Semilocal convergence and \(R\)-order for modified Chebyshev-Halley methods

DOI10.1007/S11075-012-9657-8zbMath1279.65065OpenAlexW2053121587MaRDI QIDQ369457

Jisheng Kou, Xiuhua Wang

Publication date: 24 September 2013

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-012-9657-8

zbMATH Keywords

Newton's methodsemilocal convergencerecurrence relationsa priori error bounds\(R\)-orderChebyshev-Halley methodsnonlinear integral equation of mixed Hammerstein typenonlinear operator equation in Banach spacesweak continuity condition

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Integral operators (47G10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (8)

Semilocal convergence of Modified Chebyshev-Halley method for nonlinear operators in case of unbounded third derivative ⋮ Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative ⋮ Local convergence for multi-point-parametric Chebyshev-Halley-type methods of high convergence order ⋮ Convergence for a class of multi-point modified Chebyshev-Halley methods under the relaxed conditions ⋮ Semilocal convergence of a computationally efficient eighth-order method in Banach spaces under \(w\)-continuity condition ⋮ Ball convergence for two optimal eighth-order methods using only the first derivative ⋮ Higher-order reverse automatic differentiation with emphasis on the third-order ⋮ Ball convergence of a novel Newton-Traub composition for solving equations

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