Local convergence of Newton's method under majorant condition
Provides a more general convergence theory for Newton's method, relaxing standard assumptions, which is incremental for numerical analysis researchers.
The paper analyzes local convergence of Newton's method under a majorant condition that relaxes Lipschitz assumptions, establishing optimal convergence radius, uniqueness range, and convergence rates without requiring convexity of the majorant's derivative.
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 an application.