Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
"Kneser"/Riemann mapping method code for *complex* bases
(08/15/2011, 03:44 AM)mike3 Wrote: Hi.

It's been a while but I figured I could post my attempt to tetrate complex bases with the "Kneser"/Riemann mapping algorithm.

This is the code I've got, which will tetrate a complex base, here base :
It does not work for all complex bases, though. It seems to work only for those relatively near the real axis. Increasing the ImagOffset (how far off the real axis we sample the Fourier integrals) appears to extend the range, however. When it fails, it looks like the iteration used to analytically continue the Schroder function gets sucked into the wrong fixed point. Any way to resolve this? The aforementioned increasing of the ImagOffset causes losses in accuracy and efficiency, and is not a cure-all that allows for tetrating all complex bases outside the STR with the possible exception of the possibly singular base 0.


Very nice!

For base=3+i, I can calculate two repelling fixed points, each with different periods. Presumably, the upper half of the complex plane converges towards the first fixed point, and the lower half of the complex plane converges towards the second fixed point, while the merged function allows you to maintaining the definition of sexp(0)=1, and sexp(1)=base.
L1=0.324536386411256 + 1.00148180609593*I
L2=-0.0976763924712228 - 1.39768129114470*I

I assume the algorithm works when both bases are repelling?
- Sheldon

Messages In This Thread
RE: "Kneser"/Riemann mapping method code for *complex* bases - by sheldonison - 08/15/2011, 02:59 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Natural complex tetration program + video MorgothV8 1 2,368 04/27/2018, 07:54 PM
Last Post: MorgothV8
  complex base tetration program sheldonison 23 47,142 10/26/2016, 10:02 AM
Last Post: Gottfried
  fast accurate Kneser sexp algorithm sheldonison 38 84,312 01/14/2016, 05:05 AM
Last Post: sheldonison
  C++ program for generatin complex map in EPS format MorgothV8 0 3,078 09/17/2014, 04:14 PM
Last Post: MorgothV8
  C++ code for tet, ate and hexp MorgothV8 0 3,365 07/10/2014, 04:24 PM
Last Post: MorgothV8
  Green Eggs and HAM: Tetration for ALL bases, real and complex, now possible? mike3 27 40,990 07/02/2014, 10:13 PM
Last Post: tommy1729
  Which method is currently "the best"? MorgothV8 2 5,435 11/15/2013, 03:42 PM
Last Post: MorgothV8
  Attempt to make own implementation of "Kneser" algorithm: trouble mike3 9 17,767 06/16/2011, 11:48 AM
Last Post: mike3
  An incremental method to compute (Abel) matrix inverses bo198214 3 10,042 07/20/2010, 12:13 PM
Last Post: Gottfried
  Single-exp series computation code mike3 0 3,234 04/20/2010, 08:59 PM
Last Post: mike3

Users browsing this thread: 1 Guest(s)