Regular smoothness and newton' method

DOI10.1080/01630569408816595zbMath0814.65054OpenAlexW2004870945MaRDI QIDQ4323503

Z. Waksman, A. M. Galperin

Publication date: 22 February 1995

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569408816595

zbMATH Keywords

convergenceBanach spacesiterative methodnonlinear operator equationNewton methodsdegree of smoothnessregular smoothness

Mathematics Subject Classification ID

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

Related Items (11)

On a class of systems of difference equations and their invariants ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Ulm's method under regular smoothness ⋮ Secant method with regularly continuous divided differences ⋮ Kantorovich's Majorization and Functional Equations ⋮ 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

• A note on Newton type iterative methods
• Semilocal analysis of equations with smooth operators
• A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
• Sharp error bounds for Newton's process
• Newton's method under a weak smoothness assumption
• 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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