Abstracts of Plenary Talks
Updating indefinite matrix approximations
Paul van Dooren (Catholic University of Louvain, Belgium), joint work with Nicola Mastronardi, CNR Bari, ItalyAbstract: Indefinite symmetric matrices occur in many applications, such as optimization, partial differential equations and variational problems where they are for instance linked to a so-called saddle point problem. In these applications one is often interested in computing an estimate of the dominant eigenspace of such matrices. In this paper we propose an incremental method to compute an estimate of the dominant eigenbasis of such matrices. This method is well-suited for large scale problems since it is efficient in terms of complexity as well as data management.
Parametric model reduction
Athanasios C. Antoulas (Jacobs University Bremen, Germany & Rice University, USA)Abstract: We present an approach to model reduction of systems depending on one parameter. It is based on a generalization of the Loewner matrix for 2-variate functions. The key is the establishment of a method which guarantees a trade-off between model complexity (in both variables) and accuracy of fit.
Model order reduction for discrete unstable system
Caroline Böß (Allianz Global Corporate & Specialty (AGCS))
Abstract: Mathematical modeling of problems occurring in natural and engineering
sciences often results in very large dynamical systems. Efficient
techniques for model order reduction are therefore required to reduce
the complexity of the system. There exists a variety of methods for
systems with different properties. In this talk the focus is on
discrete unstable systems on a finite time horizon. Such systems occur
in different applications, for example in the field of numerical
weather prediction, where large discrete forecast models are used to
determine the best estimate of the current state of the atmosphere.
Balanced truncation is a well-known and approved model reduction
method, but in its original form it is not suitable to reduce the
order of unstable models. There already exist approaches for extending
this technique to unstable systems, but they do not work properly if
the system has many unstable modes. In this talk the model reduction
method of alpha-bounded balanced truncation is proposed.
It captures the full behavior of the original system successfully,
independently of the number of unstable poles. An error bound on the
finite time horizon can be derived. In numerical experiments with
unstable test models the benefit of using the alpha-bounded
approximation method is illustrated.
