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We study the local convergence of a sixth-order Newton–Traub method to approximate a locally-unique solution of a system of nonlinear equations. Earlier studies show convergence under hypotheses on the sixth 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. Our analysis avoids...
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...
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