Systems of Nonlinear Equations

Abstract

This chapter extends chapter 2 from solving one nonlinear equation in one unknown to systems of nonlinear equations. Assume that we are given a system of n nonlinear equations for an $n \in \mathbb{N}$ with n ≥ 2:

$$ \begin{cases} f_1 (x_1 ,x_2 , \ldots ,x_n ) = 0, \hfill \\ f_2 (x_1 ,x_2 , \ldots ,x_n ) = 0, \hfill \\ \vdots \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \vdots \hfill \\ f_n (x_1 ,x_2 , \ldots ,x_n ) = 0. \hfill \\ \end{cases}$$

((6.1))