---
res:
  bibo_abstract:
  - We consider the problem of approximating all real roots of a square-free polynomial
    f. Given isolating intervals, our algorithm refines each of them to a width at
    most 2-L, that is, each of the roots is approximated to L bits after the binary
    point. Our method provides a certified answer for arbitrary real polynomials,
    only requiring finite approximations of the polynomial coefficient and choosing
    a suitable working precision adaptively. In this way, we get a correct algorithm
    that is simple to implement and practically efficient. Our algorithm uses the
    quadratic interval refinement method; we adapt that method to be able to cope
    with inaccuracies when evaluating f, without sacrificing its quadratic convergence
    behavior. We prove a bound on the bit complexity of our algorithm in terms of
    degree, coefficient size and discriminant. Our bound improves previous work on
    integer polynomials by a factor of deg f and essentially matches best known theoretical
    bounds on root approximation which are obtained by very sophisticated algorithms.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Michael
      foaf_name: Kerber, Michael
      foaf_surname: Kerber
      foaf_workInfoHomepage: http://www.librecat.org/personId=36E4574A-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-8030-9299
  - foaf_Person:
      foaf_givenName: Michael
      foaf_name: Sagraloff, Michael
      foaf_surname: Sagraloff
  bibo_doi: 10.1145/1993886.1993920
  dct_date: 2011^xs_gYear
  dct_language: eng
  dct_publisher: Springer@
  dct_title: Root refinement for real polynomials@
...