Semilocal convergence of a family of third-order Chebyshev-type methods under a mild differentiability condition

DOI10.1080/00207160903026626zbMath1208.65075OpenAlexW1964940258MaRDI QIDQ3066984

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Publication date: 20 January 2011

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160903026626

zbMATH Keywords

Chebyshev methodBanach spacenonlinear operator equationR-order convergencemultipoint third-order methodsrecurence relation

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 (15)

On semilocal convergence of two step Kurchatov method ⋮ Convergence of a continuation method under majorant conditions ⋮ Semilocal convergence of Modified Chebyshev-Halley method for nonlinear operators in case of unbounded third derivative ⋮ Convergence of a two-step iterative method for nondifferentiable operators in Banach spaces ⋮ On the semi-local convergence of Halley's method under a center-Lipschitz condition on the second Fréchet derivative ⋮ Unnamed Item ⋮ On the convergence of a modified Chebyshev-like method for solving nonlinear equations ⋮ Two-step Newton methods ⋮ Three step Kurchatov method for nondifferentiable operators ⋮ Deformed super-Halley's iteration in Banach spaces and its local and semilocal convergence ⋮ Local convergence analysis for Chebyshev's method ⋮ On the semi-local convergence analysis of higher order iterative method in two folds ⋮ Study of semilocal convergence analysis of Chebyshev's method under new type majorant conditions ⋮ Fourth-order convergence theorem by using majorizing functions for super-Halley method in Banach spaces ⋮ Semilocal convergence for Super-Halley's method under \(\omega\)-differentiability condition

Cites Work

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• Recurrence relations for rational cubic methods. II: The Chebyshev method
• Convergence of the variants of the Chebyshev-Halley iteration family under the Hölder condition of the first derivative
• General study of iterative processes of \(R\) -order at least three under weak convergence conditions
• Recurrence relations for the super-Halley method
• Reduced recurrence relations for the Chebyshev method
• Second-derivative-free variant of the Chebyshev method for nonlinear equations
• On the \(R\)-order of the Halley method
• Convergence of the family of the deformed Euler--Halley iterations under the Hölder condition of the second derivative
• On a new multiparametric family of Newton-like methods
• Numerical Solvability of Hammerstein Integral Equations of Mixed Type
• Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method
• Chebyshev's approximation algorithms and applications

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