http://www.stanford.edu/~glynn/PDF/0208.pdf
The first looks like Brent's suggestion for a corrected mean computation, with no memory required. The additional computational cost that I complained about is docuemented to be 3x the flops cost of the direct computation, but the computation is claimed to be more stable. So the question is: do we pay the flops cost to get the numerical stability? The example in the paper is compelling; but it uses small words (err, numbers I mean -- sorry, slipped in to my native Fortran for a moment there ;-)). So how do we go about deciding whether the stability in the mean computation is worth the increased computational effort? I would prefer not to answer "let the user decide". To make the decision harder, we should note that it is actually worse than 3x, since in the no storage version, the user may request the mean only rarely (if at all) and the 3x comparison is against computiing the mean for each value added.
The variance formula looks better than what we have now, still requiring no memory. Should we implement this for the no storage case?
Phil
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