Nedzhibov, Gyurhan H. A family of multi-point iterative methods for solving systems of nonlinear equations. (English) Zbl 1154.65037 J. Comput. Appl. Math. 222, No. 2, 244-250 (2008). 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. Reviewer: Jinhai Chen (Hongkong) Cited in 21 Documents MSC: 65H10 Numerical computation of solutions to systems of equations Keywords:systems of nonlinear equations; iterative method; order of convergence; Chebyshev-Halley family; multi-point family; local convergence; numerical examples PDF BibTeX XML Cite \textit{G. H. Nedzhibov}, J. Comput. Appl. Math. 222, No. 2, 244--250 (2008; Zbl 1154.65037) Full Text: DOI OpenURL 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.