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Some sixth-order variants of Ostrowski root-finding methods. (English) Zbl 1193.65055
Summary: We present some sixth-order class of modified Ostrowski’s methods for solving nonlinear equations. Per iteration each class member requires three function and one first derivative evaluations, and is shown to be at least sixth-order convergent. Several numerical examples are given to illustrate the performance of some of the presented methods.

65H05Single nonlinear equations (numerical methods)
Full Text: DOI
[1] Ostrowski, A. M.: Solution of equations in Euclidean and Banach space. (1973) · Zbl 0304.65002
[2] C. Chun, Some improvements of Jarratt’s method with sixth-order convergence, Appl. Math. Comput. (in press). doi:10.1016/j.amc.2007.02.023. · Zbl 1122.65329
[3] 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
[4] J. Kou, Y. Li, X. Wang, An improvement of the Jarrat method, Appl. Math. Comput. (in press). doi:10.1016/j.amc.2006.12.062.
[5] J. Kou, Y. Li, The improvements of Chebyshev -- Halley methods with fifth-order convergence, Appl. Math. Comput. (in press). doi:10.1016/j.amc.2006.09.097. · Zbl 1118.65036
[6] Grau, M.; Díaz-Barrero, J. L.: An improvement to Ostrowski root-finding method. J. math. Anal. appl. 173, 450-456 (2006) · Zbl 1090.65053
[7] J.R. Sharma, R.K. Guha, A family of modified Ostrowski methods with accelerated sixth-order convergence, Appl. Math. Comput. (in press). doi:10.1016/j.amc.2007.01.009. · Zbl 1126.65046
[8] Chun, C.: Iterative methods improving Newton’s method by the decomposition method. Comput. math. Appl. 50, 1559-1568 (2005) · Zbl 1086.65048
[9] Gautschi, W.: Numerical analysis: an introduction. (1997) · Zbl 0877.65001