On a theorem of S. Smale about Newton's method for analytic mappings
A theorem of \textit{S. Smale} [Proc. Symp. Honor G. S. Young, Laramie/Wyo. 1985, 185-196 (1986; Zbl 0613.65058)] on the convergence of Newton's method for analytic functions holds only for mappings which are analytic on the entire space. The result is generalized to functions which are analytic on an open subset and, for the original case, when this subset is the entire space the controlling constant given by Smale is improved.
scientific article; zbMATH DE number 4026700