Applying the iteration methods to simpler functions  Printable Version + Tetration Forum (https://math.eretrandre.org/tetrationforum) + Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) + Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) + Thread: Applying the iteration methods to simpler functions (/showthread.php?tid=84) Pages:
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RE: Applying the iteration methods to simpler functions  jaydfox  11/12/2007 Although the f(x)=x+d is nice and simple as a proof of concept, I think the case of f(x)=cx+d may be more important to demonstrate, because it has a logarithmic singularity and hence should have roughly similar convergence properties to the slog. It should also, for example, be possible to accelerate the convergence in a similar manner to my accelerated slog solution, as an independent verification of the process. And I think I've got the Bell vs. Carleman thing figured out now. I'll stick with Bell matrices then, since A) I'm used to working with column vectors, and B) it's similar to RPN notation, e.g., reading left to right, start with the operand, and then apply functions (or in this case, Bell matrices of functions). However, since they're just transposes with order reverses, it shouldn't really matter as long as we're clear which we're doing. RE: Applying the iteration methods to simpler functions  andydude  11/13/2007 Gottfried Wrote:Did you notice, that the fractional entries are just the bernoullinumbers, Woah! Neat! 