Convergence of Newton's method and inverse function theorem in Banach space
Mathematics of Computation
Kantorovich's theorem on Newton's method in Riemannian Manifolds
Journal of Complexity
Newton method under weak Lipschitz continuous derivative in Banach spaces
Applied Mathematics and Computation
The Kantorovich Theorem and interior point methods
Mathematical Programming: Series A and B
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
Improved local convergence of Newton's method under weak majorant condition
Journal of Computational and Applied Mathematics
Local convergence analysis of inexact Gauss-Newton like methods under majorant condition
Journal of Computational and Applied Mathematics
Convergence analysis of a proximal Gauss-Newton method
Computational Optimization and Applications
Computers & Mathematics with Applications
| Hi-index | 0.00 |
We prove Kantorovich's theorem on Newton's method using a convergence analysis which makes clear, with respect to Newton's method, the relationship of the majorant function and the non-linear operator under consideration. This approach enables us to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new estimate of this rate based on a directional derivative of the derivative of the majorant function. Moreover, the majorant function does not have to be defined beyond its first root for obtaining convergence rate results.