Block-decoupling multivariate polynomials using the tensor block-term decomposition

Abstract

We present a tensor-based method to decompose a given set of multivariate functions into linear combinations of a set of multivariate functions of linear forms of the input variables. The method proceeds by forming a three-way array (tensor) by stacking Jacobian matrix evaluations of the function behind each other. It is shown that a blockterm decomposition of this tensor provides the necessary information to block-decouple the given function into a set of functions with small input-output dimensionality. The method is validated on a numerical example.