Approximate sum of a sorted list Recently,  I worked on the problem for computing the approximate sum of a list of sorted nonnegative numbers. For any fixed $\epsilon&gt;0$,  an $O(\log n)$ time approximation scheme has been derived such that it gives an $(1+\epsilon)$-approximation for the sum. The paper is posted at http://arxiv.org/abs/1112.0520, which has not been finalized.

I have been looking for existing works for this problem, but I only got a few remotely related papers,  and cited them.  Was this problem studied before?   If someone knows any existing researches about this problem, please let me know. I will appreciate the help, and update the citations accordingly. If the results are old, the paper will be dumped into a garbage can.
This problem is solved in the following paper, where more general problems are mostly addressed: http://valis.cs.uiuc.edu/~sariel/papers/06/integrate/ .