On the distance to a root of polynomials
type: Item
instance of: scholarly article
title: On the distance to a root of polynomials
zbMATH Open document ID: 1253.37049
DOI: 10.1155/2011/495312
author: Somjate Chaiya
published in: Abstract and Applied Analysis
publication date: 2012-01-16T00:00:00Z
review text: Summary: In [Ergodic Theory Dyn. Syst. 22, No. 3, 935--945 (2002; Zbl 1011.37024)], \textit{D. Schleicher} gave an explicit estimate of an upper bound for the number of iterations of Newton's method it takes to find all roots of polynomials with prescribed precision. In this paper, we provide a method to improve the upper bound given by Schleicher. We give here an iterative method for finding an upper bound for the distance between a fixed point \(z\) in an immediate basin of a root \(\alpha\) to \(\alpha\), which leads to a better upper bound for the number of iterations of Newton's method.
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 65H04
zbMATH DE Number: 5997802
zbMATH Keywords: Newton's method
zbMATH Keywords: roots of polynomials
zbMATH Keywords: dynamical systems
zbMATH Keywords: basin of attraction
Wikidata QID: Q58654247
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/495312
OpenAlex ID: W2032231543
cites work: Q3482588
cites work: Q3653985
cites work: On the number of iterations of Newton's method for complex polynomials
Recommended article: On the distance between the roots of a polynomial
Recommended article: ON THE DISTANCE BETWEEN ROOTS OF INTEGER POLYNOMIALS
Recommended article: Distances from differences of roots of polynomials to the nearest integers
Recommended article: Q3203113
Recommended article: The distance to square-free polynomials
Recommended article: ON THE DISTANCE TO A ROOT OF COMPLEX POLYNOMIALS UNDER NEWTON'S METHOD
Recommended article: On the approximate roots of polynomials
Recommended article: Q3062306
Recommended article: On the bounds for the roots of a polynomial
Recommended article: Q3714319
description: scientific article; zbMATH DE number 5997802