Iranian Journal of Numerical Analysis and Optimization

Article 4, Volume 13, Issue 3 - Serial Number 26, January 0, Pages 426-443   

Document Type: Research Article

DOI: 10.22067/ijnao.2022.75865.1118

References

[1] Babajee, D. and Dauhoo, M. An analysis of the properties of the variants of Newton’s method with third order convergence, Appl. Math. Comput. 183(1) (2006), 659–684.

[2] Cătinaş, E. How many steps still left to x∗?, SIAM Rev. 63(3) (2021), 585–624.
[3] Cătinaş, E. A survey on the high convergence orders and computational convergence orders of sequences, Appl. Math. Comput., 343 (2019), 1–20.
[4] Cheney, E.W. and Kincaid, D.R. Numerical analysis: mathematics of scientific computing, 1996: Brooks/Cole Publ.
[5] Chun, C. and Neta, B. Comparison of several families of optimal eighth order methods, Appl. Math. Comput., 274 (2016), 762–773.
[6] Dong, C. A family of multiopoint iterative functions for finding multiple roots of equations, Int. J. Comput. Math. 21(3-4) (1987), 363–367.
[7] Ferngndez-Torres, G. and Vgsquez-Aquino, J. Three new optimal fourth-order iterative methods to solve nonlinear equations, Adv. Numer. Anal. 2013, Art. ID 957496, 8 pp.
[8] Gander, W. On Halley’s iteration method, Amer. Math. Monthly, 92(2) (1985), 131–134.
[9] Grau, M. and Daaz-Barrero, J.L. An improvement to Ostrowski root-finding method, Appl. Math. Comput., 173(1) (2006), 450–456.
[10] Gutiérrez, J.M., Magre￿g M.A. and Varona, J.L. The ”Gauss-Seidelization” of iterative methods for solving nonlinear equations in the complex plane, Appl. Math. Comput., 218(6) (2011), 2467–2479.
[11] Hansen, E. and Patrick, M. A family of root finding methods, Numer. Math. 27(3) (1976/77), 257–269.
[12] Jarratt, P. Some fourth order multipoint iterative methods for solving equations, Math. Comput., 20(95) (1966), 434–437.
[13] King, R.F. A family of fourth order methods for nonlinear equations, SIAM J. Numer. Anal. 10(5) (1973), 876–879.
[14] Kou, J., Li, Y. and Wang, X. A composite fourth-order iterative method for solving non-linear equations, Appl. Math. Comput., 184(2) (2007), 471–475.
[15] Kung, H. and Traub, J.F.Optimal order of one-point and multipoint iteration, J. Assoc. Comput. Mach. 21(4) (1974), 643–651.
[16] Nedzhibov, G.H. and Petkov, M.G. On a family of iterative methods for simultaneous extraction of all roots of algebraic polynomial, Appl. Math. Comput., 162(1) (2005), 427–433.

[17] Neta, B., Chun, C. and Scott, M.Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations, Appl. Math. Comput., 227 (2014), 567–592.
[18] Noor, M.A., Waseem, M., Noor, K.I., Ali, M.A. New iterative technique for solving nonlinear equations, Appl. Math. Comput., 256 (2015), 1115–1125.
[19] Noor, M.A., Ahmad, F. and Javeed, S. Two-step iterative methods for nonlinear equations, Appl. Math. Comput., 181(2) (2006), 1068–1075.
[20] Ortega, J.M. and Rheinboldt, W.C. Iterative solution of nonlinear equa-tions in several variables, Reprint of the 1970 original. Classics in Ap-plied Mathematics, 30. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000.
[21] Osada, N. An optimal multiple root-finding method of order three, J. Comput. Appl. Math. 51(1) (1994), 131–133.
[22] Ostrowski, A.M. Solution of Equations and Systems of Equations, Pure and Applied Mathematics, Vol. IX. Academic Press, New York-London, 1960 ix+202 pp.
[23] Potra, F. and Ptak, V. Nondiscrete induction and iterative processes, Research Notes in Mathematics, 103. Pitman (Advanced Publishing Pro-gram), Boston, MA, 1984.
[24] Shah, F.A. and Noor, M.A. Some numerical methods for solving nonlin-ear equations by using decomposition technique, Appl. Math. Comput., 251 (2015), 378–386.
[25] Sharma, J.R. and Guha, R.K. A family of modified Ostrowski methods with accelerated sixth order convergence, Appl. Math. Comput., 190(1) (2007), 111–115.
[26] Traub, J. Iterative Methods for the Solution of Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1964.
[27] Varona, J.L. Graphic and numerical comparison between iterative meth-ods, Math. Intell. 24(1) (2002), 37–47.
[28] Yun, J.H. A note on three-step iterative method for nonlinear equations, Appl. Math. Comput., 202(1) (2008), 401–405.