On the semi-local convergence of Halley's method under a center-Lipschitz condition on the second Fréchet derivative

DOI10.1016/j.amc.2012.04.078zbMath1281.65083OpenAlexW1983139135MaRDI QIDQ387681

Hongmin Ren, Ioannis K. Argyros

Publication date: 23 December 2013

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

Full work available at URL: https://doi.org/10.1016/j.amc.2012.04.078

zbMATH Keywords

Halley's methodBanach spaceHammerstein integral equationnonlinear operator equationsemi-local convergencecenter Lipschitz condition

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (4)

On the domain of starting points of Newton's method under center Lipschitz conditions ⋮ Newton-type methods on Riemannian manifolds under Kantorovich-type conditions ⋮ An iteratively regularized Gauss-Newton-Halley method for solving nonlinear ill-posed problems ⋮ Convergence theorem for a family of new modified Halley's method in Banach space

Uses Software

• NewtonLib

Cites Work

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• Third-order family of methods in Banach spaces
• Semilocal convergence for Halley's method under weak Lipschitz condition
• The convergence of a Halley-Chebysheff-type method under Newton- Kantorovich hypotheses
• Local convergence of inexact Newton-like iterative methods and applications
• On the semilocal convergence of the Halley method using recurrent functions
• Ball convergence theorems for Halley's method in Banach space
• Third-order iterative methods under Kantorovich conditions
• On the Halley method in Banach spaces
• Semilocal convergence of a family of third-order Chebyshev-type methods under a mild differentiability condition
• Newton's method under weak Kantorovich conditions

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