Overdetermined Systems of Polynomial Equations: Tensor-Based Solution and Application

Raphaël Widdershoven, Nithin Govindarajan, Lieven De Lathauwer

Abstract: Overdetermined systems of polynomial equations are the natural extension of overdetermined systems of linear equations. While the latter are solved systematically through well-established numerical linear algebra techniques, we contribute to the development of tensor-based tools to handle the more general polynomial case, specifically for applications in signal processing and related areas. The method involves computing the nullspace of the so-called Macaulay matrix and determining the Canonical Polyadic Decomposition (CPD) of a third-order tensor. The practical utility of this method is demonstrated for a blind multi-source localization problem.