On the guaranteed convergence of the square-root iteration method
type: Item
instance of: scholarly article
title: On the guaranteed convergence of the square-root iteration method
zbMATH Open document ID: 1054.65048
author: M. S. Petković
author: Lidija Z. Rančić
published in: Journal of Computational and Applied Mathematics
publication date: 2004-08-10T00:00:00Z
review text: The paper is devoted to the convergence analysis of the so-called Ostrowski-like iterative method for the simultaneous approximation of all simple zeros \(z_{i}\) of a given polynomial \(P\). (This method is an extension of the well-known square-root method \[ z^{m+1}_{i}=z^{m}_{i}-\frac{P(z^{m}_{i})}{\sqrt{P'(z^{m}_{i})-P(z^{m}_{i})P''(z^{m}_{i})}}, \] also known as Ostrowski's method). The main result of the paper (Theorem 1) asserts that for a polynomial of degree \(n\geq3\) with simple zeros, satisfying a certain initial condition, the Ostrowski-like simultaneous method is convergent and its order of convergence is four.
reviewed by: Vasile Berinde
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 2085563
zbMATH Keywords: simple zeros
zbMATH Keywords: Ostrowski-like iteration
zbMATH Keywords: initial condition
zbMATH Keywords: convergence
zbMATH Keywords: zeros of polynomials
zbMATH Keywords: point estimation
zbMATH Keywords: square-root method
MaRDI profile type: Publication
full work available at URL: j.cam.2003.12.040
OpenAlex ID: W2014908629
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DOI: 10.1016/J.CAM.2003.12.040
description: scientific article; zbMATH DE number 2085563