Recently, I worked on the problem for computing the approximate sum of a list of sorted nonnegative numbers. For any fixed $\epsilon>0$, 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.