Local convergence of two competing third order methods in Banach space

DOI10.4064/am41-4-5zbMath1316.65056OpenAlexW2316533937MaRDI QIDQ2939954

Santhosh George, Ioannis K. Argyros

Publication date: 23 January 2015

Published in: Applicationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/am41-4-5

zbMATH Keywords

third-order methodsBanach spacenonlinear operator equationlocal convergenceconvergence ballmidpoint method

Mathematics Subject Classification ID

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

Related Items (4)

Extending the applicability of a third-order scheme with Lipschitz and Hölder continuous derivative in Banach spaces ⋮ Extending the applicability of a Newton-Simpson-like method ⋮ On the local convergence of a third-order iterative scheme in Banach spaces ⋮ Ball Convergence of Modified Homeier-Like's Method in Banach Spaces under Weak Continuity Condition

Cites Work

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• Weaker conditions for the convergence of Newton's method
• Third-order family of methods in Banach spaces
• Recurrence relations for rational cubic methods. II: The Chebyshev method
• Recurrence relations for rational cubic methods. I: The Halley method
• Recurrence relations for semilocal convergence of a Newton-like method in Banach spaces
• Recurrence relations for the super-Halley method
• Third-order iterative methods for operators with bounded second derivative
• Geometric constructions of iterative functions to solve nonlinear equations
• Computational theory of iterative methods.
• Quadratic equations and applications to Chandrasekhar's and related equations

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