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We consider the problem of isolating the real roots of a square-freepolynomial with integer coefficients using (variants of) the continued fractionalgorithm (CF). We introduce a novel way to compute a lower bound on thepositive real roots of univariate polynomials. This allows us to derive a worstcase bound of $\sOB(d^6 + d^4\tau^2 + d^3\tau^2)$ for isolating the real rootsof a polynomial with integer coefficients using the classic variant\cite{Akritas:implementation} of CF, where $d$ is the degree of the polynomialand $\tau$ the maximum bitsize of its coefficients. This improves the previousbound of Sharma \cite{sharma-tcs-2008} by a factor of $d^3$ and matches thebound derived by Mehlhorn and Ray \cite{mr-jsc-2009} for another variant of CF;it also matches the worst case bound of the subdivision-based solvers.

Improved complexity bounds for real root isolation using Continued Fractions