학술저널
ON A LOCAL CHARACTERIZATION OF SOME NEWTON-LIKE METHODS OF R-ORDER AT LEAST THREE UNDER WEAK CONDITIONS IN BANACH SPACES
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 28, No. 4
-
2015.11513 - 523 (11 pages)
- 2
We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fr´echet-derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third Frechet derivative. Numerical examples are also provided in this study.
1. Introduction
2. Local convergence analysis
(0)
(0)