Amat, S.; Argyros, I.; Busquier, S.; Hernández-Verón, M. A. On two high-order families of frozen Newton-type methods. (English) Zbl 1424.65072 Numer. Linear Algebra Appl. 25, No. 1, e2126, 13 p. (2018). This paper considers a two-step method to approximate the solution of a nonlinear equation that increases the order of Newton-type methods but without evaluating any second Fréchet derivative. The results are generalized to new families of iterative methods. The semilocal convergence analysis using weaker conditions is established. Some numerical examples are presented. Reviewer: Hang Lau (Montréal) Cited in 7 Documents MSC: 65J15 Numerical solutions to equations with nonlinear operators Keywords:frozen derivatives; high-order; Newton-type methods; semilocal convergence Software:Maple PDFBibTeX XMLCite \textit{S. Amat} et al., Numer. Linear Algebra Appl. 25, No. 1, e2126, 13 p. (2018; Zbl 1424.65072) Full Text: DOI