Multiparameter Eigenvalue Problems and Shift-invariance
Katrien De Cock, Bart De Moor · IFAC-PapersOnLine · 2021
We discuss four eigenvalue problems of increasing generality and complexity: rooting a univariate polynomial, solving the polynomial eigenvalue problem, rooting a set of multivariate polynomials and solving multi-parameter eigenvalue problems. In doing so, we provide a unifying framework for solving these eigenvalue problems, where we exploit properties of (block-) (multi-) shift-invariant subspaces and use multi-dimensional realization algorithms.