Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[Update] Comparision of 5 methods of interpolation to continuous tetration
#5
(10/13/2013, 02:20 PM)Gottfried Wrote: I've just updated my discussion from 2010 where I provided pictures and short commentars for the basic introduction into different interpolation proposals for the tetration. I included now also the comaprision with the Kneser-method, where I used one of the Pari/GP-scripts which Sheldon has kindly provided here.
Here is the link:

http://go.helms-net.de/math/tetdocs/Comp...ations.pdf

Gottfried,
I was able to reproduce your graph on page 9, by plotting sexp(z+k), where , and z varied from -7 to 1. You might try other values of k. As imag(k) increases, the Kneser technique behaves more and more like the Schroeder function. For example, try k=0.5i, graphing sexp(z+k) from z=-7 to z=1, and you see a very nice well defined spiral towards to fixed point, just like the Schroeder function solution. Here interpolation works very well, since interpolation naturally approaches the Schroeder function solution.

Closer to the real axis, the singularities at integer values <=-2 become more and more pronounced, which causes problems for interpolation.
- Sheldon
Reply


Messages In This Thread
RE: [Update] Comparision of 5 methods of interpolation to continuous tetration - by sheldonison - 10/14/2013, 10:07 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
Question Continuous Hyper Bouncing Factorial Catullus 9 117 08/15/2022, 07:54 AM
Last Post: JmsNxn
  Qs on extension of continuous iterations from analytic functs to non-analytic Leo.W 17 819 08/10/2022, 11:34 PM
Last Post: JmsNxn
  Unifying continuous and discrete physics Daniel 0 39 07/31/2022, 01:26 PM
Last Post: Daniel
  A related discussion on interpolation: factorial and gamma-function Gottfried 9 17,758 07/10/2022, 06:23 AM
Last Post: Gottfried
  Question about tetration methods Daniel 17 699 06/22/2022, 11:27 PM
Last Post: tommy1729
  Small research update MphLee 2 1,104 10/26/2021, 12:22 AM
Last Post: MphLee
  My interpolation method [2020] tommy1729 1 3,244 02/20/2020, 08:40 PM
Last Post: tommy1729
  Possible continuous extension of tetration to the reals Dasedes 0 3,126 10/10/2016, 04:57 AM
Last Post: Dasedes
  Tribonacci interpolation ? tommy1729 0 3,712 09/08/2014, 10:37 AM
Last Post: tommy1729
  How many methods have this property ? tommy1729 1 4,928 05/22/2014, 04:56 PM
Last Post: sheldonison



Users browsing this thread: 3 Guest(s)