Analysis of the quasi-Laguerre method
type: Item
instance of: scholarly article
title: Analysis of the quasi-Laguerre method
zbMATH Open document ID: 0942.65051
published in: Numerische Mathematik
publication date: 1999-11-01T00:00:00Z
review text: The quasi-Laguerre method is an iterative process for finding real or complex roots of a polynomial \(p\). It is based on the logarithmic derivative \(q={p'\over p}\) and starts with two values \(x_0\), \(x_1\) and the logarithmic derivatives \(q_0\), \(q_1\) at \(x_0\) and \(x_1\), respectively. The author presents three derivations of his method and proves theoretical results concerning global and local convergence and monotonicity of the sequence of iterates. In addition, he shows that under suitable conditions the convergence order of the method is \(1+\sqrt 2\).
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 1356180
zbMATH Keywords: roots of polynomials
zbMATH Keywords: iterative method
zbMATH Keywords: quasi-Laguerre method
zbMATH Keywords: convergence
zbMATH Keywords: monotonicity
author: Xiulin Zou
reviewed by: Günter Mayer
MaRDI profile type: Publication
full work available at URL: s002110050428
OpenAlex ID: W1974176735
DOI: 10.1007/S002110050428
description: scientific article; zbMATH DE number 1356180