Convergence ball and error analysis of a family of iterative methods with cubic convergence

DOI10.1016/J.AMC.2008.12.057zbMath1177.65083OpenAlexW2040738563MaRDI QIDQ1008603

Hongmin Ren, Qing-Biao Wu

Publication date: 30 March 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2008.12.057

zbMATH Keywords

numerical exampleserror analysisiterative methodscubic convergencevariants of Newton's methodConvergence ball

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (12)

Ball convergence of an efficient eighth order iterative method under weak conditions ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Local convergence for some high convergence order Newton-like methods with frozen derivatives ⋮ Ball convergence for Traub-Steffensen like methods in Banach space ⋮ Ball convergence for an eighth order efficient method under weak conditions in Banach spaces ⋮ Improved local analysis for a certain class of iterative methods with cubic convergence ⋮ Unnamed Item ⋮ Convergence of the modified Halley's method for multiple zeros under Hölder continuous derivative ⋮ Convergence ball and error analysis of the Ostrowski-Traub method ⋮ Generalized Kung-Traub method and its multi-step iteration in Banach spaces ⋮ Unified convergence for multi-point super Halley-type methods with parameters in Banach space

Cites Work

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• An analysis of the properties of the variants of Newton's method with third order convergence
• Convergence ball and error analysis of Muller's method
• A note on a paper by D.K.R. Babajee and M.Z. Dauhoo
• A modified Newton method for rootfinding with cubic convergence.
• The convergence ball of Newton's method and the uniqueness ball of equations under Hölder-type continuous derivatives
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• Convergence ball of a modified secant method for finding zero of derivatives
• The convergence ball of the secant method under Hölder continuous divided differences
• Convergence and Complexity of Newton Iteration for Operator Equations
• A variant of Newton's method with accelerated third-order convergence

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