Two weighted eight-order classes of iterative root-finding methods

References

• S. Artidiello, F. Chicharro, A. Cordero, and J.R. Torregrosa, Local convergence and dynamical analysis of a new family of optimal fourth-order iterative methods, Int. J. Comput. Math. 90(10) (2013), pp. 2049–2060. doi: 10.1080/00207160.2012.748900
   Web of Science ®Google Scholar
• P. Blanchard, The dynamics of Newton's method, Proc. Symposia Appl. Math. 49 (1994), pp. 139–154.
   Google Scholar
• F. Chicharro, A. Cordero, and J.R. Torregrosa, Drawing dynamical and parameters planes of iterative families and methods, Sci. World J. 2013 (2013), Article ID:780153, 11 pp. doi: 10.1155/2013/780153
   Web of Science ®Google Scholar
• A. Cordero, J.R. Torregrosa, and M. Vassileva, Tree-step iterative method with a optimal eighth order of convergence, J. Comput. Appl. Math. 235 (2011), pp. 3189–3194. doi: 10.1016/j.cam.2011.01.004
   Web of Science ®Google Scholar
• J. Džunić and M. Petković, A family of three-point methods of Ostrowski's type for solving nonlinear equations, J. Appl. Math. 2012 (2012), 9 pp. 10.1155/2012/425867.
   Web of Science ®Google Scholar
• J. Džunić, M.S. Petković, and L.D. Petković, A family of optimal three-point methods for solving nonlinear equations using two parametric functions, Appl. Math. Comput. 217 (2011), pp. 7612–7619. doi: 10.1016/j.amc.2011.02.055
   Web of Science ®Google Scholar
• P.R. Escobal. Methods of Orbit Determination, Robert E. Krieger Publishing Company, Malabar, FL, 1965.
   Google Scholar
• Y. Khan, M. Fardi, and K. Sayevand, A new general eighth-order family of iterative methods for solving nonlinear equations, Appl. Math. Lett. 25 (2012), pp. 2262–2266. doi: 10.1016/j.aml.2012.06.014
   Web of Science ®Google Scholar
• Y.I. Kim, A triparametric family of three-step optimal eighth-order multipoint iterative methods for solving nonlinear equations, Int. J. Comput. Math. 89 (2012), pp. 1051–1059.
   Web of Science ®Google Scholar
• J. Kou and X. Wang, Some improvements of Ostrowski's method, Appl. Math. Lett. 23 (2010), pp. 92–96. doi: 10.1016/j.aml.2009.08.010
   Web of Science ®Google Scholar
• H.T. Kung and J.F. Traub, Optimal order of one-point and multipoint iteration, J. Assos. Comput. Math. 21 (1974), pp. 643–651. doi: 10.1145/321850.321860
   Web of Science ®Google Scholar
• Z. Liu, Q. Zheng, and P. Zhao, A variant of Steffensen's method of fourth-order convergence and its applications, Appl. Math. Comput. 216 (2010), pp. 1978–1983. doi: 10.1016/j.amc.2010.03.028
   Web of Science ®Google Scholar
• A.M. Ostrowski, Solution of Equations and System of Equations, Prentice-Hall, Englewood Cliffs, NJ, 1964.
   Google Scholar
• M.S. Petković, S. Ilić, and J. Džunić, Derivative free two-point methods with and without memory for solving nonlinear equations, Appl. Math. Comput. 217 (2010), pp. 1887–1895. doi: 10.1016/j.amc.2010.06.043
   Web of Science ®Google Scholar
• M. Petković, B. Neta, L. Petković, and J. Džunić, Multipoint Methods for Solving Nonlinear Equations, Academic Press, Amsterdam, 2012.
   Google Scholar
• H. Ren, Q. Wu, and W. Bi, A class of two-step Steffensen type methods with fourth-order convergence, Appl. Math. Comput. 209 (2009), pp. 206–210. doi: 10.1016/j.amc.2008.12.039
   Web of Science ®Google Scholar
• J.R. Sharma and R. Sharma, A new family of modified Ostrowski's methods with accelerated eighth-order convergence, Numer. Algorithms. 54 (2010), pp. 445–458. doi: 10.1007/s11075-009-9345-5
   Web of Science ®Google Scholar
• F. Soleymani and S.K. Khattri, Finding simple roots by seventh- and eighth-order derivative-free methods, Int. J. Math. Models Methods Appl. Sci. 1 (2012), pp. 45–52.
   Google Scholar
• F. Soleymani, M. Sharifi, and B.S. Mousavi, An improvement of Ostrowski's and King's techniques with optimal convergence order eight, J. Optim. Theory Appl. 153 (2012) 225–236.
   Web of Science ®Google Scholar
• J.F. Traub, Iterative Methods for the Solution of Equations, Chelsea Publishing Company, New York, 1977.
   Google Scholar
• S. Weerakoon and T.G.I. Fernando, A variant of Newton's method with accelerated third-order convergence, Appl. Math. Lett. 13 (2000), pp. 87–93. doi: 10.1016/S0893-9659(00)00100-2
   Web of Science ®Google Scholar
• Q. Zheng, J. Li, and F. Huang, An optimal Steffensen-type family for solving nonlinear equations, Appl. Math. Comput. 217 (2011), pp. 9592–9597. doi: 10.1016/j.amc.2011.04.035
   Web of Science ®Google Scholar