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Ball convergence of a sixth-order Newton-like method based on means under weak conditions
(Journal of Mathematical Chemistry, 2018-08)
We study the local convergence of a Newton-like method of convergence order six to approximate a locally unique solution of a nonlinear equation. Earlier studies show convergence under hypotheses on the seventh derivative ...
Extending the domain of starting points for Newton's method under conditions on the second derivative
(Journal of Computational and Applied Mathematics, 2018-10)
In this paper, we propose a center Lipschitz condition for the second Frechet derivative together with the use of restricted domains in order to improve the domain of starting points for Newton's method. In addition, we ...