Application of iterative processes of \(R\)-order at least three to operators with unbounded second derivative

DOI10.1016/j.amc.2006.07.081zbMath1115.65063OpenAlexW2157478146MaRDI QIDQ870229

Natalia Romero, Miguel A. Hernández

Publication date: 12 March 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.07.081

zbMATH Keywords

Banach spacesChebyshev methodsemilocal convergenceEuler methodnonlinear operator equationNewton-like methodsHalley methodOstrowski methodKantorovich type theorem

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (5)

Third-order iterative methods with applications to Hammerstein equations: a unified approach ⋮ On the semilocal convergence behavior for Halley's method ⋮ Solving nonlinear integral equations of Fredholm type with high order iterative methods ⋮ A Qualitative Analysis of a Family of Newton-Like Iterative Process with R-Order of Convergence At Least Three ⋮ On the semi-local convergence analysis of higher order iterative method in two folds

Cites Work

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• A local convergence theorem for the super-Halley method in a Banach space
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• Geometric constructions of iterative functions to solve nonlinear equations
• On a characterization of some Newton-like methods of \(R\)-order at least three
• Newton-like methods under mild differentiability conditions with error analysis
• A family of Chebyshev-Halley type methods in Banach spaces
• Classroom Note:Geometry and Convergence of Euler's and Halley's Methods
• New Kantorovich-Type Conditions for Halley's Method
• On the Geometry of Halley's Method

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