Newton's method under a weak smoothness assumption

DOI10.1016/0377-0427(91)90208-2zbMath0755.65057OpenAlexW2030736178MaRDI QIDQ1176798

Z. Waksman, A. M. Galperin

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0377-0427(91)90208-2

zbMATH Keywords

Banach spacesLipschitz conditionNewton-Kantorovich methodSharp error bounds

Mathematics Subject Classification ID

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

Related Items (10)

On a class of systems of difference equations and their invariants ⋮ Unnamed Item ⋮ Regular smoothness and newton' method ⋮ Ulm's method under regular smoothness ⋮ Secant method with regularly continuous divided differences ⋮ On Convergence Domains of Newton's and Modified Newton Methods ⋮ Newton—type methods under regular smoothness ⋮ Optimal Iterative Methods for Nonlinear Equations ⋮ Ulm's method without derivatives ⋮ On Newton's method under mild differentiability conditions and applications

Cites Work

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• Semilocal analysis of equations with smooth operators
• Sharp error bounds for Newton's process
• On Newton's method and nondiscrete mathematical induction
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Optimal Error Bounds for the Newton–Kantorovich Theorem

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