Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Matrix Operator Method
#38
Gottfried Wrote:Just derived a method to compute exact entries for powers of the (square) matrix-operator for T-tetration.
It is applicable to positive integer powers only, but for any base.
...
Code:
T^2 = U*dV(b^^0) * T*dV(b^^1)
T^3 = U*dV(b^^0) * U*dV(b^^1) * T*dV(b^^2)
...
T^h = prod_{k=0}^{h-2} (U * dV(b^^k))
           * (T * dV(b^^(h-1)))
So the finding is that though the matrix multiplication of the T's is infinite, the result is expressible in finite terms (polynomials) of ?

Quote:This finding is interesting, because in my matrix-method I had to use fixpoint-shift to get exact entries even for integer powers, and since the fixpoints for T-tetration are real only for a small range of bases we had to deal with complex-valued U-matrices when considering the general case. Here we do not need a fixpoint-shift.

I did not check how this computation is related to Ioannis Galidakis' method for exact entries yet, but I think, this is interesting too.

That would be useful to compare. Can you derive a recurrence from your matrix formula?
Reply


Messages In This Thread
Matrix Operator Method - by Gottfried - 08/12/2007, 08:08 PM
RE: Matrix Operator Method - by bo198214 - 08/13/2007, 04:15 AM
RE: Matrix Operator Method - by jaydfox - 08/13/2007, 05:40 AM
RE: Matrix Operator Method - by Gottfried - 08/13/2007, 09:22 AM
RE: Matrix Operator Method - by bo198214 - 08/14/2007, 03:43 PM
RE: Matrix Operator Method - by Gottfried - 08/14/2007, 04:15 PM
RE: Matrix Operator Method - by bo198214 - 08/26/2007, 12:18 AM
RE: Matrix Operator Method - by Gottfried - 08/26/2007, 11:24 AM
RE: Matrix Operator Method - by bo198214 - 08/26/2007, 11:39 AM
RE: Matrix Operator Method - by Gottfried - 08/26/2007, 04:22 PM
RE: Matrix Operator Method - by Gottfried - 08/26/2007, 10:54 PM
RE: Matrix Operator Method - by bo198214 - 08/27/2007, 08:29 AM
RE: Matrix Operator Method - by Gottfried - 08/27/2007, 11:04 AM
RE: Matrix Operator Method - by bo198214 - 08/27/2007, 11:35 AM
RE: Matrix Operator Method - by Gottfried - 08/27/2007, 11:58 AM
RE: Matrix Operator Method - by bo198214 - 08/27/2007, 12:13 PM
RE: Matrix Operator Method - by Gottfried - 08/27/2007, 01:19 PM
RE: Matrix Operator Method - by Gottfried - 08/27/2007, 02:29 PM
RE: Matrix Operator Method - by bo198214 - 08/27/2007, 02:36 PM
RE: Matrix Operator Method - by Gottfried - 08/27/2007, 03:09 PM
RE: Matrix Operator Method - by bo198214 - 08/27/2007, 07:15 PM
RE: Matrix Operator Method - by Gottfried - 08/27/2007, 08:15 PM
RE: Matrix Operator Method - by bo198214 - 08/29/2007, 05:28 PM
RE: Matrix Operator Method - by Gottfried - 08/27/2007, 12:43 PM
RE: Matrix Operator Method - by Gottfried - 10/08/2007, 12:11 PM
RE: Matrix Operator Method - by Gottfried - 10/14/2007, 09:32 PM
RE: Matrix Operator Method - by Gottfried - 04/04/2008, 09:41 AM
RE: Matrix Operator Method - by Gottfried - 04/17/2008, 09:21 PM
RE: Matrix Operator Method - by bo198214 - 04/25/2008, 03:39 PM
RE: Matrix Operator Method - by Gottfried - 04/26/2008, 06:09 PM
RE: Matrix Operator Method - by bo198214 - 04/26/2008, 06:47 PM
RE: Matrix Operator Method - by Gottfried - 04/18/2008, 01:55 PM
RE: Matrix Operator Method - by Gottfried - 07/08/2008, 06:46 AM
RE: Exact entries for T-tetration Bell-matrix - by bo198214 - 09/26/2008, 07:30 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 87 09/09/2019, 10:55 PM
Last Post: tommy1729
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 6,204 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Tetration and Sign operator tetration101 0 247 05/15/2019, 07:55 PM
Last Post: tetration101
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,273 12/21/2016, 01:27 PM
Last Post: tommy1729
  Tommy's matrix method for superlogarithm. tommy1729 0 1,478 05/07/2016, 12:28 PM
Last Post: tommy1729
  [split] Understanding Kneser Riemann method andydude 7 7,108 01/13/2016, 10:58 PM
Last Post: sheldonison
  [2015] New zeration and matrix log ? tommy1729 1 2,884 03/24/2015, 07:07 AM
Last Post: marraco
  Kouznetsov-Tommy-Cauchy method tommy1729 0 1,875 02/18/2015, 07:05 PM
Last Post: tommy1729
  Problem with cauchy method ? tommy1729 0 1,709 02/16/2015, 01:51 AM
Last Post: tommy1729
  Regular iteration using matrix-Jordan-form Gottfried 7 7,903 09/29/2014, 11:39 PM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)