Section: New Results
Worst case complexity of the Continued Fraction (CF) algorithm.
In  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 for isolating the real roots of a polynomial with integer coefficients using the classic variant of CF, where is the degree of the polynomial and the maximum bitsize of its coefficients. This improves the previous bound of Sharma by a factor of 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 STURM, DESCARTES, and BERNSTEIN.