A new method for solving a system of the nonlinear equations S. Effati * , A.R. Nazemi Department of Mathematics, Teacher Training University of Sabzevar, Sabzevar, Iran Abstract In this paper we use measure theory in the discrete case to solve a wide range of the nonlinear equations systems. First, by defining an error function, we transform the problem to an optimal control problem in discrete case. The new problem is modified into one consisting of the minimization of a linear functional over a set of Radon mea- sures; the optimal measure then is approximated by a finite combination of atomic mea- sures and the problem converted approximately to a finite-dimensional nonlinear programming. Finally, we obtain an approximate solution for the original problem, fur- thermore, we obtain the path from the initial point up to the approximate solution. Ó 2004 Elsevier Inc. All rights reserved. Keywords: Nonlinear equations system; Measure theory; Optimal control; Nonlinear programming 1. Introduction A well-known iterative method for solving a system of nonlinear equations is Newton method, other famous methods are HalleyÕs method, Secant method 0096-3003/$ - see front matter Ó 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2004.09.029 * Corresponding author. E-mail addresses: effati911@yahoo.com (S. Effati), nazemi20042003@yahoo.com (A.R. Nazemi). Applied Mathematics and Computation 168 (2005) 877–894 www.elsevier.com/locate/amc