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 behaviour of inexact Newton methods
Mathematics of Computation
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Historical developments in convergence analysis for Newton's and Newton-like methods
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Convergence behaviour of inexact Newton methods under weak Lipschitz condition
Journal of Computational and Applied Mathematics
Local convergence of Newton's method under majorant condition
Journal of Computational and Applied Mathematics
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
Local convergence analysis of inexact Gauss-Newton like methods under majorant condition
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
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In this paper, inexact Gauss---Newton methods for nonlinear least squares problems are studied. Under the hypothesis that derivative satisfies some kinds of weak Lipschitz conditions, the local convergence properties of inexact Gauss---Newton and inexact Gauss---Newton like methods for nonlinear problems are established with the modified relative residual control. The obtained results can provide an estimate of convergence ball for inexact Gauss---Newton methods.