Speaker: Dr. Viktor Levandovskyy (RWTH Aachen)

Title: Exact linear modeling with polynomial Ore algebras

Time and Place: Friday, July 9, 2010, 1:00 p.m.,
                UFO, RISC, Hagenberg


Abstract:

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".