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CASC
2009
Springer

On the Complexity of Reliable Root Approximation

13 years 10 months ago
On the Complexity of Reliable Root Approximation
This work addresses the problem of computing a certified ǫ-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.
Michael Kerber
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CASC
Authors Michael Kerber
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