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 short compilation:fractional iteration-> eigendecomposition Gottfried Ultimate Fellow Posts: 765 Threads: 119 Joined: Aug 2007 01/20/2008, 07:50 AM (This post was last modified: 01/20/2008, 08:04 AM by Gottfried.) For considerations of the characteristic of the powerseries of U-tetration I recently uploaded an empirical table, but this link may have been overlooked in our threads. Here it is again: coefficients for fractional iteration I think, I've to correct my estimation there about growth of absolute values of terms. Better estimation (instead of hypergeometric) seems to be |term_k| ~ const*exp(k^2) asymptotically by inspection of first 96 terms with fractional heights. There is a "bump" at one index k, from where the absolute values grow after they have initially decreased. This "bump" moves to higher k with |1/2-fractional(h)|-> 1/2, and maybe we can say, it moves out to infinity, if h is integer, and the beginning of growth of absolute values of terms does not occur anywhere. An older and shorter treatize of height-dependent coefficients is in coefficients depending on h (older) Unfortunately I choose the letter U for the matrix, which would be the matrix "POLY" in my article, so this should no more be confusing (I'll change this today or tomorrow) Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread short compilation:fractional iteration-> eigendecomposition - by Gottfried - 01/19/2008, 09:37 AM RE: short compilation:fractional iteration-> eigendecomposition - by andydude - 01/19/2008, 09:50 AM RE: short compilation:fractional iteration-> eigendecomposition - by Gottfried - 01/19/2008, 11:17 AM RE: short compilation:fractional iteration-> eigendecomposition - by bo198214 - 01/19/2008, 01:20 PM RE: short compilation:fractional iteration-> eigendecomposition - by Gottfried - 01/19/2008, 02:29 PM RE: short compilation:fractional iteration-> eigendecomposition - by Gottfried - 01/20/2008, 02:32 PM RE: short compilation:fractional iteration-> eigendecomposition - by Gottfried - 01/20/2008, 07:50 AM RE: short compilation:fractional iteration-> eigendecomposition - by Gottfried - 01/21/2008, 06:45 PM RE: short compilation:fractional iteration-> eigendecomposition - by Gottfried - 01/23/2008, 07:35 AM

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