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A new modified secant-like method for solving nonlinear equations. (English) Zbl 1202.65064

Summary: We present a new secant-like method for solving nonlinear equations. Analysis of the convergence shows that the asymptotic convergence order of this method is \(1+\sqrt{3}\). Some numerical results are given to demonstrate its efficiency.

MSC:

65H05 Numerical computation of solutions to single equations
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[1] Ostrowski, A. M., Solution of Equations in Euclidean and Banach Space (1973), Academic Press: Academic Press New York · Zbl 0304.65002
[2] Traub, J. F., Iterative Methods for the Solution of Equations (1964), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0121.11204
[3] Amat, S.; Busquier, S.; Gutierrez, J. M., Geometric constructions of iterative functions to solve nonlinear equations, J. Comput. Appl. Math., 157, 197-205 (2003) · Zbl 1024.65040
[4] Kanwar, V.; Tomar, S. K., Modified families of Newton, Halley and Chebyshev methods, Appl. Math. Comput., 192, 20-26 (2007) · Zbl 1193.65065
[5] Frontini, M.; Sormani, E., Some variants of Newton’s method with third-order convergence, Appl. Math. Comput., 140, 419-426 (2003) · Zbl 1037.65051
[6] Homeier, H. H.H., On Newton-type methods with cubic convergence, J. Comput. Appl. Math., 176, 425-432 (2005) · Zbl 1063.65037
[7] Kou, J.; Li, Y.; Wang, X., Third-order modification of Newton’s method, J. Comput. Appl. Math., 205, 1-5 (2007) · Zbl 1118.65039
[8] Özban, A. Y., Some new variants of Newton’s method, Appl. Math. Lett., 17, 677-682 (2004) · Zbl 1065.65067
[9] 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
[10] Argyros, I. K.; Chen, D.; Qian, Q., The Jarratt method in Banach space setting, J. Comput. Appl. Math., 51, 103-106 (1994) · Zbl 0809.65054
[11] Chun, C., Some second-derivative-free variants of Chebyshev-Halley methods, Appl. Math. Comput., 191, 410-414 (2007) · Zbl 1193.65054
[12] Chun, C., On the construction of iterative methods with at least cubic convergence, Appl. Math. Comput., 189, 1384-1392 (2007) · Zbl 1122.65326
[13] Kanwar, V.; Tomar, S. K., Modified families of multi-point iterative methods for solving nonlinear equations, Numer. Algor., 44, 381-389 (2007) · Zbl 1216.65057
[14] Kou, J.; Li, Y.; Wang, X., A modification of Newton method with third-order convergence, Appl. Math. Comput., 181, 1106-1111 (2006) · Zbl 1172.65021
[15] Petkovi, L. D.; Petkovi, M. S., A note on some recent methods for solving nonlinear equations, Appl. Math. Comput., 185, 368-374 (2007)
[16] Potra, F. A.; Pták, V., Nondiscrete induction and iterative processes, (Research Notes in Mathematics, vol. 103 (1984), Pitman: Pitman Boston) · Zbl 0549.41001
[17] Sharma, J. R., A composite third order Newton-Steffensen method for solving nonlinear equations, Appl. Math. Comput., 169, 242-246 (2005) · Zbl 1084.65054
[18] Thukral, R., Introduction to a Newton-type method for solving nonlinear equations, Appl. Math. Comput., 195, 663-668 (2008) · Zbl 1154.65034
[19] Ujević, Nenad, An iterative method for solving nonlinear equations, J. Comput. Appl. Math., 201, 208-216 (2007) · Zbl 1110.65038
[20] Parhia, S. K.; Gupta, D. K., A sixth order method for nonlinear equations, Appl. Math. Comput., 203, 50-55 (2008) · Zbl 1154.65327
[21] Rafiq, A.; Awais, M.; Zafar, F., Modified efficient variant of super-Halley method, Appl. Math. Comput., 189, 2004-2010 (2007) · Zbl 1122.65345
[22] Zhang, Hui; Li, De-Sheng; Liu, Yu-Zhong, A new method of secant-like for nonlinear equations, Commun. Nonlinear Sci. Numer. Simulat., 14, 2923-2927 (2009) · Zbl 1221.65114
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