Smale's \(\alpha \)-theory for inexact Newton methods under the \(\gamma \)-condition

DOI10.1016/j.jmaa.2010.01.056zbMath1193.65090OpenAlexW2042404024MaRDI QIDQ982563

Chong Li, Wei-Ping Shen

Publication date: 7 July 2010

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.01.056

zbMATH Keywords

convergencenumerical exampleBanach spacenonlinear operator equationapproximate zeroinexact Newton method\(\gamma \)-condition

Mathematics Subject Classification ID

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

Related Items (12)

An inexact Newton-like conditional gradient method for constrained nonlinear systems ⋮ Newton-Kantorovich convergence theorem of a modified Newton's method under the gamma-condition in a Banach space ⋮ Weaker Kantorovich type criteria for inexact Newton methods ⋮ Expanding the applicability of Newton's method using Smale's \(\alpha\)-theory ⋮ A robust Kantorovich's theorem on the inexact Newton method with relative residual error tolerance ⋮ Semilocal convergence analysis for inexact Newton method under weak condition ⋮ Superlinear convergence of Broyden's method and BFGS algorithm using Kantorovich-type assumptions ⋮ Semilocal convergence analysis of \(S\)-iteration process of Newton-Kantorovich like in Banach spaces ⋮ A Newton conditional gradient method for constrained nonlinear systems ⋮ On the convergence of inexact Newton-like methods under mild differentiability conditions ⋮ An extension of a theorem by Wang for Smale's \(\alpha\)-theory and applications ⋮ Gauss-Newton methods with approximate projections for solving constrained nonlinear least squares problems

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