A convergence analysis and applications for the Newton-Kantorovich method in \(K\)-normed spaces

DOI10.1007/BF02872876zbMath1194.65077OpenAlexW2025294710MaRDI QIDQ2569856

Ioannis K. Argyros

Publication date: 20 October 2005

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02872876

zbMATH Keywords

Banach spaceNewton-Kantorovich methodradius of convergencemajorizing sequenceNewton-Kantorovich hypothesis\(K\)-normed space

Mathematics Subject Classification ID

Newton-type methods (49M15) Numerical computation of solutions to systems of equations (65H10) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Extrapolation to the limit, deferred corrections (65B05) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (1)

A Krasnosel'skii-Zincenko-type method in \(K\)-normed spaces for solving equations

Cites Work

• \(K\)-metric and \(K\)-normed linear spaces: Survey
• On the Newton-Kantorovich method in \(K\)-normed spaces
• Local Convergence of Inexact Newton Methods
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• A unifying theorem on newton's method
• On a new Newton-Mysovskii-type theorem with applications to inexact Newton-like methods and their discretizations
• Newton’s Method for Convex Operators in Partially Ordered Spaces
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