References
- D.K.R. Babajee, Analysis of higher order variants of Newton's method and their applications to differential and integral equations and in ocean acidation, Ph.D. thesis, University of Mauritius, December, 2010.
- Chun , C. and Neta , B. 2009 . A third-order modification of Newton's method for multiple roots . Appl. Math. Comput. , 211 : 474 – 479 . (doi:10.1016/j.amc.2009.01.087)
- Chun , C. , Bae , H. J. and Neta , B. 2009 . New families of nonlinear third-order solvers for finding multiple roots . Comput. Math. Appl. , 57 : 1574 – 1582 . (doi:10.1016/j.camwa.2008.10.070)
- Grau-Sánchez , M. and Díaz-Barrero , J. L. 2011 . Zero-finder methods derived using Runge–Kutta techniques . Appl. Math. Comput. , 217 : 5366 – 5376 . (doi:10.1016/j.amc.2010.11.059)
- Honorato , G. , Plaza , S. and Romero , N. 2011 . Dynamics of a higher-order family of iterative methods . J. Complexity , 27 ( 2 ) : 221 – 229 . (doi:10.1016/j.jco.2010.10.005)
- Ikhile , M. N.O. 2011 . The root and Bell's disk iteration methods are of the same error propagation characteristics in the simultaneous determination of the zeros of a polynomial, Part II: Round-off error analysis by use of interval arithmetic . Comput. Math. Appl. , 61 ( 11 ) : 3191 – 3217 . (doi:10.1016/j.camwa.2011.03.106)
- Iliev , A. and Kyurkchiev , N. 2002 . On a generalization of Weierstrass–Dochev method for simultaneous extraction of only a part of all roots of algebraic polynomials: Part I . C. R. Acad. Bulgare Sci. , 55 : 23 – 26 .
- Iliev , A. and Kyurkchiev , N. 2002 . Some methods for simultaneous extraction of only a part of all roots of algebraic polynomials: Part II . C. R. Acad. Bulgare Sci. , 55 : 17 – 22 .
- Iliev , A. and Kyurkchiev , N. 2005 . Some methods for simultaneous extraction of a part of all multiple roots of algebraic polynomials . Computing , 75 : 85 – 97 . (doi:10.1007/s00607-004-0116-9)
- Iliev , A. and Kyurkchiev , N. 2010 . Nontrivial Methods in Numerical Analysis: Selected Topics in Numerical Analysis , Saarbrucken , , Germany : LAP LAMBERT Academic Publishing, GmbH & Co. KG .
- Khattri , S. K. and Argyros , I. K. 2011 . Sixth order derivative free family of iterative methods . Appl. Math. Comput. , 217 ( 12 ) : 5500 – 5507 . (doi:10.1016/j.amc.2010.12.021)
- Khattri , S. K. and Torgrim , L. 2011 . Constructing third-order derivative-free iterative methods . Int. J. Comput. Math. , 88 ( 7 ) : 1509 – 1518 . (doi:10.1080/00207160.2010.520705)
- Kyurkchiev , N. and Iliev , A. 2002 . On the R-order of convergence of a family of methods for simultaneous extraction of part of all roots of algebraic polynomials . BIT , 42 : 879 – 885 . (doi:10.1023/A:1021964823349)
- Li , S. G. , Cheng , L. Z. and Neta , B. 2010 . Some fourth-order nonlinear solvers with closed formulae for multiple roots . Comput. Math. Appl. , 59 : 126 – 135 . (doi:10.1016/j.camwa.2009.08.066)
- McNamee , J. M. 2007 . Numerical Methods for Roots of Polynomials , Amsterdam : Part I, Elsevier .
- McNamee , J. M. and Pan , V. Y. 2012 . Efficient polynomial root-refiners: A survey and new record efficiency estimates . Comput. Math. Appl. , 63 ( 1 ) : 239 – 254 . (doi:10.1016/j.camwa.2011.11.015)
- Nedzhibov , G. H. and Petkov , M. G. 2005 . On a family of iterative methods for simultaneous extraction of all roots of algebraic polynomial . Appl. Math. Comput. , 162 ( 1 ) : 427 – 433 . (doi:10.1016/j.amc.2003.12.103)
- Nedzhibov , G. H. 2005 . An acceleration of iterative processes for solving nonlinear equations . Appl. Math. Comput. , 168 ( 1 ) : 320 – 332 . (doi:10.1016/j.amc.2004.08.020)
- Nedzhibov , G. H. , Hasanov , V. I. and Petkov , M. G. 2006 . On some families of multipoint iterative methods for solving nonlinear equations . Numer. Algorithms , 4 ( 2 ) : 127 – 136 . (doi:10.1007/s11075-006-9027-5)
- G.H. Nedzhibov, On some modifications of Weierstrass-Dochev method for simultaneous extraction of only a part of all roots of polynomials, Application of Mathematics in Engineering and Economics: 36th International Conference, AIP Conference Proceedings 1293, 2010, pp. 141–148.
- Nedzhibov , G. 2012 . A derivative free iterative method for simultaneous computing arbitrary number of zeros of nonlinear equations . Comput. Math. Appl. , 63 ( 7 ) : 1185 – 1191 . (doi:10.1016/j.camwa.2011.12.037)
- Neta , B. and Johnson , A. N. 2008 . High order nonlinear solver for multiple roots . Comput. Math. Appl. , 55 : 2012 – 2017 . (doi:10.1016/j.camwa.2007.09.001)
- Neta , B. 2008 . New third order nonlinear solvers for multiple roots . Appl. Math. Comput. , 202 : 162 – 170 . (doi:10.1016/j.amc.2008.01.031)
- Neta , B. 2010 . Extension of Murakami's high order nonlinear solver to multiple roots . Int. J. Comput. Math. , 8 : 1023 – 1031 . (doi:10.1080/00207160802272263)
- Neta , B. , Scott , M. and Chun , C. 2012 . Basin attractors for various methods for multiple roots . Appl. Math. Comput. , 218 ( 9 ) : 5043 – 5066 . (doi:10.1016/j.amc.2011.10.071)
- Noor , M. A. 2007 . New iterative schemes for nonlinear equations . Appl. Math. Comput. , 187 ( 2 ) : 937 – 943 . (doi:10.1016/j.amc.2006.09.028)
- Ortega , J. M. and Rheiboldt , W. C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academic Press .
- Pan , V. Y. and Zheng , A. L. 2011 . Root-finding by expansion with independent constraints . Comput. Math. Appl. , 62 ( 8 ) : 3164 – 3182 . (doi:10.1016/j.camwa.2011.08.029)
- Petković , L. D. and Petković , M. S. 2007 . A note on some recent methods for solving nonlinear equations . Appl. Math. Comput. , 185 : 368 – 374 . (doi:10.1016/j.amc.2006.06.118)
- Petković , L. D. , Rančić , L. and Petković , M. S. 2008 . An efficient higher order family of root finders . J. Comput. Appl. Math. , 216 : 56 – 72 . (doi:10.1016/j.cam.2007.04.015)
- Petković , L. D. , Rančic , L. and Petković , M. S. 2008 . An efficient higher order family of root finders . J. Comput. Appl. Math. , 216 ( 1 ) : 56 – 72 . (doi:10.1016/j.cam.2007.04.015)
- Petković , M. S. , Petković , L. D. and Herceg , D. 2010 . On Schroder's families of root-finding methods . J. Comput. Appl. Math. , 233 ( 8 ) : 1755 – 1762 . (doi:10.1016/j.cam.2009.09.012)
- Petković , M. S. , Petković , L. D. and Dzunić , J. 2010 . Accelerating generators of iterative methods for finding multiple roots of nonlinear equations . Comput. Math. Appl. , 59 ( 8 ) : 2784 – 2793 . (doi:10.1016/j.camwa.2010.01.048)
- Petković , M. S. , Rančić , L. and Milošević , M. R. 2011 . On the new fourth-order methods for the simultaneous approximation of polynomial zeros . J. Comput. Appl. Math. , 235 ( 14 ) : 4059 – 4075 . (doi:10.1016/j.cam.2011.02.032)
- Prešić , S. 1966 . Un procédé itératif pour la factorisation des polynomes . C.R. Acad. Sci. Paris , 262 : 862 – 863 .
- Proinov , P. D. 2010 . New general convergence theory for iterative processes and its applications to Newton–Kantorovich type theorems . J. Complexity , 26 ( 1 ) : 3 – 42 . (doi:10.1016/j.jco.2009.05.001)
- Traub , J. F. 1964 . Iterative Methods for the Solution of Equations , Englewood Cliffs , NJ : Prentice Hall .
- Victory , H. D. and Neta , B. 1983 . A higher order method for multiple zeros of nonlinear functions . Int. J. Comput. Math. , 12 : 329 – 335 . (doi:10.1080/00207168208803346)
- Zhang , X. , Peng , H. and Hu , G. 2006 . A high order iteration formula for the simultaneous inclusion of polynomial zeros . Appl. Math. Comput. , 179 ( 2 ) : 545 – 552 . (doi:10.1016/j.amc.2005.11.117)