Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Matrix Operator Method
#24
Gottfried Wrote:With A1 = A-I then log(A) = A1 - A1*A1/2 + A1*A1*A1/3 ....
which is a nice exercise... since it comes out, that A1 is nilpotent and we can compute an exact result using only as many terms as the dimension of A is. For the infinite dimensional case one can note, that the coefficients are constant when dim is increased step by step, only new coefficients are added below the previously last row.

Are you sure about this? For me it rather looks as if they converge.
The Eigenvalues are quite different depending on the truncation.
Even in the case where you can compute the logarithm via the infinite matrix power series, it should depend on where you truncate the matrix.
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

Possibly Related Threads...
Thread Author Replies Views Last Post
  Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 133 09/09/2019, 10:55 PM
Last Post: tommy1729
  A fundamental flaw of an operator who's super operator is addition JmsNxn 4 6,347 06/23/2019, 08:19 PM
Last Post: Chenjesu
  Tetration and Sign operator tetration101 0 283 05/15/2019, 07:55 PM
Last Post: tetration101
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,321 12/21/2016, 01:27 PM
Last Post: tommy1729
  Tommy's matrix method for superlogarithm. tommy1729 0 1,516 05/07/2016, 12:28 PM
Last Post: tommy1729
  [split] Understanding Kneser Riemann method andydude 7 7,237 01/13/2016, 10:58 PM
Last Post: sheldonison
  [2015] New zeration and matrix log ? tommy1729 1 2,942 03/24/2015, 07:07 AM
Last Post: marraco
  Kouznetsov-Tommy-Cauchy method tommy1729 0 1,901 02/18/2015, 07:05 PM
Last Post: tommy1729
  Problem with cauchy method ? tommy1729 0 1,737 02/16/2015, 01:51 AM
Last Post: tommy1729
  Regular iteration using matrix-Jordan-form Gottfried 7 8,014 09/29/2014, 11:39 PM
Last Post: Gottfried



Users browsing this thread: 1 Guest(s)