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 Matrix Operator Method bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/27/2007, 02:36 PM Hm, then I somewhere must have an error in my computation. I wanted to compute the Matrix logarithm via the formula $\log(A)=\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} (A-I)^n$. For A being the power derivation matrix of $e^x$ at 0, i.e. truncated to 6x6 $ A=\left( \begin{matrix} 1&0&0&0&0&0\\ 1&1&1/2&1/6&1/24&{\frac {1}{120}}\\ 1&2&2&4/3&2/3&{\frac {4}{ 15}}\\ 1&3&9/2&9/2&{\frac {27}{8}}&{\frac {81}{40}} \\ 1&4&8&{\frac {32}{3}}&{\frac {32}{3}}&{\frac {128} {15}}\\ 1&5&{\frac {25}{2}}&{\frac {125}{6}}&{\frac { 625}{24}}&{\frac {625}{24}} \end{matrix} \right) $ (which is transposed to the matrix you usually uses). This Matrix is diagonalizable, but if I compute the logarithm via the above sum then the entries do not converge. For example: $\sum_{n=1}^{10} \frac{(-1)^{n+1}}{n} (A-I)^n\\= \left( \begin{matrix} 0.0& 0.0& 0.0& 0.0& 0.0& 0.0\\ - 44101769800.0&- 145224229100.0&- 279795780200.0& - 388116737400.0&- 423988471200.0&- 383041240500.0\\ - 594655919700.0&- 1958162913000.0&- 3772688135000.0&- 5233257693000.0 &- 5716942159000.0&- 5164821148000.0\\ - 3307574479000.0&- 10891625760000.0&- 20984315030000.0&- 29108244400000.0&- 31798577400000.0&- 28727589090000.0 \\ - 11906282180000.0&- 39206606270000.0&- 75537279400000.0&- 104781003800000.0&- 114465400800000.0&- 103410758300000.0\\ - 33057719360000.0&- 108856901800000.0&- 209728793100000.0&- 290923814800000.0&- 317812483800000.0&- 287119336600000.0 \end{matrix} \right)$ « 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

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