We consider two algorithms that use the block Macaulay matrix to solve (rectangular)
multiparameter eigenvalue problems (MEPs). On the one hand, a multidimensional …

We propose recursive algorithms to update an orthogonal numerical basis matrix of the null
space of the block row,(banded) block Toeplitz, and block Macaulay matrix, which is the …

As a crucial first step towards finding the (approximate) common roots of a (possibly
overdetermined) bivariate polynomial system of equations, the problem of determining an …

We show that globally optimal least-squares identification of autoregressive moving-average
(ARMA) models is an eigenvalue problem (EP). The first order optimality conditions of this …

We show how least squares optimal realization of autonomous linear time-invariant
dynamical systems from given data, reduces to the solution of an eigenvalue problem. In this …

We discuss four eigenvalue problems of increasing generality and complexity: rooting a
univariate polynomial, solving the polynomial eigenvalue problem, rooting a set of …

We outline the solution of a long-standing open problem in system identification, on how to
find the best least squares realisation of an autonomous linear time-invariant (LTI) …

We propose a novel approach to solve systems of multivariate polynomial equations, using
the column space of the Macaulay matrix that is constructed from the coefficients of these …

In Part I we proposed a multilinear algebra framework to solve 0-dimensional systems of
polynomial equations with simple roots. We extend this framework to incorporate multiple …

One of the most pervasive tools from (numerical) linear algebra is, without any doubt, the
standard eigenvalue decomposition. Eigenvalues describe the intrinsic system dynamics of …