Two-point methods for solving equations and systems of equations

Tom 47 / 2020

Ioannis K. Argyros, Santhosh George Applicationes Mathematicae 47 (2020), 255-272 MSC: 45G10, 65J15, 47H17. DOI: 10.4064/am2365-5-2018 Opublikowany online: 20 September 2019

Streszczenie

The aim of this study is to present a convergence analysis of a frozen secant-type method for solving nonlinear systems of equations defined on the $k$-dimensional Euclidean space. The novelty of the paper lies in the fact that the method is defined using a special divided difference which is well defined for distinct iterates making it suitable for solving systems involving a nondifferentiable mapping. The local and semi-local convergence analysis is based on generalized Lipschitz-type scalar functions that are only nondecreasing, whereas their continuity is not assumed as in earlier studies. Numerical examples involving systems of equations are provided to further validate the theoretical results.

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