Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
fast accurate Kneser sexp algorithm
#14
This is an update to support an sexp(z) mapping for bases<eta. The program starts with the regular entire superfunction developed from the repelling fixed point, and calculates , where decays to zero as imag(z) goes to +I*infinity. Thus the solution for bases<eta differs from the standard solution, developed from the attracting fixed point. See this post for discussion, and graphs.

This version will converge for converge for 1.449<=B<=1000000, and 1.02<bases<1.444. This program is very very slow for bases close to but greater than eta; in those cases, I recommend using "\p 28" for less accurate, but faster results (using 5 iterations). second update, added cosmetic changes, warning message for sexp(imag(z)>i. Converges for B>1.02.
-Sheldon
For the most recent code version: go to the Nov 21st, 2011 thread.


Attached Files
.gp   kneser.gp (Size: 24.27 KB / Downloads: 352)
Reply


Messages In This Thread
The pari-GP code - by sheldonison - 08/07/2010, 09:17 PM
updated kneser.gp code - by sheldonison - 08/19/2010, 02:35 AM
RE: updated kneser.gp code - by nuninho1980 - 08/19/2010, 12:08 PM
RE: updated kneser.gp code - by sheldonison - 08/20/2010, 01:05 AM
update to support B<eta - by sheldonison - 11/15/2010, 02:53 PM
RE: update to support B<eta - by nuninho1980 - 11/15/2010, 03:26 PM
another new version - by sheldonison - 11/17/2010, 06:52 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  "Kneser"/Riemann mapping method code for *complex* bases mike3 2 6,775 08/15/2011, 03:14 PM
Last Post: Gottfried
  Attempt to make own implementation of "Kneser" algorithm: trouble mike3 9 15,991 06/16/2011, 11:48 AM
Last Post: mike3
  Numerical algorithm for Fourier continuum sum tetration theory mike3 12 19,944 09/18/2010, 04:12 AM
Last Post: mike3
  regular sexp: curve near h=-2 (h=-2 + eps*I) Gottfried 2 6,030 03/10/2010, 07:52 AM
Last Post: Gottfried
  Attempting to compute the kslog numerically (i.e., Kneser's construction) jaydfox 11 18,682 10/26/2009, 05:56 PM
Last Post: bo198214
  regular sexp:different fixpoints Gottfried 6 11,934 08/11/2009, 06:47 PM
Last Post: jaydfox
  sexp(strip) is winding around the fixed points Kouznetsov 8 13,201 06/29/2009, 10:05 AM
Last Post: bo198214
  sexp and slog at a microcalculator Kouznetsov 0 3,200 01/08/2009, 08:51 AM
Last Post: Kouznetsov



Users browsing this thread: 1 Guest(s)