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Kou, Jisheng; Li, Yitian; Wang, Xiuhua

Some modifications of Newton’s method with fifth-order convergence. (English) Zbl 1130.41005

J. Comput. Appl. Math. 209, No. 2, 146-152 (2007).
Summary: We present some new modifications of Newton’s method for solving nonlinear equations. Analysis of convergence shows that these methods have order of convergence five. Numerical tests verifying the theory are given and based on these methods, a class of new multistep iterations is developed.

Cited in 1 Review
Cited in 24 Documents

MSC:

41A25 Rate of convergence, degree of approximation
65D99 Numerical approximation and computational geometry (primarily algorithms)

Keywords:

Newton’s method; nonlinear equations; iterative method; root-finding
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\textit{J. Kou} et al., J. Comput. Appl. Math. 209, No. 2, 146--152 (2007; Zbl 1130.41005)
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References:

[1] Frontini, M.; Sormani, E., Some variants of Newton’s method with third-order convergence, Appl. Math. Comput., 140, 419-426 (2003) · Zbl 1037.65051
[2] Frontini, M.; Sormani, E., Modified Newton’s method with third-order convergence and multiple roots, J. Comput. Appl. Math., 156, 345-354 (2003) · Zbl 1030.65044
[3] Frontini, M.; Sormani, E., Third-order methods from quadrature formulae for solving systems of nonlinear equations, Appl. Math. Comput., 149, 771-782 (2004) · Zbl 1050.65055
[4] Gautschi, W., Numerical Analysis: An Introduction (1997), Birkhäuser: Birkhäuser Basel · Zbl 0877.65001
[5] Grau, M.; Díaz-Barrero, J. L., An improvement of the Euler-Chebyshev iterative method, J. Math. Anal. Appl., 315, 1-7 (2006) · Zbl 1113.65048
[6] Homeier, H. H.H., A modified Newton method for rootfinding with cubic convergence, J. Comput. Appl. Math., 157, 227-230 (2003) · Zbl 1070.65541
[7] Homeier, H. H.H., A modified Newton method with cubic convergence: the multivariate case, J. Comput. Appl. Math., 169, 161-169 (2004) · Zbl 1059.65044
[8] Homeier, H. H.H., On Newton-type methods with cubic convergence, J. Comput. Appl. Math., 176, 425-432 (2005) · Zbl 1063.65037
[9] Ostrowski, A. M., Solution of Equations in Euclidean and Banach Space (1973), Academic Press: Academic Press New York · Zbl 0304.65002
[10] Özban, A. Y., Some new variants of Newton’s method, Appl. Math. Lett., 17, 677-682 (2004) · Zbl 1065.65067
[11] Weerakoon, S.; Fernando, T. G.I., A variant of Newton’s method with accelerated third-order convergence, Appl. Math. Lett., 13, 87-93 (2000) · Zbl 0973.65037
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