Convergence of Newton's method and uniqueness of the solution of equations in Banach spaces. II

DOI10.1007/s10114-002-0238-yzbMath1027.65078OpenAlexW2765794259MaRDI QIDQ1396024

Xinghua Wang, Chong Li

Publication date: 5 January 2004

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-002-0238-y

zbMATH Keywords

convergenceBanach spacenonlinear equationNewton-type method

Mathematics Subject Classification ID

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

Related Items (23)

Inexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant condition ⋮ Newton's Method for Underdetermined Systems of Equations Under the γ-Condition ⋮ Newton-Kantorovich convergence theorem of a modified Newton's method under the gamma-condition in a Banach space ⋮ Local convergence of Newton's method under majorant condition ⋮ Convergence analysis of a proximal Gauss-Newton method ⋮ The convergence analysis of inexact Gauss-Newton methods for nonlinear problems ⋮ Semilocal convergence analysis for inexact Newton method under weak condition ⋮ A new semi-local convergence theorem for the inexact Newton methods ⋮ Kantorovich's type theorems for systems of equations with constant rank derivatives ⋮ Newton-Kantorovich theorem for a family of modified Halley's method under Hölder continuity conditions in Banach space ⋮ Local convergence of inexact methods under the Hölder condition ⋮ Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition ⋮ Convergence and uniqueness properties of Gauss-Newton's method ⋮ Third-order convergence theorem by using majorizing function for a modified Newton method in Banach space ⋮ Smale's \(\alpha \)-theory for inexact Newton methods under the \(\gamma \)-condition ⋮ Convergence behavior of Gauss-Newton's method and extensions of the Smale point estimate theory ⋮ Newton-Kantorovich type convergence theorem for a family of new deformed Chebyshev method ⋮ General local convergence theory for a class of iterative processes and its applications to Newton's method ⋮ Convergence analysis for a deformed Newton's method with third-order in Banach space under γ-condition ⋮ Kantorovich-type convergence criterion for inexact Newton methods ⋮ General 2 \({\times}\) 2 system of nonlinear integral equations and its approximate solution ⋮ Newton-Kantorovich and Smale uniform type convergence theorem for a deformed Newton method in Banach spaces ⋮ Fourth-order convergence theorem by using majorizing functions for super-Halley method in Banach spaces

Cites Work

• Estimations for the separation number of a polynomial system
• Convergence and Complexity of Newton Iteration for Operator Equations
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space

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