We study the local convergence of a fifth-order Newton–Gauss method in order to approximate a locally-unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the fifth derivative or even higher, although only the first derivatives are used in the method. The convergence in this study is shown under hypotheses only on the first derivative. Hence, the applicability of the method is expanded. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies can not apply.
SeMA Journal – Springer Journals
Published: Sep 23, 2016
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