bo198214 Wrote:I really have no idea about the structure of Eigenvalues of truncations in this case. But somehow the non-integer iterations seem to converge in this case too (?)

Hmm, two untested ideas, just from tinking about this:

1) The infinite alternating series of 1 - b^1 + b^b^1 - b^b^b^1 + ... -... corresponds with the matrix M= (I + Bb)^-1 , and M's eigenvalues, if b=eta, should then all be 1/2, and converge to this value by increasing size of truncation. If the observed eigenvalues of the truncated matrices actually converge to this, we may conclude for the matrix Bb itself?

2) the "b^x - 1" - iteration is closely related to the original tetration and expressible by a triangular matrix-operator with an obvious set of eigenvalues. Perhaps from here we can deduce an answer?

I'll look at this these days (maybe thursday)

Gottfried

Gottfried Helms, Kassel