×

zbMATH — the first resource for mathematics

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.

MSC:
65H10 Numerical computation of solutions to systems of equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
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.