On the \(R\)-order of some accelerated methods for the simultaneous finding of polynomial zeros
type: Item
instance of: scholarly article
title: On the \(R\)-order of some accelerated methods for the simultaneous finding of polynomial zeros
zbMATH Open document ID: 0781.65042
DOI: 10.1007/BF02248695
published in: Computing
publication date: 1993-05-04T00:00:00Z
review text: Starting from fixed-point relations derived in previous work, generalized iterative methods for the simultaneous approximation of the roots of a polynomial are investigated. Assuming fairly good initial guesses, the single step methods considered are shown to have an \(R\)-order of convergence not less than four. After a tedious proof of convergence using initial knowledge about the separation of the roots, the \(R\)-order is derived by appealing to a lower bound estimate through the spectral radius of a matrix. Furthermore the computational efficiency on a serial machine is derived, considering the processor time for different operations. Numerical examples demonstrating these claims are provided.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 151893
zbMATH Keywords: multiple complex zeros
zbMATH Keywords: iterative methods
zbMATH Keywords: roots of a polynomial
zbMATH Keywords: single step methods
zbMATH Keywords: \(R\)-order of convergence
zbMATH Keywords: computational efficiency
zbMATH Keywords: Numerical examples
author: M. S. Petković
author: Lidija V. Stefanović
author: Z. M. Marjanović
reviewed by: Hermann G. Matthies
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02248695
OpenAlex ID: W185361392
description: scientific article; zbMATH DE number 151893