Abstract
We discuss the local convergence of a derivative-free eighth order method in a Banach space setting. The present study provides the radius of convergence and bounds on errors under the hypothesis based on the first Fréchet-derivative only. The approaches of using Taylor expansions, containing higher order derivatives, do not provide such estimates since the derivatives may be nonexistent or costly to compute. By using only first derivative, the method can be applied to a wider class of functions and hence its applications are expanded. Numerical experiments show that the present results are applicable to the cases wherein previous results cannot be applied.
Subject
Computational Mathematics,Computational Theory and Mathematics,Numerical Analysis,Theoretical Computer Science
Reference19 articles.
1. An Adaptive Continuation Process for Solving System of Nonlinear Equations;Rheinbolt,1978
2. Computational Theory of Iterative Methods;Argyros,2007
3. Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method
4. A note on the local convergence of iterative methods based on Adomian decomposition method and 3-node quadrature rule
5. On the semilocal convergence of Newton-Kantrovich method under center-Lipschitz conditions;Gutiérrez;Appl. Math. Comput.,2013
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