Iterative methods for multiple roots with memory using self-accelerating technique

Ortega, 1970 Wu, 2000, A new continuation Newton-like method and its deformation, Appl. Math. Comput., 112, 75, 10.1016/S0096-3003(99)00049-1 Schröder, 1870, Über unendlich viele Algorithmen zur Auflösung der Gleichungen, Math. Ann., 2, 317, 10.1007/BF01444024 Jarratt, 1969, Some efficient fourth order multipoint methods for solving equations, BIT, 9, 119, 10.1007/BF01933248 Sharma, 2010, Modified Jarratt method for computing multiple roots, Appl. Math. Comput., 217, 878, 10.1016/j.amc.2010.06.031 Li, 2010, Some fourth-order nonlinear solvers with closed formulae for multiple roots, Comput. Math. Appl., 59, 126, 10.1016/j.camwa.2009.08.066 Zhou, 2011, Constructing higher-order methods for obtaining the multiple roots of nonlinear equations, Comput. Math. Appl., 235, 4199, 10.1016/j.cam.2011.03.014 Zhou, 2013, Families of third and fourth order methods for multiple roots of nonlinear equations, Appl. Math. Comput., 219, 6030, 10.1016/j.amc.2012.12.041 Liu, 2013, A new family of fourth-order methods for multiple roots of nonlinear equations, Nonlinear Anal. Model. Control., 18, 143, 10.15388/NA.18.2.14018 Kansal, 2019, Modified optimal class of Newton-like fourth-order methods for multiple roots, Symmetry, 11, 526, 10.3390/sym11040526 Geum, 2015, A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics, Appl. Math. Comput., 270, 387, 10.1016/j.amc.2015.08.039 Geum, 2016, A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points, Appl. Math. Comput., 283, 120, 10.1016/j.amc.2016.02.029 Thukral, 2013, Introduction to higher-order iterative methods for finding multiple roots of nonlinear equations, J. Math., 2013, 10.1155/2013/404635 Geum, 2016, A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points, Appl. Math. Comput., 283, 120, 10.1016/j.amc.2016.02.029 Behl, 2017, An eighth-order family of optimal multiple root finders and its dynamics, Numer. Algorithms, 77, 1249, 10.1007/s11075-017-0361-6 Petković, 2019, Construction and efficiency of multipoint root-ratio methods for finding multiple zeros, J. Comput. Appl. Math., 351, 54, 10.1016/j.cam.2018.10.042 Neta, 2013, On the development of iterative methods for multiple roots, Appl. Math. Comput., 224, 358, 10.1016/j.amc.2013.08.077 Kanwar, 2013, New optimal class of higher-order methods for multiple roots, permitting f′(xn)=0, Appl. Math. Comput., 222, 564, 10.1016/j.amc.2013.06.097 Zafar, 2019, Stability analysis of a family of optimal fourth-order methods for multiple roots, Numer. Algorithms, 81, 947, 10.1007/s11075-018-0577-0 Lee, 2017, On the dynamics of tri-parametric family of optimal fourth-order multiple-zero finders with a weight function of the principal mth root of a function-function ratio, Appl. Math. Comput., 315, 564, 10.1016/j.amc.2017.08.005 Petković, 2010, Derivative free two-point methods with and without memory for solving nonlinear equations, Appl. Math. Comput., 217, 1887, 10.1016/j.amc.2010.06.043 Zheng, 2010, Variants of Steffensen-secant method and applications, Appl. Math. Comput., 216, 3486, 10.1016/j.amc.2010.04.058 Cordero, 2015, An efficient two-parametric family with memory for nonlinear equations, Numer. Algorithms, 68, 323, 10.1007/s11075-014-9846-8 Džunić, 2013, On efficient two-parameter methods for solving nonlinear equations, Numer. Algorithms, 63, 549, 10.1007/s11075-012-9641-3 Soleymani, 2015, Several iterative methods with memory using-accelerators, Appl. Math. Comput., 254, 452, 10.1016/j.amc.2015.01.045 Alefeld, 1983 Cordero, 2007, Variants of Newton’s method using fifth-order quadrature formulas, Appl. Math. Comput., 190, 686, 10.1016/j.amc.2007.01.062