On the Complexity of Reliable Root Approximation

  • Michael Kerber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5743)


This work addresses the problem of computing a certified ε-approximation of all real roots of a square-free integer polynomial. We proof an upper bound for its bit complexity, by analyzing an algorithm that first computes isolating intervals for the roots, and subsequently refines them using Abbott’s Quadratic Interval Refinement method. We exploit the eventual quadratic convergence of the method. The threshold for an interval width with guaranteed quadratic convergence speed is bounded by relating it to well-known algebraic quantities.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Michael Kerber
    • 1
  1. 1.Max-Planck Institut für InformatikSaarbrückenGermany

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