Abstract. We exploit the well-known correspondence between a nonlinear polynomial system and a system of constant coefficient linear homogenous PDE (partial differential equations). This equivalence is used to write the polynomial system in the form of a PDE system, to which the symbolic-numeric completion method is applied. After a finite number of symbolic prolongations and numerical eliminations via SVD (Singular Value Decomposition), we obtain an involutive system which is locally solvable and contains all integrability conditions. The solutions of the polynomial system can be determined by applying eigenvalue-eigenvector techniques to the null space of the involutive system. The stability and robustness of the new method are demonstrated by its applications in solving the camera pose problem.