Interval methods that are guaranteed to underestimate (and the resulting new justification of Kaucher arithmetic)

@article{Kreinovich1996IntervalMT,
  title={Interval methods that are guaranteed to underestimate (and the resulting new justification of Kaucher arithmetic)},
  author={Vladik Kreinovich and Vyacheslav M. Nesterov and Nina A. Zheludeva},
  journal={Reliable Computing},
  year={1996},
  volume={2},
  pages={119-124}
}
AbstractOne of the main objectives of interval computations is, given the functionf(x1, ...,xn), andn intervals $$\bar x_1 ,...,\bar x_n$$ , to compute the range $$\bar y = f(\bar x_1 ,...,\bar x_n )$$ . Traditional methods of interval arithmetic compute anenclosure $$Y \supseteq \bar y$$ for the desired interval $$\bar y$$ , an enclosure that is often an overestimation. It is desirable to know how close this enclosure is to the desired range interval.For that purpose, we develop a new… 
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