Abstract
We analyze the disadvantages of Chebyshev-Halley methods and propose a new iterative method,which converges cubically and can be used as an alternative to Chebyshev-Halley methods and other iterative methods.A simple numerical example is provided to show that our result can apply, while Chebyshev-Halley methods may not.
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References
Ostrowski, A.M.: Solution of Equations in Euclidean and Banach Space. Academic Press, New York (1973)
Weerakoon, S., Fernando, T.G.I.: A variant of Newton’s method with accelerated third-order convergence. Appl. Math. Lett. 13, 87–93 (2000)
Homeier, H.H.H.: On Newton-type methods with cubic convergence. J. Comput. Appl. Math. 176, 425–432 (2005)
Ozban, A.Y.: Some new variants of Newton’s method. Appl. Math. Lett. 17, 677–682 (2004)
Chun, C.: Some third-order families of iterative methods for solving nonlinear equations. Appl. Math. Comput. 188, 924–933 (2007)
Frontini, M., Sormani, E.: Some variants of Newton’s method with third-order convergence. J. Comput. Appl. Math. 140, 419–426 (2003)
Kou, J., Li, Y., Wang, X.: A modification of Newton method with third-order convergence. Appl. Math. Comput. 181, 1106–1111 (2006)
Kou, J., Li, Y., Wang, X.: Third-order modification of Newton’s method. J. Comput. Appl. Math. 205, 1–5 (2007)
Gutiérrez, J.M., Hernández, M.A.: A family of Chebyshev-Halley type methods in Banach spaces. Bull. Aust. Math. Soc. 55, 113–130 (1997)
Kou, J., Li, Y., Wang, X.: On a family of second-derivative-free variants of Chebyshevs method. Appl. Math. Comput. 181, 982–987 (2006)
Kou, J., Li, Y., Wang, X.: A uniparametric Chebyshev-type method free from second derivatives. Appl. Math. Comput. 179, 296–300 (2006)
Kou, J., Li, Y.: Modified Chebyshev’s method free from second derivative for non-linear equations. Appl. Math. Comput. 187, 1027–1032 (2007)
Chun, C.: Some variants of Chebyshev-Halley methods free from second derivative. Appl. Math. Comput. 191, 193–198 (2007)
Wu, X.: Newton-like method with some remarks. Appl. Math. Comput. 188, 433–439 (2007)
Wu, X.: A new continuation Newton-like method and its deformation. Appl. Math. Comput. 112, 75–78 (2000)
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Hu, Z., Ma, X., Li, J. (2011). A Note on Chebyshev-Halley Method with Data Analysis. In: Lin, S., Huang, X. (eds) Advances in Computer Science, Environment, Ecoinformatics, and Education. CSEE 2011. Communications in Computer and Information Science, vol 216. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23345-6_87
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DOI: https://doi.org/10.1007/978-3-642-23345-6_87
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23344-9
Online ISBN: 978-3-642-23345-6
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