Argyros, Ioannis K. A local convergence analysis and applications of Newton’s method under weak assumptions. (English) Zbl 1029.65056 Southwest J. Pure Appl. Math. 2003, No. 1, 82-87 (2003). A local convergence theorem for Newton’s method in a Banach space is provided. The author uses Lipschitz as well as center Lipschitz conditions and small majorizing sequences to obtain more precise error bounds and a larger convergence radius than before. This study is completed with a numerical example. Reviewer: Karel Najzar (Praha) MSC: 65J15 Numerical solutions to equations with nonlinear operators 47J25 Iterative procedures involving nonlinear operators Keywords:Newton’s method; Banach space; Lipschitz conditions; convergence; majorizing sequences; error bounds; numerical examples PDFBibTeX XMLCite \textit{I. K. Argyros}, Southwest J. Pure Appl. Math. 2003, No. 1, 82--87 (2003; Zbl 1029.65056) Full Text: EuDML EMIS