Local convergence of efficient secant-type methods for solving nonlinear equations

DOI10.1016/j.amc.2012.01.036zbMath1298.65094OpenAlexW2060066247MaRDI QIDQ433325

Ioannis K. Argyros, Hongmin Ren

Publication date: 13 July 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2012.01.036

zbMATH Keywords

local convergenceradius of convergencedivided differencesecant-type methodderivative free methodnonlinear equation in Banach spaces

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Numerical solutions to equations with nonlinear operators (65J15) Nonlinear evolution equations (47J35)

Related Items (11)

Improving the accessibility of Steffensen's method by decomposition of operators ⋮ An improvement of the Kurchatov method by means of a parametric modification ⋮ A significant improvement of a family of secant-type methods ⋮ Dynamics and local convergence of a family of derivative-free iterative processes ⋮ On the Convergence of Secant-Like Methods ⋮ Convergence and dynamics of improved Chebyshev-secant-type methods for non differentiable operators ⋮ On the local convergence of a Newton-Kurchatov-type method for non-differentiable operators ⋮ On the ball of convergence of secant-like methods for non-differentiable operators ⋮ Convergence of Steffensen's method for non-differentiable operators ⋮ Unnamed Item ⋮ Two-point methods for solving equations and systems of equations

Cites Work

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• New sufficient convergence conditions for the secant method
• On the convergence of two-step Newton-type methods of high efficiency index
• Convergence and Complexity of Newton Iteration for Operator Equations
• A variant of Newton's method with accelerated third-order convergence

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