The inexact, inexact perturbed, and quasi-Newton methods are equivalent models

DOI10.1090/S0025-5718-04-01646-1zbMath1054.65050OpenAlexW2116210979MaRDI QIDQ4821049

Emil Cătinaş

Publication date: 7 October 2004

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-04-01646-1

zbMATH Keywords

convergencequasi-Newton methodinexact perturbed method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items (28)

A truncated-CG style method for symmetric generalized eigenvalue problems ⋮ Improved semilocal convergence analysis in Banach space with applications to chemistry ⋮ On an improved convergence analysis of Newton's method ⋮ Optimizing the applicability of a theorem by F. Potra for Newton-like methods ⋮ Improved convergence analysis for Newton-like methods ⋮ Local convergence of an at least sixth-order method in Banach spaces ⋮ Weak convergence conditions for the Newton's method in Banach space using general majorizing sequences ⋮ On the convergence of inexact two-point Newton-like methods on Banach spaces ⋮ One-step convergence of inexact Anderson acceleration for contractive and non-contractive mappings ⋮ Estimating upper bounds on the limit points of majorizing sequences for Newton's method ⋮ Weaker conditions for the convergence of Newton's method ⋮ A perturbed version of an inexact generalized Newton method for solving nonsmooth equations ⋮ The majorant method in the theory of Newton-Kantorovich approximations and generalized Lipschitz conditions ⋮ Expanding the applicability of the secant method under weaker conditions ⋮ Local convergence of a relaxed two-step Newton like method with applications ⋮ New improved convergence analysis for Newton-like methods with applications ⋮ Two-step Newton methods ⋮ A survey on the high convergence orders and computational convergence orders of sequences ⋮ Fixed points for operators with generalized Hölder derivative ⋮ Weaker conditions for inexact mutitpoint Newton-like methods ⋮ Estimating the radius of an attraction ball ⋮ Improved convergence analysis of the Secant method using restricted convergence domains with real-world applications ⋮ Parametric continuation method with correction and its applications ⋮ Extending the applicability of Newton’s method using nondiscrete induction ⋮ Weaker convergence criteria for Traub's method ⋮ On a Steffensen-Hermite method of order three ⋮ Inexact Newton Methods and Dennis--Moré Theorems for Nonsmooth Generalized Equations ⋮ How Many Steps Still Left to $x$*?

Uses Software

• GMBACK
• KELLEY

Cites Work

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• Global approximate Newton methods
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• Inexact methods: Forcing terms and conditioning
• On the characterization of \(Q\)-superlinear convergence of quasi-Newton interior-point methods for nonlinear programming
• Analysis of a Minimum Perturbation Algorithm for Nonsymmetric Linear Systems
• Local Convergence of Inexact Newton Methods
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Parameter Selection for Newton-Like Methods Applicable to Nonlinear Partial Differential Equations
• Inexact Newton Methods
• Asymptotic Mesh Independence of Newton–Galerkin Methods via a Refined Mysovskii Theorem
• Quasi-Newton Methods, Motivation and Theory
• Quasi-Nonexpansivity and Two Classical Methods for Solving Nonlinear Equations
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• Convergence behaviour of inexact Newton methods
• A Local Convergence Theory for Combined Inexact-Newton/Finite-Difference Projection Methods
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• GMBACK: A Generalised Minimum Backward Error Algorithm for Nonsymmetric Linear Systems
• Choosing the Forcing Terms in an Inexact Newton Method
• Inexact perturbed Newton methods and applications to a class of Krylov solvers
• \(Q\)-superlinear convergence of the iterates in primal-dual interior-point methods

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