Ball convergence of some fourth and sixth-order iterative methods

DOI10.1142/S1793557116500340zbMath1354.47040MaRDI QIDQ2805942

Santhosh George, Ioannis K. Argyros

Publication date: 13 May 2016

Published in: Asian-European Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Newton's methodnonlinear equations in Banach spacesBanach spaceFréchet derivativeKung-Traub conjecturedynamics of iterative methodshigh-order iterative method

Mathematics Subject Classification ID

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

Cites Work

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• Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems
• Third-order family of methods in Banach spaces
• Geometric constructions of iterative functions to solve nonlinear equations
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• On the local convergence of fast two-step Newton-like methods for solving nonlinear equations
• Computational theory of iterative methods.
• Results on the Chebyshev method in banach spaces
• On a sixth-order Jarratt-type method in Banach spaces
• Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method

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