Toward accurate polynomial evaluation in rounded arithmetic

@article{Demmel2005TowardAP,
  title={Toward accurate polynomial evaluation in rounded arithmetic},
  author={James Demmel and Ioana Dumitriu and Olga Holtz},
  journal={ArXiv},
  year={2005},
  volume={abs/math/0508350}
}
Given a multivariate real (or complex) polynomial p and a domain D, we would like to decide whether an algorithm exists to evaluate p(x) accurately for all x ∈ D using rounded real (or complex) arithmetic. Here "accurately" means with relative error less than 1, i.e., with some correct leading digits. The answer depends on the model of rounded arithmetic: We assume that for any arithmetic operator op(a, b), for example a+b or ab, its computed value is op(a, b)� (1+δ), where |δ| is bounded by… 

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