Abstract:
The paper is devoted to the solution of a nonlinear system of equations $F(x)=0_n$, where $F$ is a quadratic mapping acting from $\mathbb{R}^n$ to $\mathbb{R}^n$. The derivative $F'$is assumed to be degenerate at the solution point, which is a major characteristic property of nonlinearity of the mapping. Based on constructions of the $p$-regularity theory, a $2$-factor method is proposed for solving the system of equations, which converges at a quadratic rate. Moreover, an exact formula is obtained for solving this quadratic system of equations in the case of a $2$-regular mapping $F(x)$.
