The super-Halley method using divided differences

DOI10.1016/S0893-9659(97)00065-7zbMath0883.65048MaRDI QIDQ1372312

Ioannis K. Argyros

Publication date: 1 March 1998

Published in: Applied Mathematics Letters (Search for Journal in Brave)

zbMATH Keywords

semilocal convergenceBanach spacesuper-Halley methodmonotone convergencedivided differencespartially ordered

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Related Items (10)

Newton-Kantorovich convergence theorem of a new modified Halley's method family in a Banach space ⋮ Derivative free algorithm for solving nonlinear equations ⋮ Newton-Kantorovich theorem for a family of modified Halley's method under Hölder continuity conditions in Banach space ⋮ Constructing third-order derivative-free iterative methods ⋮ Unnamed Item ⋮ The convergence ball of the secant method under Hölder continuous divided differences ⋮ Improving order and efficiency: Composition with a modified Newton's method ⋮ An improved semilocal convergence analysis for the Chebyshev method ⋮ An iteration method with maximal order based on standard information ⋮ Convergence theorem for a family of new modified Halley's method in Banach space

Cites Work

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• On the solution of equations with nondifferentiable and Ptak error estimates
• On the method of tangent hyperbolas in Banach spaces
• Some notions of nonstationary multistep iteration processes
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)

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