Annular Bounds for the Zeros of a Polynomial

Abstract

The problem of obtaining the smallest possible region containing all the zeros of a polynomial has been attracting more and more attention recently, and in this paper, we obtain several results providing the annular regions that contain all the zeros of a complex polynomial. Using MATLAB, we construct specific examples of polynomials and show that for these polynomials our results give sharper regions than those obtainable from some of the known results.

Solution to Polynomial Equations, a New Approach

“…[1] [2]) and many authors have presented techniques to estimate the bound of the roots and the number of the real roots of a polynomial (e.g. [3]- [9]). Starting with cubic equations, despite that formulas for the roots of the equations have existed for many years, using those formulas requires taking the roots of complex numbers repeatedly which introduces significant approximations into the results.…”