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Article Dans Une Revue Theoretical Computer Science Année : 2012

Improved bounds for the CF algorithm

Elias Tsigaridas

Résumé

We consider the problem of isolating the real roots of a square-free polynomial with integer coefficients using the classic variant of the continued fraction algorithm (CF), introduced by Akritas. %% We compute a lower bound on the positive real roots of univariate polynomials using exponential search. This allows us to derive a worst case bound of \sOB(d4τ2) for isolating the real roots of a polynomial with integer coefficients using the {\em classic variant of CF}, where d is the degree of the polynomial and τ the maximum bitsize of its coefficients. This improves the previous bound of Sharma by a factor of d3 and matches the bound derived by Mehlhorn and Ray for another variant of CF which is combined with subdivision; it also matches the worst case bound of the classical subdivision-based solvers \func{sturm}, \func{descartes}, and \func{bernstein}.
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Dates et versions

hal-00776230 , version 1 (15-01-2013)

Identifiants

  • HAL Id : hal-00776230 , version 1

Citer

Elias Tsigaridas. Improved bounds for the CF algorithm. Theoretical Computer Science, 2012, pp.1-12. ⟨hal-00776230⟩
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