A Generalized Kahan-Babuška-Summation-Algorithm

@article{Klein2005AGK,
  title={A Generalized Kahan-Babu{\vs}ka-Summation-Algorithm},
  author={Andr{\'e} Klein},
  journal={Computing},
  year={2005},
  volume={76},
  pages={279-293}
}
In this article, we combine recursive summation techniques with Kahan-Babuška type balancing strategies [1], [7] to get highly accurate summation formulas. An i-th algorithm have only error beyond 1upl and thus allows to sum many millions of numbers with high accuracy. The additional afford is a small multiple of the naive summation. In addition we show that these algorithms could be modified to provide tight upper and lower bounds for use with interval arithmetic. 
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