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Author: search.filters.author.Argyros, C.I.Subject: search.filters.subject.Convergence

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    Kantorovich-type results for generalized equations with applications
    (Springer Science and Business Media B.V., 2022) Regmi, S.; Argyros, I.K.; George, S.; Argyros, C.I.
    Kantorovich-type results for generalized equations are extended with no additional conditions using Newton procedures. Iterates are shown to belong in a smaller domain resulting to tighter Lipschitz constants and a finer convergence analysis than in earlier works. © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.
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    Hybrid Newton-like Inverse Free Algorithms for Solving Nonlinear Equations
    (Multidisciplinary Digital Publishing Institute (MDPI), 2024) Argyros, I.K.; George, S.; Regmi, S.; Argyros, C.I.
    Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines. © 2024 by the authors.