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Author: search.filters.author.Erappa, S.M.Subject: search.filters.subject.Semi-local convergence

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    Inexact Newton’s Method to Nonlinear Functions with Values in a Cone Using Restricted Convergence Domains
    (Springer, 2017) Argyros, I.K.; George, S.; Erappa, S.M.
    Using our new idea of restricted convergence domains, a robust convergence theorem for inexact Newton’s method is presented to find a solution of nonlinear inclusion problems in Banach space. Using this technique, we obtain tighter majorizing functions. Consequently, we get a larger convergence domain and tighter error bounds on the distances involved. Moreover, we obtain an at least as precise information on the location of the solution than in earlier studies. Furthermore, a numerical example is presented to show that our results apply to solve problems in cases earlier studies cannot. © 2017, Springer (India) Private Ltd.
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    Extending the applicability of high-order iterative schemes under Kantorovich hypotheses and restricted convergence regions
    (Springer-Verlag Italia s.r.l. springer@springer.it, 2020) Argyros, I.K.; George, S.; Erappa, S.M.
    We use restricted convergence regions to locate a more precise set than in earlier works containing the iterates of some high-order iterative schemes involving Banach space valued operators. This way the Lipschitz conditions involve tighter constants than before leading to weaker sufficient semilocal convergence criteria, tighter bounds on the error distances and an at least as precise information on the location of the solution. These improvements are obtained under the same computational effort since computing the old Lipschitz constants also requires the computation of the new constants as special cases. The same technique can be used to extend the applicability of other iterative schemes. Numerical examples further validate the new results. © 2019, Springer-Verlag Italia S.r.l., part of Springer Nature.