The convergence of a family of parallel zero-finding methods
type: Item
instance of: scholarly article
title: The convergence of a family of parallel zero-finding methods
zbMATH Open document ID: 1069.65052
publication date: 2005-03-08T00:00:00Z
review text: The aim of the paper is to introduce computationally verifiable initial conditions which could guarantee the convergence of the recently introduced class of fourth-order methods [cf. \textit{T. Sakurai} and \textit{M. S. Petković}, J. Comput. Appl. Math. 72, 275--291 (1996; Zbl 0859.65048)] for simultaneous finding polynomial zeros. First, the authors introduce some basic facts on circular complex arithmetic. Then they prove several technical lemmas. Finally, they state two significant theorems concerning the initial conditions for the convergence. These conditions depend only on polynomial coefficients, its degree and initial approximations of zeros, thus they can be easily verified.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 12D10
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 2142473
zbMATH Keywords: zeros of polynomials
zbMATH Keywords: simultaneous methods
zbMATH Keywords: convergence
zbMATH Keywords: circular complex arithmetic
author: M. S. Petković
author: Snežana Ilić
author: Lidija Z. Rančić
reviewed by: Przemysław Stpiczyński
MaRDI profile type: Publication
full work available at URL: j.camwa.2004.01.010
OpenAlex ID: W113723831
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DOI: 10.1016/J.CAMWA.2004.01.010
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142473