Áñôöóú Óùòò× Óö Óòøøòùùù Öö Blockinøøóò× Úöööòø× Óö Öööð Öóóø ×óððøøóò

We onsider the problem of isolating the real roots of a square-free polynomial with integer oeÆ ients using (variants of) the ontinued fra tion algorithm (CF). We introdu e a novel way to ompute a lower bound on the positive real roots of univariate polynomials. This allows us to derive a worst ase bound of e OB(d6 + d4 2 + d3 2) for isolating the real roots of a polynomial with integer oeÆ ients using the lassi variant [1℄ of CF, where d is the degree of the polynomial and the maximum bitsize of its oeÆ ients. This improves the previous bound of Sharma [30℄ by a fa tor of d3 and mat hes the bound derived by Mehlhorn and Ray [19℄ for another variant of CF; it also mat hes the worst ase bound of the subdivision-based solvers.