Local convergence analysis of inexact Newton-like methods under majorant condition
This is an incremental theoretical contribution for researchers in numerical analysis, extending existing convergence theory by relaxing Lipschitz continuity assumptions.
The paper presents a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions, providing an estimate of the convergence radius and establishing a relationship between the majorant function and the nonlinear operator.
We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations under majorant conditions. This analysis provides an estimate of the convergence radius and a clear relationship between the majorant function, which relaxes the Lipschitz continuity of the derivative, and the nonlinear operator under consideration. It also allow us to obtain some important special cases