On a Moser–Steffensen Type Method for Nonlinear Systems of Equations

This paper is devoted to the construction and analysis of a Moser–Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of convergence for systems of equations, hypotheses ensuring the local...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2016-12, Vol.13 (6), p.4109-4128
Main Authors: Amat, S., Grau-Sanchez, M., Hernández-Verón, M. A., Rubio, M. J.
Format: Article
Language:English
Subjects:
47 Operator theory
47H Nonlinear operators and their properties
65 Numerical analysis
65H Nonlinear algebraic or transcendental equations
Anàlisi matemàtica
Anàlisi numèrica
Classificació AMS
Convergence
Differential equations, Nonlinear
Equacions diferencials no lineals
Iterative methods
Local convergence
Matemàtiques i estadística
Mathematical analysis
Mathematics
Mathematics and Statistics
Moser’s strategy
Nonlinear operators
Nonlinear systems
Numerical analysis
Operadors no lineals
Recurrence relations
Steffensen’s method
Àrees temàtiques de la UPC
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Summary:This paper is devoted to the construction and analysis of a Moser–Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of convergence for systems of equations, hypotheses ensuring the local convergence, and finally, we focus our attention to its numerical behavior. The conclusion is that the method improves the applicability of both Newton and Steffensen methods having the same order of convergence.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-016-0735-3