A Family of Improved Secant-Like Method with Super-Linear Convergence
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A Family of Improved Secant-Like Method with Super-Linear Convergence

Authors: Liang Chen

Abstract:

A family of improved secant-like method is proposed in this paper. Further, the analysis of the convergence shows that this method has super-linear convergence. Efficiency are demonstrated by numerical experiments when the choice of α is correct.

Keywords: Nonlinear equations, Secant method, Convergence order, Secant-like method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1087896

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[1] A. M. Ostrowski, Solution of Equations and Systems of Equations, Academic Press, New York, 1973. 11.
[2] J. F. TRAUB, Iterative Methods for the Solution of Equations, Prentice- Hall, Englewood Cliffs, NJ, 1964.
[3] J.E. Dennis and R.B. Schnable. Numerical methods for Unconstrained Optimisation and Nonlinear Equations, Prentice Hall, 1983.
[4] Alfio Quarteroni, Riccardo Sacco, Fausto Saleri. Numerical Mathematics, Springer, 2000.
[5] C.T. Kelly, Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia, PA, 1995.
[6] I. K. Argyros, S. Hilout, An improved local convergence analysis for Newton-Steffensen-type method, J. Appl. Math. Comput. 32(2010) 111- 118.
[7] S. Amat, M. Hern´andez, N. Romero, A modified Chebyshev’s iterative method with at least sixth order of convergence, Appl. Math. Comput. 206(2008) 164 - 174.
[8] M. Frontini, E. Sormani, Some variants of Newton’s method with thirdorder convergence, Appl. Math. Comput. 140 (2003) 419-426.
[9] A.Y. O¨ zban, Some new variants of Newton’s method, Appl. Math. Lett. 17 (2004) 677-682.
[10] S. Weerakoon, T.G.I. Fernando, A variant of Newton’s method with accelerated third-order convergence, Appl. Math. Lett. 13 (2000) 87-93.
[11] C. Chun, On the construction of iterative methods with at least cubic convergence, Appl. Math. Comput. 189 (2007) 1384-1392.
[12] L.D. Petkovi, M.S. Petkovi, A note on some recent methods for solving nonlinear equations, Appl. Math. Comput. 185 (2007) 368-374.
[13] Hongmin Ren, Qingbiao Wu, Weihong Bi, On convergence of a new secant-like method for solving nonlinear equations, Appl. Math. Comput. 217 (2010) 583-589.
[14] Hui Zhang, De-Sheng Li, Yu-Zhong Liu. A new method of secant-like for nonlinear equations, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009) 2923-2927.
[15] Xiuhua Wang, Jisheng Kou, Chuanqing Gu, A new modified secant-like method for solving nonlinear equations, Comput. Math. Appl. 60(2010) 1633-1638.
[16] Liang Chen, Yanfang Ma. A new modified King-Werner method for solving nonlinear equations, Comput. Math. Appl. 62(2011) 3700-3705.
[17] V. Kanwar, J.R. Sharma, Mamta, A new family of Secant-like method with super-linear convergence, Appl. Math. Comput. 171(2005) 104-107.