• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Applying the iteration methods to simpler functions bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 11/12/2007, 11:23 AM andydude Wrote:You are confusing Bell matrices and Carleman matrices again.No, I consistently swapped them till now! So for everyone the correct usage: The $n$-th row of the Carleman matrix contains the coefficients of the $n$-th power of the power series. The $n$-th column of the Bell matrix contains the coefficients of the $n$-th power of the power series. The Bell and Carleman matrix are transposed to each other. Quote:doing the choppy thing gives: $\mathbf{C}(\mathbf{B}_x[x + d] - \mathbf{I})\mathbf{D}= \left[\begin{tabular}{ccc} 1 & 0& 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{tabular}\right]\left[\begin{tabular}{ccc} 0 & d & d^2 & d^3 \\ 0 & 0 & 2d & 3d^2 \\ 0 & 0 & 0 & 3d \\ 0 & 0 & 0 & 0 \end{tabular}\right]\left[\begin{tabular}{ccc} 0 & 0 & 0 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{tabular}\right] = \left[\begin{tabular}{ccc} d & d^2 & d^3 \\ 0 & 2d & 3d^2 \\ 0 & 0 & 3d \end{tabular}\right]$ ... I wanted to show a matrix-based way of doing the chopping process. Thanks for this. « Next Oldest | Next Newest »

 Messages In This Thread Applying the iteration methods to simpler functions - by bo198214 - 11/05/2007, 11:39 PM RE: Applying the iteration methods to simpler functions - by Gottfried - 11/06/2007, 12:30 AM RE: Applying the iteration methods to simpler functions - by andydude - 11/06/2007, 03:32 AM RE: Applying the iteration methods to simpler functions - by bo198214 - 11/06/2007, 10:36 AM RE: Applying the iteration methods to simpler functions - by jaydfox - 11/09/2007, 05:34 AM RE: Applying the iteration methods to simpler functions - by bo198214 - 11/09/2007, 08:36 AM RE: Applying the iteration methods to simpler functions - by andydude - 11/12/2007, 09:40 AM RE: Applying the iteration methods to simpler functions - by Gottfried - 11/12/2007, 10:40 AM RE: Applying the iteration methods to simpler functions - by andydude - 11/13/2007, 12:39 AM RE: Applying the iteration methods to simpler functions - by bo198214 - 11/12/2007, 11:23 AM RE: Applying the iteration methods to simpler functions - by jaydfox - 11/12/2007, 04:41 PM

 Possibly Related Threads... Thread Author Replies Views Last Post The AB functions ! tommy1729 0 1,957 04/04/2017, 11:00 PM Last Post: tommy1729 the inverse ackerman functions JmsNxn 3 6,917 09/18/2016, 11:02 AM Last Post: Xorter Look-alike functions. tommy1729 1 2,521 03/08/2016, 07:10 PM Last Post: hixidom Inverse power tower functions tommy1729 0 2,230 01/04/2016, 12:03 PM Last Post: tommy1729 [2014] composition of 3 functions. tommy1729 0 2,115 08/25/2014, 12:08 AM Last Post: tommy1729 How many methods have this property ? tommy1729 1 3,031 05/22/2014, 04:56 PM Last Post: sheldonison Intresting functions not ? tommy1729 4 6,091 03/05/2014, 06:49 PM Last Post: razrushil [Update] Comparision of 5 methods of interpolation to continuous tetration Gottfried 30 35,401 02/04/2014, 12:31 AM Last Post: Gottfried applying continuum sum to interpolate any sequence. JmsNxn 1 3,367 08/18/2013, 08:55 PM Last Post: tommy1729 generalizing the problem of fractional analytic Ackermann functions JmsNxn 17 25,940 11/24/2011, 01:18 AM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)