Systems of Polynomial Equations, Higher-Order Tensor Decompositions, and Multidimensional Harmonic Retrieval: A Unifying Framework. Part II: The Block Term Decomposition

In Part I we proposed a multilinear algebra framework to solve 0-dimensional systems of polynomial equations with simple roots. We extend this incorporate multiple roots: block term decomposition (BTD) the null space Macaulay matrix reveals dual (sub)space disjoint root in each term. The BTD is joint triangularization multiplication tables and three-way generalization Jordan canonical form case, intimately related border rank tensor. hint at illustrate flexible numerical optimization-based algorithms.