scientific article; zbMATH DE number 3362906
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Publication:5636239
zbMath0228.65041MaRDI QIDQ5636239
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Publication date: 1971
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General theory of numerical analysis in abstract spaces (65J05) Numerical solutions to equations with nonlinear operators (65J15)
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A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions ⋮ Majorizing Sequences and Error Bounds for Iterative Methods ⋮ A convergence theorem for Newton-like methods in Banach spaces ⋮ New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems ⋮ Weak convergence conditions for the Newton's method in Banach space using general majorizing sequences ⋮ Sharp error bounds for Newton's process ⋮ A Superquadratic Variant of Newton's Method ⋮ Estimating upper bounds on the limit points of majorizing sequences for Newton's method ⋮ Weaker conditions for the convergence of Newton's method ⋮ An updated version of the Kantorovich theorem for Newton's method ⋮ The majorant method in the theory of Newton-Kantorovich approximations and generalized Lipschitz conditions ⋮ Extension of Newton's method to nonlinear functions with values in a cone ⋮ Extending the applicability of Newton’s method using nondiscrete induction ⋮ Historical developments in convergence analysis for Newton's and Newton-like methods ⋮ A short survey on Kantorovich
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