Document Type
Article
Publication Date
12-2010
Keywords
Roots of polynomials, Minimum root separation
Abstract
Let T=α 0 I+α 1 D+⋅⋅⋅+α n D n , where D is the differentiation operator and α0≠0 , and let f be a square-free polynomial with large minimum root separation. We prove that the roots of Tf are close to the roots of f translated by −α 1/α 0.
Publication Title
Constructive Approximation
Volume
32
Issue
3
First Page
523
Last Page
541
DOI
http://dx.doi.org/10.1007/s00365-009-9061-3
Required Publisher's Statement
© Springer International Publishing AG, Part of Springer Science+Business Media
This is the author's final version of the paper, the final publication is available at Springer via http://dx.doi.org/10.1007/s00365-009-9061-3
Recommended Citation
Ćurgus, Branko and Mascioni, Vania, "Stability of Roots of Polynomials Under Linear Combinations of Derivatives" (2010). Mathematics Faculty Publications. 66.
https://cedar.wwu.edu/math_facpubs/66
Subjects - Topical (LCSH)
Polynomials; Linear operators; 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
