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 Cheta with base-change: preliminary results bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/12/2009, 04:18 PM (08/12/2009, 02:43 PM)jaydfox Wrote: The variable fma in that code is the matrix I'm referring to. Hopefully you can tell from the context what Andrew's talking about. Essentially, it gives us a matrix, which we can multiply on the right by a vector of powers of n, to get a vector representing a power series in x. For fractional n, the terms diverge. Or, we can multiply on the right by a vector of powers of x (i.e., picking a fixed x), and get a power series in n, which is the iteration function. I use this latter approach. Oh you mean this matrix is only for the computation of the iteration of $\exp_\eta$? And this takes this exuberant time? You know that Walker describes an alogrithm for the iteration of $\exp_\eta$ based on a limit formula, not via powerseries development. Perhaps this is more appropriate if considering time. Particularly because he conducted some accelerations. I initially thought that the inversion of the interpolation matrix took so much time (and not the fma) thatswhy I provided the direct formula via stirling numbers. Well I would anyway ask you to make a modular solution. Input: some super-exponential to base $a$ at least defined on some real axis. Output: the taylor series of the base change to base $b$. This would give the flexibility also to check whether change of base leads from one regular super-exponential again to a regular super-exponential (at the lower fixed point). The regular super-exponentials for base $b<\eta$ are anyway drastically more gentle numerically than the one for base $\eta$. « Next Oldest | Next Newest »

 Messages In This Thread Cheta with base-change: preliminary results - by jaydfox - 08/11/2009, 05:16 PM RE: Cheta with base-change: preliminary results - by bo198214 - 08/11/2009, 06:45 PM RE: Cheta with base-change: preliminary results - by jaydfox - 08/11/2009, 06:52 PM RE: Cheta with base-change: preliminary results - by jaydfox - 08/11/2009, 08:03 PM RE: Cheta with base-change: preliminary results - by jaydfox - 08/11/2009, 09:12 PM RE: Cheta with base-change: preliminary results - by sheldonison - 08/12/2009, 01:31 AM RE: Cheta with base-change: preliminary results - by jaydfox - 08/12/2009, 02:15 AM RE: Cheta with base-change: preliminary results - by Gottfried - 08/12/2009, 12:37 PM RE: Cheta with base-change: preliminary results - by jaydfox - 08/12/2009, 02:29 PM RE: Cheta with base-change: preliminary results - by Gottfried - 08/12/2009, 03:47 PM RE: Cheta with base-change: preliminary results - by jaydfox - 08/12/2009, 04:49 PM RE: Cheta with base-change: preliminary results - by bo198214 - 08/11/2009, 08:11 PM RE: Cheta with base-change: preliminary results - by jaydfox - 08/11/2009, 08:45 PM RE: Cheta with base-change: preliminary results - by bo198214 - 08/11/2009, 08:54 PM RE: Cheta with base-change: preliminary results - by jaydfox - 08/12/2009, 12:24 AM

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