A unifying theorem on newton's method

DOI10.1080/01630569208816492zbMath0759.65034OpenAlexW2093654146MaRDI QIDQ4029156

Peter Wilhelm Meyer

Publication date: 7 March 1993

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

Full work available at URL: https://doi.org/10.1080/01630569208816492

zbMATH Keywords

monotonicityconvergencenumerical exampleerror estimatesNewton's methodpartially ordered Banach spaceinclusion estimates

Mathematics Subject Classification ID

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

Related Items (9)

Concerning the convergence of inexact Newton methods ⋮ Improving the rate of convergence of Newton methods on Banach spaces with a convergence structure and applications ⋮ A unifying theorem for Newton's method on spaces with a convergence structure ⋮ Convergence for iterative methods on Banach spaces of a convergence structure with applications to fractional calculus ⋮ Unifying semilocal and local convergence of Newton's method on Banach space with a convergence structure ⋮ A Krasnosel'skii-Zincenko-type method in \(K\)-normed spaces for solving equations ⋮ Newton methods on Banach spaces with a convergence structure and applications ⋮ A convergence analysis and applications for the Newton-Kantorovich method in \(K\)-normed spaces ⋮ On the Newton-Kantorovich method in \(K\)-normed spaces

Cites Work

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• A unified derivation of several error bounds for Newton's process
• Das modifizierte Newton-Verfahren in verallgemeinerten Banach-Räumen
• Newton's method in generalized banach spaces
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Newton’s Method for Convex Operators in Partially Ordered Spaces

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