Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
Convergence of Newton's method and uniqueness of the solution of equations in Banach space - MaRDI portal

Convergence of Newton's method and uniqueness of the solution of equations in Banach space

From MaRDI portal
Publication:4943401

DOI10.1093/imanum/20.1.123zbMath0942.65057OpenAlexW2094760120MaRDI QIDQ4943401

Xinghua Wang

Publication date: 21 August 2000

Published in: IMA Journal of Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/365e1122591bd611dc6ad3c20078d8b620426f1a




Related Items (80)

Local convergence analysis of proximal Gauss-Newton method for penalized nonlinear least squares problemsUniform convergence of higher order quasi Hermite-Fejér interpolationThe local convergence analysis of inexact quasi-Gauss-Newton method under the Hölder conditionOn iterative computation of fixed points and optimizationTwo-square theorems for infinite matrices on certain fieldsConvergence analysis of the secant type methodsInexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant conditionNewton's Method for Underdetermined Systems of Equations Under the γ-ConditionLocal convergence of inexact Newton-like method under weak Lipschitz conditionsLocal convergence results of Gauss--Newton's like method in weak conditionsInexact-Newton method for solving operator equations in infinite-dimensional spacesExtending the applicability of the Gauss-Newton method for convex composite optimization using restricted convergence domains and average Lipschitz conditionsRobust semi-local convergence analysis for inexact Newton methodEstimating the local radius of convergence for Picard iterationOn local convergence of a Newton-type method in Banach spaceConvergence of the variants of the Chebyshev-Halley iteration family under the Hölder condition of the first derivativeLocal convergence of the Newton’s method in two step nilpotent Lie groupsTwo-step secant type method with approximation of the inverse operatorLocal convergence of Newton's method under majorant conditionConvergence of the two-step combined method and uniqueness of the solution of nonlinear operator equationsConvergence analysis of a proximal Gauss-Newton methodImproved local convergence analysis of inexact Gauss-Newton like methods under the majorant condition in Banach spacesLocal convergence analysis of the Gauss-Newton method under a majorant conditionConvergence criteria of Newton's method on Lie groupsConvergence of Newton's method and uniqueness of the solution of equations in Banach spaces. IIExtending the applicability of Newton's method for variational inequality problems under Smale-Wang-\( \gamma\) criteriaLocal convergence radius for the Mann-type iterationLocal convergence of generalized Mann iterationLocal convergence analysis of inexact Newton-like methods under majorant conditionThe convergence analysis of inexact Gauss-Newton methods for nonlinear problemsConvergence of Newton's method for sections on Riemannian manifoldsSuper-Halley method under majorant conditions in Banach spacesExtending the applicability of the Gauss-Newton method under average Lipschitz-type conditionsSemilocal convergence analysis for inexact Newton method under weak conditionOn the semilocal convergence behavior for Halley's methodLocal and global behavior for algorithms of solving equationsA new semi-local convergence theorem for the inexact Newton methodsThe convergence ball of Newton's method and the uniqueness ball of equations under Hölder-type continuous derivativesConvergence criterion of Newton's method for singular systems with constant rank derivativesHomocentric convergence ball of the secant methodA robust semi-local convergence analysis of Newton's method for cone inclusion problems in Banach spaces under affine invariant majorant conditionExpanding the applicability of the Gauss-Newton method for convex optimization under a majorant conditionLocal convergence analysis of inexact Gauss-Newton method for singular systems of equations under majorant and center-majorant conditionA convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditionsSmoothing Newton method for operator equations in Banach spacesExtended semilocal convergence for the Newton-Kurchatov methodSemilocal convergence analysis of \(S\)-iteration process of Newton-Kantorovich like in Banach spacesLocal convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant conditionTwo-step solver for equations with nondifferentiable termNewton’s method for variational inequality problems: Smale’s point estimate theory under the γ-conditionConvergence and uniqueness properties of Gauss-Newton's methodConvergence ball and error analysis of the Ostrowski-Traub methodConvergence behaviour of inexact Newton methods under weak Lipschitz condition.Local convergence of Newton's method on Lie groups and uniqueness ballsConvergence radius of the modified Newton method for multiple zeros under Hölder continuous derivativeConvergence of the family of the deformed Euler--Halley iterations under the Hölder condition of the second derivativeSmale's \(\alpha \)-theory for inexact Newton methods under the \(\gamma \)-conditionConvergence behavior of Gauss-Newton's method and extensions of the Smale point estimate theoryImproved local convergence analysis of inexact Newton-like methods under the majorant conditionConvergence ball of iterations with one parameterSemilocal convergence for a family of Chebyshev-Halley like iterations under a mild differentiability conditionExtending the applicability of Newton's method on Lie groupsGeneral local convergence theory for a class of iterative processes and its applications to Newton's methodOn the convergence of inexact Newton-like methods under mild differentiability conditionsLocal convergence of Newton's method on the Heisenberg groupOn Convergence of the Accelerated Newton Method Under Generalized Lipschitz ConditionsConvergence of the iteration of Halley's family and Smale operator class in Banach spaceKantorovich-type convergence criterion for inexact Newton methodsConvergence of the Gauss–Newton method for a special class of systems of equations under a majorant conditionDeformed super-Halley's iteration in Banach spaces and its local and semilocal convergenceLocal convergence analysis of inexact Gauss-Newton like methods under majorant conditionComplexity of an Homotopy Method at the Neighbourhood of a ZeroNewton's method for approximating zeros of vector fields on Riemannian manifoldsOn the radius of convergence of Newton's method under average mild differentiability conditionsExtended Newton Methods for Multiobjective Optimization: Majorizing Function Technique and Convergence AnalysisConvergence criterion and convergence ball of the Newton-type method in Banach spaceSemilocal convergence for Halley's method under weak Lipschitz conditionConvergence of Gauss-Newton's method and uniqueness of the solutionConvergence of Newton’s method and inverse function theorem in Banach spaceImproved local convergence analysis of the Gauss-Newton method under a majorant condition




This page was built for publication: Convergence of Newton's method and uniqueness of the solution of equations in Banach space