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Author: search.filters.author.Regmi, S.Subject: search.filters.subject.Radius of convergence

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    Local comparison between two ninth convergence order algorithms for equations
    (MDPI AG rasetti@mdpi.com Postfach Basel CH-4005, 2020) Regmi, S.; Argyros, I.K.; George, S.
    A local convergence comparison is presented between two ninth order algorithms for solving nonlinear equations. In earlier studies derivatives not appearing on the algorithms up to the 10th order were utilized to show convergence. Moreover, no error estimates, radius of convergence or results on the uniqueness of the solution that can be computed were given. The novelty of our study is that we address all these concerns by using only the first derivative which actually appears on these algorithms. That is how to extend the applicability of these algorithms. Our technique provides a direct comparison between these algorithms under the same set of convergence criteria. This technique can be used on other algorithms. Numerical experiments are utilized to test the convergence criteria. © 2020 by the authors.
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    An algorithm with feasible inexact projections for solving constrained generalized equations
    (John Wiley and Sons Ltd, 2025) Regmi, S.; Argyros, I.K.; George, S.
    The goal of this article is to design a more flexible algorithm than the ones used previously for solving constrained generalized equations. It turns out that the new algorithm even if specialized provides a finer error analysis with advantages: larger radius of convergence; tighter upper error bounds on the distances; and a more precise information on the isolation of the solution. Moreover, the same advantages exist even if the generalized equation reduces to a nonlinear equation. These advantages are obtained under the same computational cost, since the new parameters and majorant functions are special cases of the ones used in earlier studies. Applications complement the theoretical results. © 2024 John Wiley & Sons Ltd.