Semilocal convergence of Stirling's method under Hölder continuous first derivative in Banach spaces

DOI10.1080/00207160902777922zbMath1208.65074OpenAlexW2114190572MaRDI QIDQ3056411

Dharmendra Kumar Gupta, Sanjaya Kumar Parhi

Publication date: 12 November 2010

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

Full work available at URL: https://doi.org/10.1080/00207160902777922

zbMATH Keywords

convergencenumerical exampleiterative methodBanach spaceFréchet derivativenonlinear operator equationsStirling methodHölder continuity conditions

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 (7)

On semilocal convergence of two step Kurchatov method ⋮ Expanding the applicability of Stirling's method under weaker conditions and restricted convergence regions ⋮ Convergence of a Stirling-like method for fixed points in Banach spaces ⋮ On semilocal convergence of three-step Kurchatov method under weak condition ⋮ Three step Kurchatov method for nondifferentiable operators ⋮ Convergence analysis of a sixth-order method under weak continuity condition with first-order Fréchet derivative ⋮ Local and semilocal convergence for Kurchatov method under \(\omega\)-continuity conditions

Cites Work

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• Newton's method under mild differentiability conditions with error analysis
• Newton–Kantorovich Approximations When the Derivative Is Hölderian: Old and New Results
• A new iterative method of asymptotic order 1+√2 for the computation of fixed points
• The Newton method for operators with Hölder continuous first derivative

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