An efficient numerical method for computation of the number of complex zeros of real polynomials inside the open unit disk

Abstract

In this paper, a simple and efficient numerical method is proposed for computing the number of complex zeros of a real polynomial lying inside the unit disk. The proposed protocol uses the Boubaker polynomial expansion scheme (BPES) to build sequence of polynomials based on the concept of Sturm sequences. The method is used in a direct way without using any restrictions in reference to other existing methods. The protocol is applied to some example polynomials of different orders and utility of the algorithm is noticed.