On two high‐order families of frozen Newton‐type methods

This paper is devoted to the study of two high‐order families of frozen Newton‐type methods. The methods are free of bilinear operators, which constitute the main limitation of the classical high‐order iterative schemes. Both families are natural generalizations of an efficient third‐order method. Although the methods are more demanding, a semilocal convergence analysis is presented using weaker conditions.