Abstract
We consider Kurchatov’smethod and construct two variants of this method for solving systems of nonlinear equations and deduce their local R-orders of convergence in a direct symbolic computation. We also propose a generalization to several variables of the efficiency used in the scalar case and analyse the efficiencies of the three methods when they are used to solve systems of nonlinear equations.
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Acknowledgements
This research is supported by the National Center for Mathematics and Interdisciplinary Sciences, and by National Natural Science Foundation of China (Grant Nos. 60931002, 11001072 and 11101381), and partially by the Spanish Ministry of Science and Innovation under Grant AYA2009-14212-C05-05.
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This work was supported in part by the project MTM2011-28636-C02-01 of the Spanish Ministry of Science and Innovation.
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Ezquerro, J.A., Grau, A., Grau-Sánchez, M. et al. On the efficiency of two variants of Kurchatov’s method for solving nonlinear systems. Numer Algor 64, 685–698 (2013). https://doi.org/10.1007/s11075-012-9685-4
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DOI: https://doi.org/10.1007/s11075-012-9685-4
Keywords
- Divided difference
- R-order of convergence
- Nonlinear equations
- Kurchatov’s method
- Iterative methods
- Computational efficiency