05/18/2008, 08:00 PM
Ya, everything alright.
However for me is the functional approach the more basic one because it works also for non-analytic functions, while the matrix approach is only applicable if you have the powerseries coefficients.
And I really wonder whether there are also iterational formulas (i.e. formulas that dont rely on the powerseries expansion, but only on function values) to compute iterations at non-fixed points ...
Well the thing about the Abel function is quite natural, it corresponds to the log and superlog functions, once I realized that I wondered how this ever could seem strange to me.
However for me is the functional approach the more basic one because it works also for non-analytic functions, while the matrix approach is only applicable if you have the powerseries coefficients.
And I really wonder whether there are also iterational formulas (i.e. formulas that dont rely on the powerseries expansion, but only on function values) to compute iterations at non-fixed points ...
Well the thing about the Abel function is quite natural, it corresponds to the log and superlog functions, once I realized that I wondered how this ever could seem strange to me.