Faster algorithms for computing Hong's bound on absolute positiveness

We show how to compute Hong’s bound for the absolute positiveness of a polynomial in d variables with maximum degree δ in O(n logd n) 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 δ.

• Type: Journal
• Year: 2010
• Where: JSC
• Authors: Kurt Mehlhorn, Saurabh Ray
• Keywords: Absolute Positiveness, Continued Fraction Algorithm, JSC 2010, Non-zero Coefficients