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On the construction of iterative methods with at least cubic convergence. (English) Zbl 1122.65326
Summary: Using the iteration formulas of order two for solving nonlinear equations, we present a basic tool for deriving new higher order iterative methods that do not require the computation of the second-order or higher-order derivatives. The presented convergence analysis shows that the order of convergence of the obtained iterative methods are three or higher. The comparison with other methods is given.

##### MSC:
 65H05 Numerical computation of solutions to single equations
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##### References:
 [1] Ostrowski, A.M., Solution of equations in Euclidean and Banach space, (1973), Academic Press New York · Zbl 0304.65002 [2] Potra, F.A.; Pták, V., Nondiscrete induction and iterative processes, Res. notes math., vol. 103, (1984), Pitman · Zbl 0549.41001 [3] Weerakoon, S.; Fernando, G.I., A variant of newton’s method with accelerated third-order convergence, Appl. math. lett., 17, 87-93, (2000) · Zbl 0973.65037 [4] Frontini, M.; Sormani, E., Some variants of newton’s method with third-order convergence, J. comput. appl. math., 140, 419-426, (2003) · Zbl 1037.65051 [5] Homeier, H.H.H., A modified Newton method for root finding with cubic convergence, J. comput. appl. math., 157, 227-230, (2003) · Zbl 1070.65541 [6] Homeier, H.H.H., On Newton-type methods with cubic convergence, J. comput. appl. math., 176, 425-432, (2005) · Zbl 1063.65037 [7] Özban, A.Y., Some new variants of newton’s method, Appl. math. lett., 17, 677-682, (2004) · Zbl 1065.65067 [8] Kou, J.; Li, Y.; Wang, X., A modification of Newton method with third-order convergence, Appl. math. comput., 181, 2, 1106-1111, (2006) · Zbl 1172.65021 [9] Johnson, L.W.; Riess, R.D., Numerical analysis, (1977), Addison-Wesley Reading, MA · Zbl 0257.65024 [10] Traub, J.F., Iterative methods for the solution of equations, (1977), Chelsea publishing company New York · Zbl 0121.11204 [11] Ostrowski, A.M., Solutions of equations and system of equations, (1960), Academic Press New York · Zbl 0115.11201 [12] Wu, X.-Y., A new continuation Newton-like method and its deformation, Appl. math. comput., 112, 75-78, (2000) · Zbl 1023.65043 [13] Mamta; Kanwar, V.; Kukreja, V.K.; Singh, S., On a class of quadratically convergent iteration formulae, Appl. math. comput., 166, 3, 633-637, (2005) · Zbl 1078.65036
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