Date: 28.01.2022

Time: 15:00 CET (Central European Time)

Title of the Talk: Multidimensional realization theory and polynomial system solving

Speaker: Dr. Philippe Dreesen  (KU Leuven, Belgium)

Event  Link: Zoom

Abstract: Multidimensional systems provide tools for estimation, simulation and control, which go beyond one-dimensional systems. In this talk, we will use multidimensional realization theory for solving a set of polynomial equations. We show that linear algebra suffices to solve the problem at hand. We view the polynomial equations as multidimensional difference equations that are associated with a Macaulay matrix, which is the multivariate generalization of the Sylvester matrix. The right null space of the Macaulay matrix can be viewed as a multidimensional observability matrix. The classical shift trick in Kung's method from realization theory reduces the task of finding all the solutions of the polynomial equations to solving an eigenvalue decomposition. We study multiple solutions and solutions at infinity.

It is a joint work with Kim Batselier and Bart De Moor.

Biography of the Speaker: Philippe Dreesen is a Mathematical Engineer, currently working as a research expert at KU Leuven, ESAT-STADIUS. He received an MSc degree in Electrical Engineering (Burgerlijk Werktuigkundig-Elektrotechnisch Ingenieur), and a PhD degree in Engineering Science from KU Leuven in 2007 and 2013. His doctoral work was a project on solving systems of polynomial equations with the use of linear algebra, funded through a fellowship of Flanders' Agency for Innovation by Science and Technology (IWT Vlaanderen). From October 2013 until July 2020 he held postdoctoral positions at Vrije Universiteit Brussel (VUB) on the development of tensor-based methods for nonlinear system identification and modelling, and from August 2020 until January 2021 at Antwerp University in CoSYS-lab. Since February 2021 he is with KU Leuven, ESAT-STADIUS, where he performs research on connections between polynomial algebra, linear algebra, tensor methods and multidimensional systems theory.