A Near-Optimal Algorithm for Computing Real Roots of Sparse Polynomials

@inproceedings{Sagraloff2014ANA,
  title={A Near-Optimal Algorithm for Computing Real Roots of Sparse Polynomials},
  author={Michael Sagraloff},
  booktitle={ISSAC},
  year={2014}
}
Let <i>p</i> ∈ Z[<i>x</i>] be an arbitrary polynomial of degree <i>n</i> with <i>k</i> non-zero integer coefficients of absolute value less than 2<sup>τ</sup>. In this paper, we answer the open question whether the real roots of <i>p</i> can be computed with a number of arithmetic operations over the rational numbers that is polynomial in the input size of the sparse representation of <i>p</i>. More precisely, we give a deterministic, complete, and certified algorithm that determines isolating… CONTINUE READING
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