Choosing improved initial values for polynomial zerofinding in extended Newbery method to obtain convergence
type: Item
instance of: scholarly article
title: Choosing improved initial values for polynomial zerofinding in extended Newbery method to obtain convergence
zbMATH Open document ID: 1251.65070
DOI: 10.1155/2012/167927
author: Saeid Saidanlu
author: Nor'aini Aris
author: Ali Abd Rahman
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: In all polynomial zerofinding algorithms, a good convergence requires a very good initial approximation of the exact roots. The objective of the work is to study the conditions for determining the initial approximations for an iterative matrix zerofinding method. The investigation is based on the Newbery's matrix construction which is similar to Fiedler's construction associated with a characteristic polynomial. To ensure that convergence to both the real and complex roots of polynomials can be attained, three methods are employed. It is found that the initial values for the Fiedler's companion matrix which is supplied by the Schmeisser's method give a better approximation to the solution in comparison to when working on these values using the Schmeisser's construction towards finding the solutions. In addition, empirical results suggest that a good convergence can still be attained when an initial approximation for the polynomial root is selected away from its real value while other approximations should be sufficiently close to their real values. Tables and figures on the errors that resulted from the implementation of the method are also given.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6106126
zbMATH Keywords: initial approximations
zbMATH Keywords: Newbery's matrix construction
zbMATH Keywords: polynomial zerofinding
describes a project that uses: MultRoot
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/167927
OpenAlex ID: W2099163837
Wikidata QID: Q58905801
cites work: Q4342463
cites work: Q5674306
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DBLP publication ID: journals/jam/SaidanluAR12
description: scientific article; zbMATH DE number 6106126