Document Type

Article

Publication Date

1-2003

Keywords

Roots of polynomials, critical points of polynomials, separation of roots

Abstract

Given a polynomial p of degree n ≥ 2 and with at least two distinct roots let Z(p) = { z: p(z) = 0}. For a fixed root α ∈ Z(p) we define the quantities ω(p, α) := min (formula) and (formula). We also define ω (p) and τ (p) to be the corresponding minima of ω (p,α) and τ (p,α) as α runs over Z(p). Our main results show that the ratios τ (p,α)/ω (p,α) and τ (p)/ω (p) are bounded above and below by constants that only depend on the degree of p. In particular, we prove that (formula), for any polynomial of degree n.

Publication Title

Proceedings of the American Mathematical Society

Volume

131

Issue

1

First Page

253

Last Page

264

Required Publisher's Statement

First published in "Proceedings of the American Mathematical Society" in 2003, published by the American Mathematical Society.

Comments

Communicated by N. Tomczak-Jaegermann

Subjects - Topical (LCSH)

Polynomials; Roots, Numerical

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

Included in

Mathematics Commons

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