A note about "Faster algorithms for computing Hong's bound on absolute positiveness" by K. Mehlhorn and S. Ray

TL;DR

This paper corrects a previously proposed linear-time algorithm for computing Hong's bound on positive roots of polynomials, ensuring accurate and efficient root bound calculations.

Contribution

It identifies errors in the original algorithm and provides a corrected, reliable version for computing Hong's bound.

Findings

Original algorithm was incorrect

Corrected algorithm runs in linear time

Ensures accurate computation of Hong's bound

Abstract

We show that a linear-time algorithm for computing Hong's bound for positive roots of a univariate polynomial, described by K. Mehlhorn and S. Ray in an article "Faster algorithms for computing Hong's bound on absolute positiveness", is incorrect. We present a corrected version.