Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Eigensystem of tetration-matrices
It seems, that the eigensystem-based method works now fine.
Using the fixpoint-tracer and the values it supplies, I could construct the Bs-matrices with a few basic examples for s>e^(1/e) (or b>eta in the other notation here) based on the complex values for t and log(t).
The constructed matrices matched perfectly the naive-versions for integer-tetration Bs and Bs^h.

This settles then the continuous tetration for all s>e^-e (except the known singularities by the method)

The complex fixpoints t=h(s) for s>e^(1/e) are taken from the branch, which reaches into the real halfplane with real(t)>1 (the other branches there have real(t)<1) and is shown in the graphs at Fixpoint principal branch.

Phew. ;-)

It seeems, what remains is now consideration of numerical aspects and optimization of summing, where intermediate non-converging series occur.

Gottfried Helms, Kassel

Messages In This Thread
Eigensystem of tetration-matrices - by Gottfried - 08/29/2007, 11:11 AM
RE: Eigensystem of tetration-matrices - by Gottfried - 09/20/2007, 07:06 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  All Maps Have Flows & All Hyperoperators Operate on Matrices Daniel 0 1,021 03/14/2020, 06:22 AM
Last Post: Daniel
Question Analytic matrices and the base units Xorter 2 4,178 07/19/2017, 10:34 AM
Last Post: Xorter
  Matrices tetrated Gottfried 0 2,615 12/26/2008, 05:00 PM
Last Post: Gottfried

Users browsing this thread: 1 Guest(s)