A New Optimal Eighth-Order Ostrowski-Type Family of Iterative Methods for Solving Nonlinear Equations

Hindawi Limited - Tập 2014 - Trang 1-7 - 2014
Taher Lotfi1, Tahereh Eftekhari2
1Department of Applied Mathematics, Hamedan Branch, Islamic Azad University, Hamedan 65138, Iran#TAB#
2Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan 987-98155, Iran#TAB#

Tóm tắt

Based on Ostrowski's method, a new family of eighth-order iterative methods for solving nonlinear equations by using weight function methods is presented. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative. Therefore, this family of methods has the efficiency index which equals 1.682. Kung and Traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2n−1. Thus, we provide a new class which agrees with the conjecture of Kung-Traub for n=4. Numerical comparisons are made to show the performance of the presented methods.

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Tài liệu tham khảo

1964

1973

10.1137/0710072

2013, Discrete Dynamics in Nature and Society, 2013, 10.1155/2013/301718

2013, Advances in Numerical Analysis, 2013, 10.1155/2013/957496

2012, Journal of Applied Mathematics, 2012, 10.1155/2012/751975

2011, Advances in Numerical Analysis, 2011, 10.1155/2011/270903

10.1155/2011/469512

10.1007/s10957-011-9929-9

10.1155/2012/568740

10.1016/j.mcm.2011.10.016

10.1007/s11075-009-9345-5

10.1016/j.amc.2007.03.074

10.1016/j.cam.2006.10.073

1974, Journal of the ACM, 21, 643, 10.1145/321850.321860

1966, Mathematical Computation, 20, 434, 10.1090/S0025-5718-66-99924-8

10.1016/j.amc.2009.03.077

10.1016/j.amc.2009.10.040

2000, Applied Mathematics Letters, 13, 87, 10.1016/S0893-9659(00)00100-2

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Hindawi Limited

Tập 2014

1-7

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