Work

On the Distance to a Root of Polynomials

Year: 2011

Type: article

Abstract: In 2002, Dierk 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 D. 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 α to α, which leads to a better upper bound for the number of iterations of Newton′s method.

Source: Abstract and Applied Analysis

DOI: 10.1155/2011/495312

Author: Somjate Chaiya

Institutions: Centre of Excellence in Mathematics, Silpakorn University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,130

Funder: Commission on Higher Education