Some three-step iterative methods free from second order derivative for finding solutions of systems of nonlinear equations. (English) Zbl 1195.65068

Darvishi, M. T.

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)

MSC:

65H10

Numerical computation of solutions to systems of equations

Keywords:

Newton’s method; three step method; root finding; nonlinear system; convergence; numerical experiments