Gareth wrote: << On Monday 09 June 2008, Andy Latto wrote:
On Sun, Jun 8, 2008 at 5:05 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Speaking of math software, can anyone tell me if there exists analytic continuation software? ... . . . and all this to a pre-specified level of numerical accuracy.
I don't think this is possible. In finite time the software can only . . .
The same argument proves that numerical integration and differentiation are impossible. And yet, if you pick a function you're interested in and ask Maple or Mathematica or whatever to integrate it for you over a given range to a given level of accuracy, they can generally do it pretty well.
Yes, though usually Maple or Mathematica has more than just the ability to evaluate the function at a given point, but an algorithm to do so -- whose details must go into determining the accuracy of the calculation of the function's derivative or integral. In fact, I can provide an algorithm for the initial function (for what I need) . . . but it would be somewhat tricky for it to work backward through a sequence of n power series to be sure that the final answer is of a given accuracy. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele