11/16/2009, 11:39 AM
(11/16/2009, 09:01 AM)bo198214 Wrote: Mike, I took the extra time to describe it in my previous post:
(11/16/2009, 12:30 AM)bo198214 Wrote: I computed the regular iteration as a mixture of the powerseries development at the lower fixed point, together with (if 1 is not inside the convergence radius of this powerseries) the equality \( \log_b^{\circ n} \circ \exp_b^{\circ t} \circ \exp_b^{\circ n} = \exp_b^{\circ t} \), i.e. the exponentials move the argument towards the fixed point until it is inside its convergence radius then the powerseries can be applied and the same number of logarithms have to finish the computation.
I assumed the convergence radius to be at least the distance of the fixed point from the image of the Shell-Thron region.
Ah, I see now. How much numerical precision was required, though?
Quote:What about the vicinity of the area \( b = e^{1/e} \)?In which form/region you want it to be shown? Different sectors, or decreasing distance to the boundary?
Region? I suppose a small circle around e^{1/e}, excluding the wedge that lies outside the STR?
