| Abstract: | We present a local convergence analysis for higher order methods in order
to approximate a locally unique solution of an equation in a Banach space setting. In
earlier studies, Taylor expansions and hypotheses on higher order Fréchet-derivatives
are used. We expand the applicability of these methods using only hypotheses on the
first Fréchet derivative. Moreover, we obtain a radius of convergence and computable
error bounds using Lipschitz constants not given before. Numerical examples are also
presented in this study. |
