Exact linear modeling with polynomial Ore algebras (Dr. Viktor Levandovskyy)

Description

This is a joint work with Eva Zerz and Kristina Schindelar. Linear exact modeling is a problem coming from system identification: Given a set of observed trajectories, the goal is find a model (usually, a system of partial differential and/or difference equations) that explains the data as precisely as possible. The case of operators with constant coefficients is well studied and known in the systems theoretic literature, whereas the operators with varying coefficients were addressed only recently. This question can be tackled either using Groebner bases for modules over Ore algebras or by following the ideas from differential algebra and computing in commutative rings. We present algorithmic methods to compute "most powerful unfalsified models" (MPUM) and their counterparts with variable coefficients (VMPUM) for polynomial and polynomial-exponential signals. We also study the structural properties of the resulting models, discuss computer algebraic techniques behind algorithms and provide several examples. In particular, we give an answer to the question "Why variable coefficients are better than constant coefficients".

Period	09 Jul 2010
Event type	Guest talk
Location	AustriaShow on map