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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 ...
Starting points for Newton’s method under a center Lipschitz condition for the second derivative
(Journal of Computational and Applied Mathematics, 2018-03)
We analyze the semilocal convergence of Newton's method under a center Lipschitz condition for the second derivative of the operator involved different from that used by other authors until now. In particular, we propose ...
Toward a general theory of point to point iterative processes free of derivatives with quadratic convergence
(AIP Conference Proceedings, 2018)
In this work, we are concerned with the problem of developing a general theory about derivative-free iterative procedures with quadratic convergence. Newton's method is the most used, well-known and studied in order to ...