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On the Regions Containing All the Zeros of a Polynomial

In: Nonlinear Analysis

Author

Listed:
  • Chadia Affane-Aji

    (Tuskegee University)

  • N. K. Govil

    (Auburn University)

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.

Suggested Citation

  • Chadia Affane-Aji & N. K. Govil, 2012. "On the Regions Containing All the Zeros of a Polynomial," Springer Optimization and Its Applications, in: Panos M. Pardalos & Pando G. Georgiev & Hari M. Srivastava (ed.), Nonlinear Analysis, edition 127, chapter 0, pages 39-55, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-3498-6_3
    DOI: 10.1007/978-1-4614-3498-6_3
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