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- Title
Local convergence for an eighth order method for solving equations and systems of equations.
- Authors
Argyros, Ioannis K.; George, Santhosh
- Abstract
The aim of this study is to extend the applicability of an eighth convergence order method from the k−dimensional Euclidean space to a Banach space setting. We use hypotheses only on the first derivative to show the local convergence of the method. Earlier studies use hypotheses up to the eighth derivative although only the first derivative and a divided difference of order one appear in the method. Moreover, we provide computable error bounds based on Lipschitz-type functions.
- Subjects
STOCHASTIC convergence; ITERATIVE methods (Mathematics); BANACH spaces; LIPSCHITZ spaces; FRECHET spaces
- Publication
Nonlinear Engineering, 2019, Vol 8, Issue 1, p74
- ISSN
2192-8010
- Publication type
Article
- DOI
10.1515/nleng-2017-0105