Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications

A generalized k-step iterative application of Newton’s method with frozen derivative is studied and used to solve a system of nonlinear equations. The maximum computational efficiency is computed. A sequence that approximates the order of convergence is generated for the examples, and it numerically confirms the calculation of the order of the method and computational efficiency. This type of method appears in many applications where the authors have heuristically chosen a given number of steps with frozen derivatives. An example is shown in which the total variation (TV) minimization model is approximated using the schemes described in this paper.

► We explore the applications of a generalized k-step iterative Newton’s method with frozen derivative.
► We analyze the order and the convergence of the family.
► We are able to compute the maximum computational efficiency in the family for a given example.
► In most of the cases, the 2-step iterative method seems the most efficient.