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 Applying the iteration methods to simpler functions Gottfried Ultimate Fellow Posts: 758 Threads: 117 Joined: Aug 2007 11/12/2007, 10:40 AM (This post was last modified: 11/12/2007, 10:41 AM by Gottfried.) andydude Wrote:$\left[\begin{tabular}{c} g_1 \\ g_2 \\ g_3 \end{tabular}\right] == \left[\begin{tabular}{ccc} \frac{1}{d} & -\frac{1}{2} & \frac{d}{6} \\ 0 & \frac{1}{2d} & -\frac{1}{2} \\ 0 & 0 & \frac{1}{3d} \end{tabular}\right]$ Hmm, nice coincidence here. Did you notice, that the fractional entries are just the bernoulli-numbers, resp binomially weighted bernoulli-numbers? It would be more obvious, if your matrix were of bigger size (but I don't know, which iterative function that required). When I was fiddling with the pascal-matrix last year I found the inverse of the shifted pascal-matrix (where -before shifting- the diagonal is removed) is just a matrix containing the bernoulli-numbers as it was found by Faulhaber and J Bernoulli, giving coefficients (with a little modification) of bernoulli-polynomials. I found, that it is part of the eigensystem for the *column-signed* pascal-matrix. Perhaps you like to have a look at my according small treatise at p-matrix Things converge... Gottfried Gottfried Helms, Kassel « 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

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