A kantorovich-type theorem for inexact newton methods

DOI10.1080/01630568908816307zbMath0653.65044OpenAlexW1984410138MaRDI QIDQ3799571

Igor Moret

Publication date: 1989

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630568908816307

zbMATH Keywords

inexact Newton methodssemilocal convergence theoremmajorizing sequencesKantorovich-type theorem

Mathematics Subject Classification ID

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

Related Items (15)

Robust semi-local convergence analysis for inexact Newton method ⋮ A posteriori error estimates, stopping criteria, and adaptivity for two-phase flows ⋮ Local convergence analysis of inexact Newton-like methods under majorant condition ⋮ 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 ⋮ Inexact Newton method for non-linear functions with values in a cone ⋮ A new convergence theorem for the inexact Newton methods based on assumptions involving the second Fréchet derivative ⋮ A new semi-local convergence theorem for the inexact Newton methods ⋮ On the convergence of some projection methods with perturbation ⋮ A convergence theorem for the Newton-like methods under some kind of weak Lipschitz conditions ⋮ On the convergence of generalized Newton methods and implicit functions ⋮ A convergence theorem for the inexact Newton methods based on Hölder continuous Fréchet derivative ⋮ The Kantorovich theorem and interior point methods ⋮ Newton—type methods under regular smoothness ⋮ A short survey on Kantorovich

Cites Work

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• On the behaviour of approximate Newton methods
• A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
• A note on a posteriori error bound of zabrejko and nguen for zincenko's iteration
• Local Convergence of Inexact Newton Methods
• The majorant method in the theory of newton-kantorovich approximations and the pták error estimates
• Inexact Newton Methods
• On Newton-Iterative Methods for the Solution of Systems of Nonlinear Equations
• A Local Convergence Theory for Combined Inexact-Newton/Finite-Difference Projection Methods
• Error bounds for Newton-like methods under Kantorovich type assumptions
• A Unified Convergence Theory for a Class of Iterative Processes

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