## Section: New Results

### Worst case complexity of the Continued Fraction (CF) algorithm.

In [16]
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 $\tilde{O}\left({d}^{4}{\tau}^{2}\right)$ for isolating the
real roots of a polynomial with integer coefficients
using the *classic variant of CF*, where $d$ is
the degree of the polynomial and $\tau $ the maximum
bitsize of its coefficients. This improves the
previous bound of Sharma by a factor of ${d}^{3}$ 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.