A new method for solving a system of the nonlinear equations

摘要

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 measures; the optimal measure then is approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional nonlinear programming. Finally, we obtain an approximate solution for the original problem, furthermore, we obtain the path from the initial point up to the approximate solution.