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 fast accurate Kneser sexp algorithm sheldonison Long Time Fellow Posts: 664 Threads: 23 Joined: Oct 2008 01/14/2016, 05:05 AM (This post was last modified: 01/14/2016, 05:33 AM by sheldonison.) (01/14/2016, 12:59 AM)andydude Wrote: Why is this called "Kneser"? can you provide the article or reference that inspired this algorithm? Take a look at these two posts; Henryk's post, http://math.eretrandre.org/tetrationforu...hp?tid=213 and Jay's post, http://math.eretrandre.org/tetrationforu...hp?tid=358 Kneser's Riemann mapping results in $\exp(2\pi i \cdot f(z))$ where $ f(z)=z+\theta(z)=\alpha(\text{sexp}(z))\;\;$ which has been wrapped around a unit circle by using the substitution $z = \frac{\log(y)}{2\pi i}$. So my approach is related, and mathematically equivalent, but not identical. In the approach used in my kneser.gp program, I iterate, generating increasingly accurate $\theta(z)$ approximations from increasingly accurate sexp(z) taylor series approximations where in the limit, $\text{sexp}(z)=\alpha^{-1}(z+\theta(z))$ - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread fast accurate Kneser sexp algorithm - by sheldonison - 08/07/2010, 06:53 AM The pari-GP code - by sheldonison - 08/07/2010, 09:17 PM RE: fast accurate Knesser sexp algorithm - by bo198214 - 08/08/2010, 03:54 PM RE: fast accurate Knesser sexp algorithm - by sheldonison - 08/08/2010, 06:46 PM RE: fast accurate Kneser sexp algorithm - by nuninho1980 - 08/15/2010, 12:09 AM updated kneser.gp code - by sheldonison - 08/19/2010, 02:35 AM RE: updated kneser.gp code - by nuninho1980 - 08/19/2010, 12:08 PM RE: updated kneser.gp code - by sheldonison - 08/20/2010, 01:05 AM RE: fast accurate Kneser sexp algorithm - by sheldonison - 10/14/2010, 10:00 PM RE: fast accurate Kneser sexp algorithm - by nuninho1980 - 10/15/2010, 04:03 PM RE: fast accurate Kneser sexp algorithm - by sheldonison - 10/15/2010, 09:20 PM kneser.gp modified for large bases - by sheldonison - 10/19/2010, 03:33 AM small update to allow more flexibility, faster - by sheldonison - 10/30/2010, 09:47 PM update to support B

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