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Applying the iteration methods to simpler functions
#9
andydude Wrote:

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
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Messages In This Thread
RE: Applying the iteration methods to simpler functions - by Gottfried - 11/12/2007, 10:40 AM

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