A symbolic-numerical method for finding a real solution of an arbitrary system of nonlinear algebraic equations (Q1281848)

A hybrid symbolic-numerical method is proposed for finding solutions of systems of polynomial equations which may be overdetermined or underdetermined. A reduction algorithm due to \textit{J. F. Ritt} [Differential equations from the algebraic standpoint (1932; Zbl 0005.39404)] is used to derive sets of regular systems from the original system. The regular systems have Jacobians which are of full rank. For such systems a Gauss-Newton method can be applied. A convergence result analogous to the Newton-Kantorovich theory is given for an appropriate starting value for a regular system. Two numerical examples are given involving an underdetermined system and an overdetermined system.