Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[Update] Comparision of 5 methods of interpolation to continuous tetration
(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 Helms, Kassel

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
Question Continuous Hyper Bouncing Factorial Catullus 2 19 12 minutes ago
Last Post: Catullus
  Unifying continuous and discrete physics Daniel 0 35 07/31/2022, 01:26 PM
Last Post: Daniel
  Qs on extension of continuous iterations from analytic functs to non-analytic Leo.W 15 767 07/14/2022, 07:18 PM
Last Post: MphLee
  A related discussion on interpolation: factorial and gamma-function Gottfried 9 17,698 07/10/2022, 06:23 AM
Last Post: Gottfried
  Question about tetration methods Daniel 17 665 06/22/2022, 11:27 PM
Last Post: tommy1729
  Small research update MphLee 2 1,079 10/26/2021, 12:22 AM
Last Post: MphLee
  My interpolation method [2020] tommy1729 1 3,236 02/20/2020, 08:40 PM
Last Post: tommy1729
  Possible continuous extension of tetration to the reals Dasedes 0 3,114 10/10/2016, 04:57 AM
Last Post: Dasedes
  Tribonacci interpolation ? tommy1729 0 3,689 09/08/2014, 10:37 AM
Last Post: tommy1729
  How many methods have this property ? tommy1729 1 4,913 05/22/2014, 04:56 PM
Last Post: sheldonison

Users browsing this thread: 1 Guest(s)