Fast and Parallel Interval Arithmetic

@article{Rump1999FastAP,
  title={Fast and Parallel Interval Arithmetic},
  author={Siegfried M. Rump},
  journal={BIT Numerical Mathematics},
  year={1999},
  volume={39},
  pages={534-554}
}
Infimum-supremum interval arithmetic is widely used because of ease of implementation and narrow results. In this note we show that the overestimation of midpoint-radius interval arithmetic compared to power set operations is uniformly bounded by a factor 1.5 in radius. This is true for the four basic operations as well as for vector and matrix operations, over real and over complex numbers. Moreover, we describe an implementation of midpoint-radius interval arithmetic entirely using BLAS… CONTINUE READING

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