• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Matrix Operator Method Gottfried Ultimate Fellow Posts: 766 Threads: 119 Joined: Aug 2007 08/27/2007, 01:19 PM (This post was last modified: 08/27/2007, 01:25 PM by Gottfried.) bo198214 Wrote:Yes, but how do you compute the infinite case. You can not simply do $\sum_{n=0}^\infty (-1)^{n+1} \frac{(A-I)^n}{n}$ as this does not converge. So do you compute it as described here via the Jordan form? Hmm, I observed that I'm not good in answering correctly in speedy discussions. But may be I've got it right in this case. If the sequence of corresponding entries of the powers of (A-I)^n/n do not converge well with finite dimension, but at least alternate in sign, I try to approximate the sums $s^{^{(\infty)}}_{i,k}$ of individual entries $b^{^{(n)}}_{i,k}$ of the n'th powers of the matrix B=(A-I) by Euler-summation via partial sums, which is sometimes an option. If the growthrate of the entries is below a certain constant limit $b^{^{(n+1)}}_{i,k} / b^{^{(n)}}_{i,k} =q_{i,k}$ constant, or $| q^{^{(n)}}_{i,k} |$ is a decreasing sequence (which is for instance the case in the scalar series for the logarithm) and no further exotic behaviour has to be expected, then Euler-summation of order q can give the final approximation to arbitrary precision for each individual entry for $s^{^{(\infty)}}_{i,k}$ of the intended result-matrix by finitely many partial sums (where "exotic" has to be precisely specified,well). Is it that what you meant? Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 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 Diagonalization for dxp/basic facts/Pari-routine - by Gottfried - 08/08/2008, 01:12 PM Exact entries for T-tetration Bell-matrix - by Gottfried - 09/24/2008, 08:22 PM RE: Exact entries for T-tetration Bell-matrix - by bo198214 - 09/26/2008, 07:30 AM RE: Exact entries for T-tetration Bell-matrix - by Gottfried - 09/26/2008, 09:56 AM

 Possibly Related Threads... Thread Author Replies Views Last Post My interpolation method [2020] tommy1729 1 315 02/20/2020, 08:40 PM Last Post: tommy1729 Kneser method question tommy1729 9 1,419 02/11/2020, 01:26 AM Last Post: sheldonison Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 613 09/09/2019, 10:55 PM Last Post: tommy1729 A fundamental flaw of an operator who's super operator is addition JmsNxn 4 7,526 06/23/2019, 08:19 PM Last Post: Chenjesu Tetration and Sign operator tetration101 0 603 05/15/2019, 07:55 PM Last Post: tetration101 2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,887 12/21/2016, 01:27 PM Last Post: tommy1729 Tommy's matrix method for superlogarithm. tommy1729 0 1,878 05/07/2016, 12:28 PM Last Post: tommy1729 [split] Understanding Kneser Riemann method andydude 7 8,763 01/13/2016, 10:58 PM Last Post: sheldonison [2015] New zeration and matrix log ? tommy1729 1 3,530 03/24/2015, 07:07 AM Last Post: marraco Kouznetsov-Tommy-Cauchy method tommy1729 0 2,214 02/18/2015, 07:05 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)