Dozenten: | Jörg Liesen, Volker Mehrmann, Reinhard Nabben |
Koordination: | Falk Ebert |
LV-Termine: | Do 10-12 in MA 376 |
Inhalt: | Vorträge von Diplomanden, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen |
Vorläufige Terminplanung: | ||||
Datum | Uhrzeit | Raum | Vortragende(r) | Titel |
---|---|---|---|---|
Do 17.04.2008 | 10:15 | MA 376 |
Elena Virnik | Model reduction of positive descriptor systems (Abstract) |
im An- schluss |
Vorbesprechung | |||
Do 24.04.2008 | 10:15 | MA 376 |
Özlem Cavusoglu | A characterization of Lyapunov operators (Abstract) |
Do 08.05.2008 | 10:15 | MA 376 |
Hannes Gruschinski | Recent investigations on optimal control and estimation of stochastic descriptor and singularly perturbed systems (Abstract) |
Do 15.05.2008 | 10:15 | MA 376 |
no talk | |
Do 22.05.2008 | 10:15 | MA 376 |
Kai Wassmuss | Ein algebraisches Mehrgitterverfahren zur Lösung der Helmholtz-Gleichung (in german) |
Do 12.06.2008 | 10:15 | MA 376 |
Lisa Poppe | H∞-Control of Discrete-Time Descriptor Systems (Abstract (pdf)) |
im Anschluss | MA 376 |
Tobias Brüll | A short introduction into dissipative systems theory (Abstract) | |
Do 19.06.2008 | 10:15 | MA 376 |
Maciek Korzec | An introduction to pseudospectral methods with applications onto sixth order equations describing the faceting of growing surfaces (Abstract) |
Do 26.06.2008 | 10:15 | MA 376 |
Elena Teidelt | Quadratic Eigenvalue Problems Arising from Noise Control Problems (Abstract (pdf)) |
Do 03.07.2008 | 10:00! | MA 376 |
Agnieszka Miedlar | Adaptive solution of elliptic eigenvalue problems (Abstract) |
im Anschluss | MA 376 |
Özlem Cavusoglu | A new Tensor SVD (Abstract) |
Interessenten sind herzlich eingeladen!
Weitere Vorträge siehe auch:
Abstracts zu den Vorträgen:
Abstract:
We consider linear time-invariant control systems of the form
\begin{eqnarray*}
E\dot x&=&Ax+Bu, \ x(t_0)=x_0\\
y&=&Cx+Du,
\end{eqnarray*}
where $A,B,C,D$ are real constant coefficient matrices of appropriate size.
The state $x$, input $u$ and output $y$ are real-valued vector functions.
Positive systems arise, when economical, biological or
chemical systems are modelled by descriptor systems, in which the state
$x$ describes concentrations, populations of species, or numbers of
cells. In positive systems it is required that the solution and the
output have to be nonnegative vector functions for appropriately chosen
initial state and input.
We review some fundamental properties of positive systems and of the
model reduction methods of balanced truncation and singular perturbation
balanced truncation, which have the advantage of a guaranteed error
bound. We present an adaptation of these methods that preserves the
positivity of the system. First, we show the results for standard
systems (joint work with Timo Reis) and then (if time is left) extend
these to the descriptor case.
Abstract:
The aim of the talk is to discuss the problem of
representing a linear matrix operator, in particular
the inverse of a Lyapunov operator, as a sum of minimum number of
elementary operators.
Some concepts and properties related to Sylvester and Lyapunov operators
as well as the concept of "Sylvester index" of a linear matrix operator
and the concept of "Lyapunov index" will be presented.
The characterization of real and complex Lyapunov operators
will be given. The concept of "Lyapunov singular values" will be
introduced.
This talk is mainly based on the research paper:
M. Konstantinov, V. Mehrmann, P. Petkov, On properties of Sylvester
and Lyapunov operators, Linear Algebra Appl.312(2000) 35-71.
Abstract:
We introduce stochastic descriptor systems (SDS) in continuous-time with properly stated leading term and point out important special cases (singularly perturbed (SP) systems with time-varying and constant perturbation number and differential-algebraic systems). For many of these classes we propose novel families for the LQR/Kalman-Bucy/LQG/$H_\infty$/Lyapunov problems. We sketch derivations and a catalogization of the so-called "Obvious" as well as "Not-So-Obvious" solutions (Riccati transformations) including their solvability conditions and mathematical ramifications. Preliminary numerical results and future projects are discussed.
Abstract:
As a first step we will introduce some existing results about a priori
and a posteriori error estimation and global convergence of adaptive
methods for elliptic eigenvalue problems. Because the goal of the project
is to reduce the complexity while retaining good accuracy we
concentrated our work on combining two currently used techniques: first
spectralize then discretize and first discretize then spectralize. Our
new approach uses Krylov subspace methods together with Galerkin
approximations. The main idea is to use fine meshes only to decide which
areas should be refined and iterative methods to solve finite
dimensional problems on the coarse grids. At the end some first
numerical results will be presented.
Abstract:
The Singular Value Decomposition is an important tool in linear algebra.
However, extension of the matrix SVD's to higher-order tensors is not straightforward.
Some basic concepts such as "rank" or "best rank-k approximations" become more complicated.
A new tensor-tensor multiplication, which constitutes an algebra, has been introduced
recently by Carla Dee Martin et. all.
In this talk I am going to present this new tensor-tensor multiplication and
how this multiplication gives rise to an SVD-like decomposition of higher-order tensors.
Finally, I will try to relate this algebra to Banach algebras, in order to
relate the approximation problem of tensors to the approximation theory in Banach algebras,
specifically algebras of Hilbert space operators.
Impressum | Falk Ebert 01.07.2008 |