Computing real zeros of a polynomial by branch and bound and branch and reduce algorithms

Abstract

In this paper we propose two algorithms based on branch and bound method and reduced interval techniques to compute all real zeros of a polynomial. Quadratic bounding functions are proposed which are better than the well known linear underestimator. Experimental result shows the efficiency of the two algorithms when facing ill-conditioned polynomials.

Keywords

• Global optimization quadratic upper function quadratic lower function root-finding Bound and Reduce Branch and Bound w-subdivision