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We present a local convergence analysis for two Traub-Steffensen-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. In earlier studies such as [16, 23] Taylor expansions and hypotheses up to the third Fréchet-derivative 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.

eISSN:
1841-3307
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Mathematics, General Mathematics