A new iterative method of asymptotic order 1+√2 for the computation of fixed points

DOI10.1080/00207160500113546zbMath1122.65051OpenAlexW2155624849MaRDI QIDQ5712019

Ioannis K. Argyros

Publication date: 22 December 2005

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160500113546

zbMATH Keywords

semilocal convergenceBanach spacelocal convergencemonotone convergenceNewton-like methodscontraction mapping theoremdivided differencespotl space

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (9)

On semilocal convergence of two step Kurchatov method ⋮ A high-order newton-like method ⋮ A third order method for fixed points in Banach spaces ⋮ Expanding the applicability of Stirling's method under weaker conditions and restricted convergence regions ⋮ A Stirling-like method with Hölder continuous first derivative in Banach spaces ⋮ Semilocal convergence of Stirling's method under Hölder continuous first derivative in Banach spaces ⋮ Convergence of Stirling's method under weak differentiability condition ⋮ SEMILOCAL CONVERGENCE OF A STIRLING-LIKE METHOD IN BANACH SPACES ⋮ An iteration method with maximal order based on standard information

Uses Software

• BRENT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Newton-like methods for the computation of fixed points
• Über ein Verfahren der Ordnung \(1+\sqrt 2\) zur Nullstellenbestimmung
• Some supplementary results on the \(1+\sqrt 2\) order method for the solution of nonlinear equations
• Convergence of general iteration schemes
• Convergence of Stirling's method in Banach spaces
• An improved error analysis for Newton-like methods under generalized conditions
• Secant-like methods for solving nonlinear integral equations of the Hammerstein type
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
• Convergence domains of certain iterative methods for solving nonlinear equations
• A family of Chebyshev-Halley type methods in Banach spaces
• Multipoint Super-Halley Type Approximation Algorithms in Banach Spaces
• Newton’s Method for Convex Operators in Partially Ordered Spaces
• A new high order method of regula falsi type for computing a root of an equation

This page was built for publication: A new iterative method of asymptotic order 1+√2 for the computation of fixed points