Computer algebra: symbolic and algebraic computation (2nd ed.)
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Almost tight recursion tree bounds for the Descartes method
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
On the complexity of real solving bivariate systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Complexity of real root isolation using continued fractions
Theoretical Computer Science
Efficient real root approximation
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Univariate real root isolation in an extension field
Proceedings of the 36th international symposium on Symbolic and algebraic computation
On the boolean complexity of real root refinement
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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This work addresses the problem of computing a certified *** -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.