exponential polynomial interpolation

[Gottfried]

There is a recurrence equation for hyperbolic iteration that Henryk describes here, and I later noticed here and since this is a "finite" recurrence equation, everything is eventually defined in terms of \( f_1^t \), which is equivalent to your \( u^h \) in the case \( f(x) = e^{ux} - 1 \).

Hi Andrew -
thanks for the hint; I just reread that. I'll try to translate this into my matrix-lingo and see, how it is related. Though my Eigensytem-solver does not require the iterates \(g = f°^t\) I think the interpolation-approach may be related to it this way.

I have also noticed that you can better describe hyperbolic iteration as a polynomial in \( f_1^t \), but I have yet to find any patterns of note.

Do you remember my diagonalization formula? (pg 21 in "ContinuousFunctionalIteration" )

Gottfried