Article
After notes on Chebyshev’s iterative method
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Abstract
This paper is a small review of Chebyshev’s method. The geometric interpretation as a generalization of Newton’s method is derived. Using this interpretation its global convergence is proved. Some dynamical properties are studied. As a higher order method, they are more complicated than in Newton’s method. Finally, some applications are revisited pointing out the advantages of Chebyshev’s method with respect Newton’s method.
Keywords
Nonlinear equations, Chebyshev’s iterative method, geometric interpretation, global convergence, dynamics, applications, 65J15
Citation
Amat, S. & Busquier, S. (2017). After notes on chebyshev’s iterative method. Applied Mathematics and Nonlinear Sciences, 2(1), 1–12. https://doi.org/10.21042/AMNS.2017.1.00001
S. Amat and S. Busquier, “After notes on chebyshev’s iterative method,” Applied Mathematics and Nonlinear Sciences, vol. 2, no. 1, pp. 1–12, 2017, doi: 10.21042/AMNS.2017.1.00001.
Amat S, Busquier S. After notes on chebyshev’s iterative method. Applied Mathematics and Nonlinear Sciences. 2017;2(1):1–12. doi:10.21042/AMNS.2017.1.00001.
Amat, S. and Busquier, S. (2017), ‘After notes on chebyshev’s iterative method’, Applied Mathematics and Nonlinear Sciences, 2(1), pp. 1–12. Available at: https://doi.org/10.21042/AMNS.2017.1.00001.
Amat, S., and S. Busquier. “After Notes on Chebyshev’s Iterative Method.” Applied Mathematics and Nonlinear Sciences, vol. 2, no. 1, 2017, pp. 1–12. https://doi.org/10.21042/AMNS.2017.1.00001.
Amat, S., and S. Busquier. “After Notes on Chebyshev’s Iterative Method.” Applied Mathematics and Nonlinear Sciences 2, no. 1 (2017): 1–12. https://doi.org/10.21042/AMNS.2017.1.00001.
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Published by: Engineering Journals
