We discuss applications of some new results on
univariate polynomials with real coefficients to the computation of
bounds for positive roots. The computation of such bounds is a key step
in CF_algorithms for real root isolation. We study the optimality and
discuss strategies for improving the computation of upper and lower
bounds. Our results are compared with classical methods and with results
of Kioustelidis, Stefanescu and Akritas-Strzebonski-Vigklas.