A free-derivative iteration method of order three having convergence of both point and interval for nonlinear equations
type: Item
instance of: scholarly article
title: A free-derivative iteration method of order three having convergence of both point and interval for nonlinear equations
zbMATH Open document ID: 1030.65047
DOI: 10.1016/S0096-3003(02)00029-2
author: Yiran Zhu
author: Xinyuan Wu
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: A new iterative formulae containing only the values of a nonlinear function \(f\) is proposed to compute the both sequences, \(\{ x_n\}\) and \(\{[a_n,b_n]\}\), converging cubically to the unique zero of \(f\). The numerical results show that the proposed algorithm leads to solution in certain cases where the Newton or Steffensen method fails.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 1977923
zbMATH Keywords: nonlinear equations
zbMATH Keywords: deviative-free method
zbMATH Keywords: comparison of methods
zbMATH Keywords: Newton emthod
zbMATH Keywords: numerical results
zbMATH Keywords: algorithm
zbMATH Keywords: Steffensen method
zbMATH Keywords: free-derivative iteration method
zbMATH Keywords: convergence
reviewed by: Jacek Gilewicz
MaRDI profile type: Publication
cites work: New high-order convergence iteration methods without employing derivatives for solving nonlinear equations
cites work: On Q-order and R-order of convergence
full work available at URL: s0096-3003(02)00029-2
OpenAlex ID: W1979349464
description: scientific article; zbMATH DE number 1977923