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. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Kerber, M. (2009). On the complexity of reliable root approximation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5743 LNCS, pp. 155–167). https://doi.org/10.1007/978-3-642-04103-7_15
Mendeley helps you to discover research relevant for your work.