On a Steffensen-like method for solving nonlinear equations
- Amat, S. 1
- Ezquerro, J.A. 2
- Hernández-Verón, M.A. 2
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1
Universidad Politécnica de Cartagena
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2
Universidad de La Rioja
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ISSN: 0008-0624
Year of publication: 2016
Volume: 53
Pages: 171-188
Type: Article
More publications in: Calcolo
Abstract
We study a generalization of Steffensen’s method in Banach spaces. Our main aim is to obtain similar convergence as Newton’s method, but without evaluating the first derivative of the operator involved. As motivation, we analyse numerical solutions of boundary-value problems approximated by the multiple shooting method that uses the proposed iterative scheme. Sufficient conditions for the semilocal convergence analysis of the method, including error estimates and the (Formula presented.)-order of convergence, are provided. Finally, the theoretical results are applied to a nonlinear system of equations related with the approximation of a Hammerstein-type integral equation. © 2015 Springer-Verlag Italia