×

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.

MSC:

65H05 Numerical computation of solutions to single equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ostrowski, A. M., Solution of equations in Euclidean and Banach space (1973), Academic Press: Academic Press New York · 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.; 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.; 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.; 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.; 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), Birkhäuser · Zbl 0877.65001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.