Faster algorithms for computing Hong's bound on absolute positiveness

Authors:
Kurt Mehlhorn;Saurabh Ray
Affiliations:
Max Planck Institut für Informatik, Saarbrücken, Germany;Max Planck Institut für Informatik, Saarbrücken, Germany
Venue:
Journal of Symbolic Computation
Year:
2010

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Abstract

We show how to compute Hong's bound for the absolute positiveness of a polynomial in d variables with maximum degree @d in O(nlog^dn) time, where n is the number of non-zero coefficients. For the univariate case, we give a linear time algorithm. As a consequence, the time bounds for the continued fraction algorithm for real root isolation improve by a factor of @d.