Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[Update] Comparision of 5 methods of interpolation to continuous tetration
(10/28/2013, 11:29 PM)tommy1729 Wrote: The only thing I can come up with is that :

1) we simply take the principal schroeder function near the fixpoint c.

2) in that domain we use analytic continuation ( monodromy ) so that by small radiuses recentered we can reach any value in the upper plane.

3) In that upper plane we find ( after many continuations ) the values equalling the reals between 0 and 1. ( and those are connected )
( for reasons yet to be explained !)
10) we have sexp analytic near the positive real line.
And if I got It right , there is still alot to be explained !!


Is your question about using Kneser's method to get numerical results, or is it about Kneser's proof of a real valued sexp(z) solution? It is not practical to use Kneser's method to generate usable results for sexp(z), though it is a proof of the existence of such a real valued solution, even though numerically, Kneser's Riemann mapping is very difficult to work with. Also, Kneser's proof is hard to follow, and I am not good at math to recreate it.

On the other hand, I wrote a pari-gp program that is numerically equivalent to Kneser's method that is practical, though I cannot rigorously prove my method converges. But assuming my method converges, than I can show it converges to the same solution as would be given by Kneser's Riemann mapping solution. Obviously, I could explain my method, and its equivalence to Kneser's solution, but that would not be relevant to your questions.
- Sheldon

Messages In This Thread
RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/29/2013, 09:37 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  My interpolation method [2020] tommy1729 1 686 02/20/2020, 08:40 PM
Last Post: tommy1729
  Possible continuous extension of tetration to the reals Dasedes 0 1,677 10/10/2016, 04:57 AM
Last Post: Dasedes
  Tribonacci interpolation ? tommy1729 0 2,280 09/08/2014, 10:37 AM
Last Post: tommy1729
  How many methods have this property ? tommy1729 1 3,017 05/22/2014, 04:56 PM
Last Post: sheldonison
  (MSE): Comparision of powertowers -.Possibly interesting thread in MSE Gottfried 0 2,244 05/22/2013, 07:02 AM
Last Post: Gottfried
  [UFO] - a contradiction in assuming continuous tetration? Gottfried 18 24,632 08/29/2010, 08:44 PM
Last Post: Gottfried
  Self tetraroot constructed via Newton series interpolation mike3 2 7,265 07/11/2010, 03:38 AM
Last Post: mike3
  Borel summation and other continuation/summability methods for continuum sums mike3 2 5,934 12/30/2009, 09:51 PM
Last Post: mike3
  A false interpolation paradigm (?); a reconsideration Gottfried 4 8,379 09/17/2009, 08:17 AM
Last Post: bo198214
  exponential polynomial interpolation Gottfried 3 7,805 07/16/2008, 10:32 PM
Last Post: andydude

Users browsing this thread: 1 Guest(s)