08/26/2009, 08:08 PM
(08/26/2009, 07:21 PM)jaydfox Wrote: Count "numerically" as a singularity? It's not a singularity, so at best it means that you just need more terms in the power series.Of course that was what I was saying. Little changes in the intput cause big changes in the output that means increasing the precision, doesnt it?
Quote: And as mentioned before, you must truncate the slog series before reverting, or of course you'll get bizarre results.As far as I remember you only suggested that for recentering. Which I dont do, I thought that became clear now. The development slog at 0, sexp at -1, behaves like expected with convergence radius 1. So there is no "of course" if I do the same procedure just with a conjugated function.
Quote:But the closest singularity is at -2, so that is what limits the radius of convergence.Well I mentioned that several times and about this discrepance is all my reasoning, for the case you didnt notice.
Quote:When I reverted a 600-term truncation of a 1200-term slog, I got a sexp function that approximated the logarithmic singularity at x=-2 very nicely.Are you talking about recentering the Abel function or about my method of shift-conjugation of the original function? Computing the Carleman matrix of exp at some other place than 0 is unexpectedly more time consuming, as I already mentioned. 100 terms take perhaps 10-20 min at my place. While 400 at 0 takes perhaps 5min (without your acceleration method of course)