On the Regions Containing All the Zeros of a Polynomial

Chadia Affane-Aji () and N. K. Govil ()
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Chadia Affane-Aji: Tuskegee University
N. K. Govil: Auburn University

Chapter Chapter 3 in Nonlinear Analysis, 2012, pp 39-55 from Springer

Abstract: Abstract Let p(z)=a 0+a 1 z+a 2 z 2+a 3 z 3+⋯+a n z n be a polynomial of degree n, where the coefficients a k may be complex. Then it is obviously of interest to study problems concerning the location of the zeros of the polynomial p(z). These problems, besides being of theoretical interest, have important applications in many areas, such as signal processing, communication theory, and control theory, and for this reason there is always a need for better and better results. In this paper we make a systematic study of these problems by presenting some results starting from the results of Gauss and Cauchy, who we believe were the earliest contributors in this subject, to some of the most recent ones. Our paper is expository.

Keywords: Complex polynomials; Location of zeros of polynomials; Complex zeros; Real zeros; 30A10; 30A15; 26C10 (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4614-3498-6_3

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DOI: 10.1007/978-1-4614-3498-6_3

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