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 the inconsistency depending on fixpoint-selection Gottfried Ultimate Fellow Posts: 790 Threads: 121 Joined: Aug 2007 03/07/2008, 07:17 PM (This post was last modified: 03/07/2008, 07:30 PM by Gottfried.) Well, Henryk, that opended eyes, thanks. With the following parametrization I got the difference. Starting with the general x' = x/e-d, x"=(x+d)*e, e*d=fixpoint and fixing e=1 e= 1 , d0=t0=fixpoint_0, d1=t1=fixpoint_1 and development of the matrices accordingly I got differences, too. So thanks for the hints! Now I'd like to understand, what is the source of the difference of selection e=1 vs d=1. The most obvious difference was in the given case f(x) = x^2 + x - 1/16 = x + (x - 1/4) (x + 1/4) = x + (x-t0)*(x-t1) that I kept the eigenvalues in both developments equal. Maybe my transformation introduces somehow a triviality - but note, that in my tetration-examples I also used d=1, e0=t0 versus e1=t1 for the definition of the triangular matrices, just this selection, that you say is "illegal" I tried with a general definition of a quadratic function (fixpoints p,q) f(x) = x + (x - p) (x - q) = x^2 + (1 - (p+q))x + pq g(z) = a*z^2 + b*z z = x/e-d f(x) = (g(z) + d)*e By comparing coefficients at powers of x in f(x) and g(z) I get conditions for a and b in g(z): a = e b = 1 - (p+q) + 2de , b-1 = 2de - (p+q) and then for d and e the condition occurs (de - p) (de - q) = 0 where either e or d is free. It seems then, if b equals for each selection of fixpoints, such that either de=p or de=q and the resulting b's are equal, then the resulting powerseries seem to be compatible and give equal results (I've to check that with more examples) But again: maybe this introduces some triviality... On the other hand: it is intriguing, that using d=1 , e=fixpoint is the appropriate selection to convert the tetration-matrices into triangular matrices for decremented iterated exponentiation. Hmmm. Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 03:06 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 05:20 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 10:14 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 11:17 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/04/2008, 11:25 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/04/2008, 11:32 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 11:43 AM RE: the inconsistency depending on fixpoint-selection - by GFR - 02/07/2008, 09:02 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 09:49 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/03/2008, 11:20 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/06/2008, 04:06 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/06/2008, 04:58 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/06/2008, 05:25 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 03:16 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/07/2008, 10:56 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 07:17 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/07/2008, 08:30 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 09:38 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 01:22 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 01:52 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 04:21 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/09/2008, 09:30 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 02:10 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 04:41 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 07:19 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 04/29/2008, 08:15 AM

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