On an iterative method for solving certain nonlinear systems

Dragoslav Herceg, Ljiljana Cvetković, Nenad Petrović

The purpose of this paper is to solve the system of nonlinear equations $Gx=0$, where $G\colon\mathbb R^n\to\mathbb R^n$ is $F$-dlfferentiable function and $G'(x)$ is a symmetric positive definite matrix for any $x\in\mathbb R^n$. These hypotheses imply that there exists a unique point $x^*\in\mathbb R^n$ such that $Gx^*=0$. In order to solve this problem, we use the MSORN (Modified Successive Overrelaxation Newton) method, sufficient conditions for global convergence of which are given.