Two-point methods for solving equations and systems of equations
Tom 47 / 2020
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.
