Faculty Publications

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Author: search.filters.author.Erappa, S.M.Subject: search.filters.subject.Newton’s method

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    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.
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    Extending the applicability of Newton’s and secant methods under regular smoothness
    (Boletim da Sociedade Paranaense de Matematica, 2020) Argyros, I.K.; George, S.; Erappa, S.M.
    The concept of regular smoothness has been shown to be an appropriate and powerfull tool for the convergence of iterative procedures converging to a locally unique solution of an operator equation in a Banach space setting. Motivated by earlier works, and optimization considerations, we present a tighter semi-local convergence analysis using our new idea of restricted convergence domains. Numerical examples complete this study. © 2020 Boletim da Sociedade Paranaense de Matematica. All rights reserved.