Iterative method for solving second degree polynomials

Abstract

Systems of nonlinear algebraic equations have a wide application. As a rule, such systems are
solved using some iterative methods, which are based on the nonlinear functional expansion in a
Taylor series in the neighborhood of the solution. However, these methods require giving the
initial approximation with sufficient accuracy, moreover, it is practically impossible to verify the
conditions of the convergence beforehand. This paper suggests a new perspective method for
solving systems of polynomial equations of the second degree with many unknowns. Recurrence
relations for finding approximate solutions of polynomial equations over the field of real numbers
are obtained. The convergence of operator continued fractions used in the computational scheme
is investigated and some of their properties are shown. The numerical experiments confirming the
efficiency of the method proposed have been conducted.