On zero finding methods of higher order from data at one point
The author generalizes to higher order methods the approach of \textit{S. Smale} [The merging of disciplines in pure, applied and computational mathematics 185-196 (1986; Zbl 0613.65058)] for the convergence analysis of iterative methods for analytic functions based on data at one point. A particular aim is here to avoid the need for schlicht-function assumptions. Two examples of cubically convergent methods are given one of which is Halley's method.
scientific article; zbMATH DE number 4106137
scientific article