Ultimately Fast Accurate Summation

@article{Rump2009UltimatelyFA,
  title={Ultimately Fast Accurate Summation},
  author={Siegfried M. Rump},
  journal={SIAM J. Sci. Comput.},
  year={2009},
  volume={31},
  pages={3466-3502}
}
  • S. Rump
  • Published 1 August 2009
  • Computer Science
  • SIAM J. Sci. Comput.
We present two new algorithms FastAccSum and FastPrecSum, one to compute a faithful rounding of the sum of floating-point numbers and the other for a result “as if” computed in $K$-fold precision. Faithful rounding means the computed result either is one of the immediate floating-point neighbors of the exact result or is equal to the exact sum if this is a floating-point number. The algorithms are based on our previous algorithms AccSum and PrecSum and improve them by up to 25%. The first… 
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