Decoupling multivariate polynomials using first-order information and tensor decompositions

Abstract. We present a method to decompose a set of multivariate real polynomials into linear combinations of univariate polynomials in linear forms of the input variables. The method proceeds by collecting the first-order information of the polynomials in a set of sampling points, which is captured by the Jacobian matrix evaluated at the sampling points. The canonical polyadic decom-position of the three-way tensor of Jacobian matrices directly returns the unknown linear relations as well as the necessary information to reconstruct the univariate polynomials. The conditions un-der which this decoupling procedure works are discussed, and the method is illustrated on several numerical examples