Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[Update] Comparision of 5 methods of interpolation to continuous tetration
#13
(10/16/2013, 04:12 PM)sheldonison Wrote: The difference between your taylor series, and the Kneser solution taylor series is reasonably small. All the coefficients differ by less than 2.5^10-6. To me, it does indeed look like the Kneser solution, both in the complex plane and the real axis. (...)
Well, this is going to become ironic somehow... That "polynomial interpolation" was my very first and naive approach to the tetration (see my first messages here in the board) and then I felt its model was too unspecific and did a big exploration until I arrived at the regular tetration with the Carleman-matrix (which I called "Matrixoperator" not knowing they are already well studied) including the series-recentering towards the fixpoint and then eigendecomposition - just to come back to the beginning and meet ol' Hellmuth Kneser there...

Sometimes things go strange...

Gottfried
Gottfried Helms, Kassel
Reply


Messages In This Thread
RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by Gottfried - 10/16/2013, 05:07 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Possible continuous extension of tetration to the reals Dasedes 0 1,349 10/10/2016, 04:57 AM
Last Post: Dasedes
  Tribonacci interpolation ? tommy1729 0 1,934 09/08/2014, 10:37 AM
Last Post: tommy1729
  How many methods have this property ? tommy1729 1 2,493 05/22/2014, 04:56 PM
Last Post: sheldonison
  (MSE): Comparision of powertowers -.Possibly interesting thread in MSE Gottfried 0 1,924 05/22/2013, 07:02 AM
Last Post: Gottfried
  [UFO] - a contradiction in assuming continuous tetration? Gottfried 18 20,875 08/29/2010, 08:44 PM
Last Post: Gottfried
  Self tetraroot constructed via Newton series interpolation mike3 2 6,545 07/11/2010, 03:38 AM
Last Post: mike3
  Borel summation and other continuation/summability methods for continuum sums mike3 2 5,193 12/30/2009, 09:51 PM
Last Post: mike3
  A false interpolation paradigm (?); a reconsideration Gottfried 4 7,306 09/17/2009, 08:17 AM
Last Post: bo198214
  exponential polynomial interpolation Gottfried 3 7,028 07/16/2008, 10:32 PM
Last Post: andydude
  A related discussion on interpolation: factorial and gamma-function Gottfried 6 10,366 06/27/2008, 06:38 PM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)