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 Numerical algorithm for Fourier continuum sum tetration theory mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 09/17/2010, 10:10 AM (This post was last modified: 09/17/2010, 10:13 AM by mike3.) The problem is the initial guess. I mentioned in the main posts: Quote:It seems that with a large number of nodes, the convergence with this initial guess only works for small bases like base 2 -- not sure what's going on there, but that can be used as an initial guess for a wide variety of other bases. I wasn't specific enough -- the base has to be real small, even e seems too large, at this initial guess. Not sure why this is. Try a loop or two on base 2 first, then use the result of that as the initial guess to run base e. On my system, a single loop at base 2, followed by six loops at base e, using the parameters you give, yields tet(pi) ~ 3.716e10, which is closer to the expected value of 3.71498e10. You'll probably need more than 81 nodes and 32*I period to get more accuracy than that. Yes, the Kneser process seems to yield more precision more quickly, but is restricted only to real bases $b > e^{1/e}$ (where the conjugate symmetry holds). ADDENDUM: Actually, it does work in your case, but with more nodes than what you used, it won't. You just need to iterate it a lot more times -- try 30 or so. « Next Oldest | Next Newest »

 Messages In This Thread Numerical algorithm for Fourier continuum sum tetration theory - by mike3 - 09/15/2010, 11:00 AM RE: Numerical algorithm for Fourier continuum sum tetration theory - by mike3 - 09/15/2010, 11:06 AM RE: Numerical algorithm for Fourier continuum sum tetration theory - by nuninho1980 - 09/15/2010, 01:28 PM RE: Numerical algorithm for Fourier continuum sum tetration theory - by mike3 - 09/15/2010, 07:17 PM RE: Numerical algorithm for Fourier continuum sum tetration theory - by nuninho1980 - 09/16/2010, 01:18 AM RE: Numerical algorithm for Fourier continuum sum tetration theory - by mike3 - 09/16/2010, 08:00 PM RE: Numerical algorithm for Fourier continuum sum tetration theory - by nuninho1980 - 09/17/2010, 12:00 AM RE: Numerical algorithm for Fourier continuum sum tetration theory - by nuninho1980 - 09/17/2010, 12:16 AM RE: Numerical algorithm for Fourier continuum sum tetration theory - by mike3 - 09/17/2010, 10:10 AM RE: Numerical algorithm for Fourier continuum sum tetration theory - by sheldonison - 09/17/2010, 10:32 PM RE: Numerical algorithm for Fourier continuum sum tetration theory - by mike3 - 09/18/2010, 04:11 AM RE: Numerical algorithm for Fourier continuum sum tetration theory - by Ansus - 09/18/2010, 01:38 AM RE: Numerical algorithm for Fourier continuum sum tetration theory - by mike3 - 09/18/2010, 04:12 AM

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