Expanding the applicability of Newton's method using Smale's \(\alpha\)-theory

DOI10.1016/j.cam.2013.10.054zbMath1291.65167OpenAlexW2086276665MaRDI QIDQ390467

Saïd Hilout, Ioannis K. Argyros, Sanjay K. Khattri

Publication date: 8 January 2014

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

Full work available at URL: https://doi.org/10.1016/j.cam.2013.10.054

zbMATH Keywords

numerical resultsNewton's methodBanach spacenonlinear operator equationFréchet-derivativesemi-local convergenceSmale's \(\alpha\)-theory

Mathematics Subject Classification ID

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

Related Items (6)

Expanding the applicability of some high order Householder-like methods ⋮ On the convergence of inexact two-point Newton-like methods on Banach spaces ⋮ Convergence of starters for solving Kepler's equation via Smale's \(\alpha \)-test ⋮ An analysis of the convergence of Newton iterations for solving elliptic Kepler's equation ⋮ A monotonic starter for solving the hyperbolic Kepler equation by Newton's method ⋮ A short survey on Kantorovich

Cites Work

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• Weaker conditions for the convergence of Newton's method
• Fixed points, zeros and Newton's method
• On dominating sequence method in the point estimate and Smale's theorem
• Smale's \(\alpha \)-theory for inexact Newton methods under the \(\gamma \)-condition
• Extending the Newton-Kantorovich hypothesis for solving equations
• General local convergence theory for a class of iterative processes and its applications to Newton's method
• Kantorovich-type convergence criterion for inexact Newton methods
• 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
• The theory of Smale's point estimation and its applications
• Finding zeros of analytic functions: \(\alpha\)-theory for secant type methods
• Computational theory of iterative methods.
• Newton-type methods of high order and domains of semilocal and global convergence
• Improved local convergence of Newton's method under weak majorant condition
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• An improvement of the region of accessibility of Chebyshev’s method from Newton’s method
• A semilocal convergence analysis for directional Newton methods
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Convergence of Newton’s method and inverse function theorem in Banach space
• Adaptive Approximation of Nonlinear Operators
• Convergence of Newton–Kantorovich Approximations to an Approximate Zero
• A modification of the classical Kantorovich conditions for Newton's method

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