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A new fourth-order iterative method for finding multiple roots of nonlinear equations. (English) Zbl 1175.65054
Summary: We present a new fourth-order method for finding multiple roots of nonlinear equations. It requires one evaluation of the function and two of its first derivative per iteration. Finally, some numerical examples are given to show the performance of the presented method compared with some known third-order methods.

65H05 Numerical computation of solutions to single equations
Full Text: DOI
[1] Schröder, E., Über unendlich viele algorithmen zur auflösung der gleichungen, Math. ann., 2, 317-365, (1870)
[2] Traub, J.F., Iterative methods for the solution of equations, (1977), Chelsea Publishing Company New York · Zbl 0121.11204
[3] Hansen, E.; Patrick, M., A family of root finding methods, Numer. math., 27, 257-269, (1977) · Zbl 0361.65041
[4] Victory, H.D.; Neta, B., A higher order method for multiple zeros of nonlinear functions, Int. J. comput. math., 12, 329-335, (1983) · Zbl 0499.65026
[5] Dong, C., A basic theorem of constructing an iterative formula of the higher order for computing multiple roots of an equation, Math. numer. sinica, 11, 445-450, (1982) · Zbl 0511.65030
[6] Dong, C., A family of multipoint iterative functions for finding multiple roots of equations, Int. J. comput. math., 21, 363-367, (1987) · Zbl 0656.65050
[7] Osada, N., An optimal multiple root-finding method of order three, J. comput. appl. math., 51, 131-133, (1994) · Zbl 0814.65045
[8] Neta, B., New third order nonlinear solvers for multiple roots, Appl. math. comput., 202, 162-170, (2008) · Zbl 1151.65041
[9] Chun, C.; Neta, B., A third-order modification of newton’s method for multiple roots, Appl. math. comput., (2009) · Zbl 1162.65342
[10] Chun, C.; Bae, H.J.; Neta, B., New families of nonlinear third-order solvers for finding multiple roots, Comput. math. appl., 57, 1574-1582, (2009) · Zbl 1186.65060
[11] Neta, B.; Johnson, A.N., High order nonlinear solver for multiple roots, Comput. math. appl., 55, 2012-2017, (2008) · Zbl 1142.65044
[12] Jarratt, P., Multipoint iterative methods for solving certain equations, Comput. J., 8, 398-400, (1966) · Zbl 0141.13404
[13] B. Neta, Extension of Murakami’s high order nonlinear solver to multiple roots, Int. J. Comput. Math., doi:10.1080/00207160802272263. · Zbl 1192.65052
[14] Murakami, T., Some fifth order multipoint iterative formulae for solving equations, J. inform. process., 1, 138-139, (1978) · Zbl 0394.65015
[15] Argyros, I.K.; Chen, D.; Qian, Q., The jarratt method in Banach space setting, J. comput. appl. math., 51, 103-106, (1994) · Zbl 0809.65054
[16] Gautschi, W., Numerical analysis: an introduction, (1997), Birkhäuser · Zbl 0877.65001
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