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Ball Convergence of Multipoint Methods for Non-linear Systems
(Springer Science and Business Media Deutschland GmbH, 2021) Argyros, I.K.; George, S.; Erappa, S.M.
We study Multipoint methods using only the first derivative. Earlier studies use higher than three order derivatives not on the methods. Moreover Lipschitz constants are used to find error estimates not presented in earlier papers. Numerical examples complete this paper. Â© 2021, Springer Nature Singapore Pte Ltd.
Ball convergence for an eighth order efficient method under weak conditions in Banach spaces
(Springer Nature, 2017) Argyros, I.K.; George, S.; Erappa, S.M.
We present a local convergence analysis of an eighth order- iterative method in order to approximate a locally unique solution of an equation in Banach space setting. Earlier studies have used hypotheses up to the fourth derivative although only the first derivative appears in the definition of these methods. In this study we only use the hypothesis on the first derivative. This way we expand the applicability of these methods. Moreover, we provide a radius of convergence, a uniqueness ball and computable error bounds based on Lipschitz constants. Numerical examples computing the radii of the convergence balls as well as examples where earlier results cannot apply to solve equations but our results can apply are also given in this study. © 2016, Sociedad Española de Matemática Aplicada.