Geodesic
An Algorithm for some Sum of Reciprocals
Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part II, Tome 137 (1984), pp. 3-6 
V. I. Vichirko. An Algorithm for some Sum of Reciprocals. Zapiski Nauchnykh Seminarov POMI, Computational complexity theory. Part II, Tome 137 (1984), pp. 3-6. http://geodesic.mathdoc.fr/item/ZNSL_1984_137_a0/
@article{ZNSL_1984_137_a0,
     author = {V. I. Vichirko},
     title = {An {Algorithm} for some {Sum} of {Reciprocals}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {3--6},
     year = {1984},
     volume = {137},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_137_a0/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We describe an algorithm for approximate evaluation of the set of sums $\varphi_k=\sum_{j=1}^ncj/(\lambda_j+\lambda_k),\;1\leqslant k\leqslant n$, where $0<\alpha\leqslant \lambda_j\leqslant \beta$. The time complexity of the algorithm is $O(n(t+\log n)\Psi(t+\log n))$, when computing $\varphi_k$ with precision $2^{-t}$, where the function $\Psi(l)$ denotes the time required for snjutiplieation of two integers of binary length $l$.