Abstract
A semilocal convergence analysis for directional two-step Newton methods in a Hilbert space setting is provided in this study. Two different techniques are used to generate the sufficient convergence results, as well as the corresponding error bounds. The first technique uses our new idea of recurrent functions, whereas the second uses recurrent sequences. We also compare the results of the two techniques.
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Argyros, I.K., Hilout, S. A convergence analysis for directional two-step Newton methods. Numer Algor 55, 503–528 (2010). https://doi.org/10.1007/s11075-010-9368-y
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DOI: https://doi.org/10.1007/s11075-010-9368-y
Keywords
- Directional two-step Newton method
- Hilbert space
- Nonlinear equation
- Lipschitz/center-Lipschitz condition
- Recurrent functions
- Recurrent sequences
- Newton–Kantorovich-type hypotheses