On Newton's method for solving equations containing Fréchet-differentiable operators of order at least two

DOI10.1016/J.AMC.2009.07.005zbMath1179.65058OpenAlexW2091221376MaRDI QIDQ1036552

Ioannis K. Argyros

Publication date: 13 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.07.005

zbMATH Keywords

convergencenumerical examplessemilocal convergenceBanach spacemajorizing sequenceNewton-Kantorovich hypothesisFrechet derivativeNewton's Methodcenter-Lipschitz conditionsnonlinear integral equation of Chandrasekhar-type

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 (3)

Semilocal Convergence Theorem for a Newton-like Method ⋮ On Newton-Kantorovich method for solving the nonlinear operator equation ⋮ Newton-Kantorovich and Smale uniform type convergence theorem for a deformed Newton method in Banach spaces

Uses Software

• Mathematica

Cites Work

• A new semilocal convergence theorem for Newton's method
• A note on the Kantorovich theorem for Newton iteration
• On a class of Newton-like methods for solving nonlinear equations
• On the Newton-Kantorovich hypothesis for solving equations
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• Computational theory of iterative methods.
• Accessibility Of Solutions By Newton's Method
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