A third-order Newton-type method to solve systems of nonlinear equations. (English) Zbl 1116.65060

Summary: We present a third-order Newton-type method to solve systems of nonlinear equations. In the first part we present theoretical preliminaries of the method. Secondly, we solve some systems of nonlinear equations. All test problems show the third-order convergence of our method.


65H10 Numerical computation of solutions to systems of equations
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[1] Abbasbandy, S., Improving newton – raphson method for nonlinear equations by modified Adomian decomposition method, Appl. math. comput., 145, 887-893, (2003) · Zbl 1032.65048
[2] Chun, Ch., A new iterative method for solving nonlinear equations, Appl. math. comput., 178, 2, 415-422, (2006) · Zbl 1105.65057
[3] Chun, Ch., Iterative methods improving newton’s method by the decomposition method, Comput. math. appl., 50, 1559-1568, (2005) · Zbl 1086.65048
[4] Frontini, M.; Sormani, E., Third-order methods from quadrature formulae for solving systems of nonlinear equations, Appl. math. comput., 149, 771-782, (2004) · Zbl 1050.65055
[5] Frontini, M.; Sormani, E., Some variants of newton’s method with third-order convergence, Appl. math. comput., 140, 419-426, (2003) · Zbl 1037.65051
[6] Homeier, H.H.H., On Newton-type methods with cubic convergence, J. comput. appl. math., 176, 425-432, (2005) · Zbl 1063.65037
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