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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 105
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by:
Paper 34

On a Generalization of the Steffensen Method on Banach Spaces

S. Amat1, J.A. Ezquerro2, M.A. Hernández-Verón2 and Á.A. Magreñán2

1Department of Applied Mathematics and Statistics, Polytechnic University of Cartagena, Spain
2Department of Mathematics and Computation, University of La Rioja, Logroño, Spain

Full Bibliographic Reference for this paper
, "On a Generalization of the Steffensen Method on Banach Spaces", in , (Editors), "Proceedings of the Ninth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 34, 2014. doi:10.4203/ccp.105.34
Keywords: nonlinear equations, Steffensen's method, semilocal convergence, majorant principle, error estimates, order of convergence.

Summary
We consider a new Steffensen-like iterative method with better applicability than the classical Steffensen method. We analyse the semilocal convergence of this method by means of the majorant principle of Kantorovich. We see that the convergence conditions considered are reduced to the conditions usually imposed to the classical Steffensen method when the new method is reduced to the classical Steffensen method.

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