A family of Halley-Chebyshev iterative schemes for non-Fréchet differentiable operators

DOI10.1016/j.cam.2008.09.005zbMath1173.65036OpenAlexW2127828806MaRDI QIDQ1019821

Concepción Bermúdez, Sonia Busquier, Sergio Amat, Driss Mestiri

Publication date: 28 May 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2008.09.005

zbMATH Keywords

Banach spacesChebyshev methodNewton type methodsnonlinear operator equationsnumerical comparisonHalley methodthird order methodsconvergence nonlinear integral equationSteffensen type schemesuper-Halley-method

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 (9)

Starting points for Newton's method under a center Lipschitz condition for the second derivative ⋮ Chebyshev-secant-type methods for non-differentiable operators ⋮ A variant of the Newton-Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type ⋮ Derivative free algorithm for solving nonlinear equations ⋮ A semilocal convergence result for Newton's method under generalized conditions of Kantorovich ⋮ Extending the applicability of Newton's method for \(k\)-Fréchet differentiable operators in Banach spaces ⋮ Convergence for a family of modified Chebyshev methods under weak condition ⋮ Constructing third-order derivative-free iterative methods ⋮ The simplified topological \(\varepsilon\)-algorithms: software and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Recurrence relations for rational cubic methods. II: The Chebyshev method
• Newton-like methods for the computation of fixed points
• Recurrence relations for rational cubic methods. I: The Halley method
• Third-order iterative methods for operators with bounded second derivative
• A fast Chebyshev's method for quadratic equations.
• On a characterization of some Newton-like methods of \(R\)-order at least three
• Third-order iterative methods under Kantorovich conditions
• A modification of the Chebyshev method
• Resolution of quadratic equations in banach spaces

This page was built for publication: A family of Halley-Chebyshev iterative schemes for non-Fréchet differentiable operators