ON THE NEWTON–KANTOROVICH THEOREM

DOI10.1142/S0219530512500121zbMath1308.65079OpenAlexW2040757435MaRDI QIDQ2909063

Christinel Mardare, Philippe G. Ciarlet

Publication date: 29 August 2012

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530512500121

zbMATH Keywords

Newton's methodtwo-point boundary value problemsNewton-Kantorovich theoremsolution of nonlinear equations

Mathematics Subject Classification ID

General theory of numerical analysis in abstract spaces (65J05) Iterative procedures involving nonlinear operators (47J25) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (10)

Static Elasticity in a Riemannian Manifold ⋮ Asymptotic expansion of the angle between successive maximal distances for a 2-body system with potential \(-1/r^{1+\varepsilon}\) ⋮ Shanks Sequence Transformations and Anderson Acceleration ⋮ Kantorovich-type results for generalized equations with applications ⋮ Residual-based error corrector operator to enhance accuracy and reliability of neural operator surrogates of nonlinear variational boundary-value problems ⋮ Inexact Newton method for non-linear functions with values in a cone ⋮ The equations of elastostatics in a Riemannian manifold ⋮ A posteriori error estimates for self-similar solutions to the Euler equations ⋮ Unnamed Item ⋮ A short survey on Kantorovich

Uses Software

• NewtonLib

Cites Work

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• Functional analysis, Sobolev spaces and partial differential equations
• Optimal Error Bounds for the Newton–Kantorovich Theorem
• A Unified Convergence Theory for a Class of Iterative Processes
• The Newton-Kantorovich Theorem

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