### January 25, 2018

Ivan Markovsky (Vrije Universiteit Brussel): Survey of system identification from a numerical linear algebraic perspective @ Université des Sciences et Technologies de Lille - Lille I, "Analyse Numérique - Equations aux Dérivées Partielles" seminar.

The first part of the presentation is a tutorial introduction to sum-of-exponentials modeling from a numerical linear algebra point of view. The problem considered is related to the rational approximation, linear time-invariant system realization, and model reduction problems. Three classed of solution methods are reviewed: convex relaxations based on the nuclear norm heuristic, subspace methods, and local optimization methods. The class of subspace methods is related to Prony’s method and its generalizations. The second part of the presentation shows generalizations of the structured low-rank approximation approach to modeling of systems with inputs, dealing with missing data, and an application to the problem of computing approximate common divisors of polynomials.