This paper discusses a class of discretized Newton methods for solving systems of nonlinear equations. The number of function evaluations requred by the new discretized algorithm is about half of the classical discretized Newton method as Brown and Brent methods. The approximation given by the algorithms to F’(x) is strongly consistent. The algorithms can reduce to the Newton method when the difference stepsize h approaches to zeros but Brown and Brent methods can’t do it. Numerical results show the algorithms are efficient.
