A unifying framework for generalizations of the Enestrom-Kakeya theorem

Aaron Melman

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arXiv · 1711.09517

A unifying framework for generalizations of the Enestrom-Kakeya theorem

Aaron Melman

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Abstract

The classical Enestrom-Kakeya theorem establishes upper and lower bounds on the zeros of a polynomial with positive coefficients that are explicit functions of those coefficients. We establish a unifying framework that incorporates this theorem and several similar ones as special cases, while generating new theorems of a similar type. These establish zero inclusion and exclusion regions consisting of a single disk or the union of several disks in the complex plane. Our framework is built on two basic tools, namely a generalization of an observation by Cauchy, and a family of polynomial multipliers. Its approach is transparent and reduces algebraic manipulations to a minimum.

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Aaron Melman. 2017-11-27. A unifying framework for generalizations of the Enestrom-Kakeya theorem. https://arxiv.org/abs/1711.09517

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