On the midpoint method for solving equations

DOI10.1016/J.AMC.2010.03.076zbMath1198.65095OpenAlexW2014695839MaRDI QIDQ983980

Saïd Hilout, Yeol Je Cho, Ioannis K. Argyros

Publication date: 13 July 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.03.076

zbMATH Keywords

Banach spaceFréchet derivativeNewton-like methodsgeneralized equationmajorizing sequencesmidpoint method

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Set-valued operators (47H04) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (4)

Newton-Kantorovich convergence theorem of a modified Newton's method under the gamma-condition in a Banach space ⋮ Semilocal convergence for a fifth-order Newton's method using recurrence relations in Banach spaces ⋮ Two-step Newton methods ⋮ Unnamed Item

Cites Work

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• The midpoint method for solving nonlinear operator equations in Banach space
• Remark on the convergence of the midpoint method under mild differentiability conditions
• The midpoint method in Banach spaces and the Pták error estimates
• Modified Newton's method with third-order convergence and multiple roots
• An improved error analysis for Newton-like methods under generalized conditions
• Third-order methods from quadrature formulae for solving systems of nonlinear equations.
• On the comparison of a weak variant of the Newton--Kantorovich and Miranda theorems.
• Local convergence of inexact Newton-like iterative methods and applications
• Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space
• Results on the Chebyshev method in banach spaces
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method
• An acceleration of Newton's method: Super-Halley method
• A variant of Newton's method with accelerated third-order convergence
• A modification of the classical Kantorovich conditions for Newton's method

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