Exact formula for the solution of degenerate system of quadratic equations

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