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.
Recommended Citation
Ćurgus, Branko and Mascioni, Vania, "On the Location of Critical Points of Polynomials" (2003). Mathematics Faculty Publications. 7.
https://cedar.wwu.edu/math_facpubs/7
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
Comments
Communicated by N. Tomczak-Jaegermann