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 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.