Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton’s method. (English) Zbl 0907.65053

The paper is one of a series of papers by the author on Newton-like methods for nonlinear operator equations in Banach spaces.
Local convergence theorems are proven by using Lipschitz conditions on the first and second Fréchet-derivative of the nonlinear operator. In addition, the author looks for the smallest and largest region in which the starting point of the Newton-iteration has to lie in order to obtain convergence.
A possible application of the theoretical results to autonomous differential equations underlines their practical use.
Reviewer: E.Emmrich (Berlin)


65J15 Numerical solutions to equations with nonlinear operators
47J25 Iterative procedures involving nonlinear operators
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
Full Text: EuDML EMIS