need to use a complex fixed point for ? It converges to a real fixed point as the tower approaches infinity (namely, ).

The problem with the real fixpoint is, that the triangular Bell-matrices have (alternating signed) units on its diagonal. This prevents the computation of a matrix-logarithm as well of the diagonalization - at least in my implementations.

If I have no option for one of those, I can approximate tetration only via diagonalization of the square Bell-matrices (means: omitting the fixpoint-shifting). But here all coefficients depend on the size of the used matrix, they are in my view unpredictable and may only serve as rough approximations for a "first impression".

But well, let's see. It's surely not the highest summit of wisdom... and we also have the Newton-binomial-formula and others...

Gottfried

Gottfried Helms, Kassel