Hi Chris, disclaimer: I am no expert in numerics.
On 13 Dez., 07:34, Chris Seberino <cseber...@gmail.com> wrote: > Why isn't the error improving as I increase the number of terms that > are summed? Am I doing something wrong in Sage? (Yes it is possible > that this infinite sum converges unimaginably slowly so I wanted to > check first I wasn't doing something dumb.) I think you use a precision that is too small The summands are of course very small. So, comparing the two results in a field with 53 digits precision may be pointless: sage: sum(10^(-k^2/10000.0) for k in range(-20000,20000)) == sum(10^(-k^2/10000.0) for k in range(-10000,10000)) True Note that the denominator "10000.0" in your exponent belongs to RR, which by default has 53 digits precision. Let us raise it to 6000: sage: d = RealField(6000)(10000) sage: d.precision() 6000 Unfortunately, the sums are now taking a very long time to compute. But we are only interested in their difference. So, it suffices to do (still taking about one minute): sage: 2*sum(10^(-k^2/d) for k in range(10000,20000)) 2.02019722722490674759723772962542922944721452394745083...e-10000 So there is a small progress in the summation! But I have no idea whether at the end of the day the small progress will be enough to cover the big difference -1.27897692436818e-13 to your theoretical result. Cheers, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
