Darvishi, M. T. Some three-step iterative methods free from second order derivative for finding solutions of systems of nonlinear equations. (English) Zbl 1195.65068 Int. J. Pure Appl. Math. 57, No. 4, 557-573 (2009). The author presents, for the solution of a nonlinear system, three three-step Newton-like methods involving only the first derivative. The methods are extensions of the counterparts for the scalar equation with the derivative replaced by Jacobian. The author proves convergence. Numerical experiments show a reduction in the number of iterations (not steps), for two out of these three methods, comparing with the classical Newton’s method. Reviewer: Yanlai Chen (Providence) Cited in 9 Documents MSC: 65H10 Numerical computation of solutions to systems of equations Keywords:Newton’s method; three step method; root finding; nonlinear system; convergence; numerical experiments PDF BibTeX XML Cite \textit{M. T. Darvishi}, Int. J. Pure Appl. Math. 57, No. 4, 557--573 (2009; Zbl 1195.65068) OpenURL