Convergence and Complexity of Newton Iteration for Operator Equations
Journal of the ACM (JACM)
Convergence behaviour of inexact Newton methods under weak Lipschitz condition
Journal of Computational and Applied Mathematics
The convergence analysis of inexact Gauss---Newton methods for nonlinear problems
Computational Optimization and Applications
Local convergence of inexact methods under the Hölder condition
Journal of Computational and Applied Mathematics
Kantorovich's majorants principle for Newton's method
Computational Optimization and Applications
Local convergence analysis of inexact Newton-like methods under majorant condition
Computational Optimization and Applications
Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms
Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms
Improved local convergence of Newton's method under weak majorant condition
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
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A local convergence analysis of Newton's method for solving nonlinear equations, under a majorant condition, is presented in this paper. Without assuming convexity of the derivative of the majorant function, which relaxes the Lipschitz condition on the operator under consideration, convergence, the biggest range for uniqueness of the solution, the optimal convergence radius and results on the convergence rate are established. Besides, two special cases of the general theory are presented as applications.