Error estimation of floating-point summation and dot product

@article{Rump2012ErrorEO,
  title={Error estimation of floating-point summation and dot product},
  author={Siegfried M. Rump},
  journal={BIT Numerical Mathematics},
  year={2012},
  volume={52},
  pages={201-220}
}
  • S. Rump
  • Published 1 March 2012
  • Mathematics
  • BIT Numerical Mathematics
We improve the well-known Wilkinson-type estimates for the error of standard floating-point recursive summation and dot product by up to a factor 2. The bounds are valid when computed in rounding to nearest, no higher order terms are necessary, and they are best possible. For summation there is no restriction on the number of summands. The proofs are short by using a new tool for the estimation of errors in floating-point computations which cures drawbacks of the “unit in the last place (ulp… 

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