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A family of multi-point iterative methods for solving systems of nonlinear equations. (English) Zbl 1154.65037
This paper extends a known multi-point family of iterative methods for solving nonlinear equations to the $$n$$-dimensional case. A local convergence analysis and numerical examples are provided.

##### MSC:
 65H10 Numerical computation of solutions to systems of equations
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##### References:
 [1] Werner, W., Some improvements of classical iterative methods for the solution of nonlinear equations, (), 427-440 [2] Argyros, I.K.; Szidarovszky, F., The theory and applications of iterations methods, (1993), CRC Press Boca Raton, FL [3] Gutiérrez, J.M.; Hernández, M.A., A family of chebyshev – halley type methods in Banach spaces, Bull. austral. math. soc., 55, 113-130, (1997) · Zbl 0893.47043 [4] Amat, S.; Busquier, S.; Gutiérrez, J.M., Geometric constructions of iterative functions to solve nonlinear equations, J. comput. appl. math., 157, 197-205, (2003) · Zbl 1024.65040 [5] Frontini, M.; Sormani, E., Some variant of newton’s method with third-order convergence, Appl. math. comput., 140, 2-3, 419-426, (2003) · Zbl 1037.65051 [6] Argyros, I.K.; Chen, D.; Qian, Q., Optimal-order parameter identification in solving nonlinear systems in a Banach space, J. comput. math., 13, 267-280, (1995) · Zbl 0831.65060 [7] Han, D., The convergence on a family of iterations with cubic order, J. comput. math., 19, 5, 467-474, (2001) · Zbl 1008.65035 [8] Nedzhibov, G.H.; Hasanov, V.I.; Petkov, M.P., On some families of multi-point iterative methods for solving nonlinear equations, Numer. algor., 42, 127-136, (2006) · Zbl 1117.65067 [9] Traub, J.F., Iterative methods for the solution of equations, (1964), Prentice Hall Englewood Cliffs, New Jersey · Zbl 0121.11204 [10] Jarrat, P., Some fourth order multipoint iterative methods for solving equations, Math. comp., 20, 434-437, (1966) · Zbl 0229.65049 [11] 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 [12] Ezquerro, J.A.; Gutiérrez, J.M.; Hernández, M.A.; Salanova, M.A., A biparametric family of inverse-free multipoint iterations, Comput. appl. math., 19, 1, 109-124, (2000) · Zbl 1344.65051 [13] Ortega, J.M.; Rheinboldt, W.S., Iterative solution of nonlinear equations in several variables, (1970), Academic Press New York · Zbl 0241.65046 [14] Weerakoon, S.; Fernando, T.G.I., A variant of newton’s method with accelerated third-order convergence, Appl. math. lett., 13, 87-93, (2000) · Zbl 0973.65037
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