Inexact Newton methods for solving nonsmooth equations
Proceedings of the international meeting on Linear/nonlinear iterative methods and verification of solution
The numerical solution of large systems of stiff IVPs for ODEs
Applied Numerical Mathematics
Convergence of Newton's method and inverse function theorem in Banach space
Mathematics of Computation
Convergence and Complexity of Newton Iteration for Operator Equations
Journal of the ACM (JACM)
Convergence behaviour of inexact Newton methods
Mathematics of Computation
The Newton-arithmetic mean method for the solution of systems of nonlinear equations
Applied Mathematics and Computation
On the Kantorovich Hypothesis for Newton’s Method
SIAM Journal on Numerical Analysis
Local convergence analysis of the Gauss-Newton method under a majorant condition
Journal of Complexity
Local convergence analysis of inexact Newton-like methods under majorant condition
Computational Optimization and Applications
Convergence of an inexact generalized Newton method with a scaled residual control
Computers & Mathematics with Applications
Local convergence analysis of inexact Gauss-Newton like methods under majorant condition
Journal of Computational and Applied Mathematics
Convergence analysis of the modified Newton-HSS method under the Hölder continuous condition
Journal of Computational and Applied Mathematics
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Under weak Lipschitz condition, local convergence properties of inexact Newton methods and Newton-like methods for systems of nonlinear equations are established in an arbitrary vector norm. Processes with modified relative residual control are considered; the results easily provide an estimate of convergence ball for inexact methods. For a special case, the results are affine invariant. Some applications are given.