Convergence criterion and convergence ball of the Newton-type method in Banach space

DOI10.1007/s12190-008-0196-3zbMath1182.65086OpenAlexW2051205357MaRDI QIDQ1034956

Weiguo Li, Huaren Zhang

Publication date: 9 November 2009

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-008-0196-3

zbMATH Keywords

Banach spacessemilocal convergencenonlinear operator equationNewton-type methodconvergence ballNewton-like iterationweak Lipschitz condition with \(L\)-average

Mathematics Subject Classification ID

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

Cites Work

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• A third-order Newton-type method to solve systems of nonlinear equations
• The cubic semilocal convergence on two variants of Newton's method
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• Convergence criterion and convergence ball of the King-Werner method under the radius Lipschitz condition
• Convergence and error estimate of a deformed Newton method
• Convergence behaviour of inexact Newton methods under weak Lipschitz condition.
• Convergence of Gauss-Newton's method and uniqueness of the solution
• Convergence of Newton’s method and inverse function theorem in Banach space
• Convergence of Newton's method and uniqueness of the solution of equations in Banach space

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