Convergence behaviour of inexact Newton methods

DOI10.1090/S0025-5718-99-01135-7zbMath0933.65050MaRDI QIDQ4257692

Benedetta Morini

Publication date: 31 August 1999

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

inexact Newton methodslinear convergencesystems of nonlinear equationslocal convergenceNewton-like methodsaffine invariant conditions

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items (40)

The local convergence analysis of inexact quasi-Gauss-Newton method under the Hölder condition ⋮ Inexact Newton methods for inverse eigenvalue problems ⋮ Inexact Gauss-Newton like methods for injective-overdetermined systems of equations under a majorant condition ⋮ Local convergence analysis of inexact Newton method with relative residual error tolerance under majorant condition in Riemannian manifolds ⋮ Local convergence of inexact Newton-like method under weak Lipschitz conditions ⋮ An inexact Newton-like conditional gradient method for constrained nonlinear systems ⋮ Approximate Gauss-Newton methods for solving underdetermined nonlinear least squares problems ⋮ The inexact, inexact perturbed, and quasi-Newton methods are equivalent models ⋮ Robust semi-local convergence analysis for inexact Newton method ⋮ Split Newton iterative algorithm and its application ⋮ Weaker Kantorovich type criteria for inexact Newton methods ⋮ Extended local analysis of inexact Gauss-Newton-like method for least square problems using restricted convergence domains ⋮ Newton-MR: inexact Newton method with minimum residual sub-problem solver ⋮ Local convergence analysis of inexact Newton-like methods under majorant condition ⋮ The convergence analysis of inexact Gauss-Newton methods for nonlinear problems ⋮ 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 ⋮ A new semi-local convergence theorem for the inexact Newton methods ⋮ Local convergence analysis of inexact Gauss-Newton method for singular systems of equations under majorant and center-majorant condition ⋮ Local convergence of inexact methods under the Hölder condition ⋮ Convergence analysis of the modified Newton-HSS method under the Hölder continuous condition ⋮ A convergence theorem for the inexact Newton methods based on Hölder continuous Fréchet derivative ⋮ Convergence of an inexact generalized Newton method with a scaled residual control ⋮ Convergence behaviour of inexact Newton methods under weak Lipschitz condition. ⋮ On the local convergence of inexact Newton-type methods under residual control-type conditions ⋮ Smale's \(\alpha \)-theory for inexact Newton methods under the \(\gamma \)-condition ⋮ Improved local convergence analysis of inexact Newton-like methods under the majorant condition ⋮ A truncated conjugate gradient method with an inexact Gauss-Newton technique for solving nonlinear systems ⋮ On the convergence of inexact Newton-like methods under mild differentiability conditions ⋮ Discrete quadratic curvature energies ⋮ Some notes on split Newton iterative algorithm ⋮ Local convergence analysis of inexact Gauss-Newton like methods under majorant condition ⋮ Parametric continuation method with correction and its applications ⋮ Mesh-independent convergence of the modified inexact Newton method for a second order non-linear problem ⋮ A hybrid of the Newton-GMRES and electromagnetic meta-heuristic methods for solving systems of nonlinear equations ⋮ Inexact methods: Forcing terms and conditioning ⋮ Nonlinear orthomin\((k)\) methods ⋮ The Newton-arithmetic mean method for the solution of systems of nonlinear equations. ⋮ Inexact overlapped block Broyden methods for solving nonlinear equations ⋮ Numerical approximation of nonlinear BVPs by means of BVMs

Uses Software

• LSODA

Cites Work

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• Reduced storage matrix methods in stiff ODE systems
• Affine invariant convergence results for Newton's method
• Inexact Newton methods for solving nonsmooth equations
• The numerical solution of large systems of stiff IVPs for ODEs
• Local Convergence of Difference Newton-Like Methods
• Local Convergence of Inexact Newton Methods
• Inexact Newton Methods
• Global inexact Newton methods for very large scale nonlinear problems
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• The error committed by stopping the Newton iteration in the numerical solution of stiff initial value problems

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