The authors present new iterative schemes for solving systems of nonlinear equations based on modifications of the classical Newton method which accelerate the convergence. Using Adomian polynomials [see G. Adomian, J. Math. Anal. Appl. 135, 501–544 (1988; Zbl 0671.34053)]. they obtain a family of multipoint iterative formulas including the Newton and Traub methods as simple special cases. The convergence analysis leads to the conclusion that the order of convergence of the new iterative methods is under the same assumptions as for the classical Newton method.
Finally, the results of numerical experiments are given and the new methods are compared with the classical Newton method and the Traub method [see J. F. Traub, Iterative methods for the solution of equations. 2nd ed. New York, N.Y.: Chelsea Publishing Company (1982; Zbl 0472.65040)] to confirm the theoretical results.