Dozenten:  Jörg Liesen, Christian Mehl, Volker Mehrmann, Reinhard Nabben 
Koordination:  Falk Ebert 
LVTermine:  Do 1012 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 19.4.2007  10:15  MA 376 
  Vorbesprechung 
Do 3.5.2007  10:15  MA 376 
Daniel Kressner  Eigenvalue Computation on the PlayStation 3 (Abstract) 
Do 10.5.2007  10:15  MA 376 
Christian Schröder  Optimal execution of transactions and the nearest AFR matrix (Abstract) 
Do 24.5.2007  10:15  MA 376 
Elena Virnik  Stability of positive descriptor systems  A toolbox of (simple but nice) tricks (Abstract) 
Do 31.5.2007  10:15  MA 376 
Kathrin Schreiber  Nonlinear Rayleigh functionals (Abstract) 
Do 7.6.2007  10:15  MA 376 
Timo Reis  Circuit Synthesis  An MNA Approach (Abstract) 
im An schluss 

Rakporn Dokchan  Numerical Integration of DAEs with critical points (Abstract)  
Do 14.6.2007  10:00  MA 376 
Eva Abram  Index analysis of electromechanical systems (Abstract) 
im An schluss 

Tobias Brüll  Linear DiscreteTime Descriptor Systems (Abstract)  
Do 21.6.2007  10:15  MA 376 
no speakers  
Do 28.6.2007  10:15  MA 376 
  
Do 5.7.2007  10:00!  MA 376 
Lena Wunderlich  Trimmed First Order Formulations for Linear Higher Order DAEs (Abstract) 
im An schluss 

Sadegh Jokar  Compressed Sensing and Partial Differential Equations (Abstract)  
Do 12.7.2007  10:00!  MA 376 
Sander Wahls  A Minimum Norm Solution to the Operator Corona Problem (Abstract) 
im An schluss 

Lisa Poppe  H∞ Control of DifferentialAlgebraic Equations (Abstract) 
Interessenten sind herzlich eingeladen!
Weitere Vorträge siehe auch:
Abstracts zu den Vorträgen:
Abstract:
The Cell architecture, upon which the recently released
PlayStation 3 is based, has been demonstrated to have
tremendous potential for scientific computations in
terms of both raw performance and power efficiency. Realizing
this potential in praxis is challenging, mainly due to the
fact that the design of Cell radically differs from
conventional multiprocessor or multicore architectures.
For example, while PlayStation 3's Cell CPU achieves a peak
performance of 204 Gflops in single precision, it only
achieves 15 Gflops in double precision. To obtain both
high performance and accuracy, it is therefore desirable to
do a large part of the computation in single precision before
using the considerably slower 64bit unit. The wellknown
iterative refinment, which will be reviewed in this talk,
provides a convenient framework to achieve this goal.
For computing eigenvalues and eigenvectors, however, standard
iterative refinment schemes have some limitations, e.g., encountering
convergence problems when the eigenvalues become too
illconditioned. These limitations can be completely avoided if
instead of individual eigenvalues the complete Schur
decomposition is refined. A novel algorithm will be sketched,
which can be seen as a mixture between the Jacobi method and
Newton methods for refining invariant subspaces.
This is joint work at an early stage with Jack Dongarra.
Abstract:
We will consider the problem of selling a large amount of shares at the
stock market. After introducing the setting we will discuss a model
covering the mayor effects. The model will then be solved using techniques
from optimal control theory.
In the last part a method to approximate model parameters is presented.
This involves finding the rank1 matrix $B$ that can be written as
$B=uv^T$ with $v_i=\frac{1}{u_i}$ that is closest to a given matrix $A$.
Abstract:
We consider differentialalgebraic linear homogeneous
continuoustime systems. Positivity implies that the solution trajectory
is nonnegative for all times $t$. In the case of standard positive
systems, most classical stability criteria take a simpler form. In this
talk we establish a complete correspondence of stability criteria in the
case of standard positive systems and in the positive descriptor case.
Abstract:
After a short review of Rayleigh quotients for Hermitian and
general matrices we introduce appropriate Rayleigh functionals $p(u)$
and $p(u,v)$ defined by $(T(p(u))u,u)=0$, $T(p(u,v))u,v)=0$ resp. for
nonlinear eigenvalue problems $T(\lambda)x=0$, where $u$, $v$ are
approximations for right and left eigenvectors. Local existence and
uniqueness of $p$ is shown as well as "stationarity" (technically $p$ is
not differentiable). Bounds for the distance of $p$ and the exact
eigenvalue are provided, which are of the same order as in the linear
case.
We give a numerical example of Rayleigh functional iteration and related
methods applied to a quadratic problem.
Abstract:
Given is a descriptor system. We consider the following question: Can we
perform state space transformations such that the descriptor system has the
form of the equations of modified nodal analysis arising in theory of
electrical circuits? For the class of passive and reciprocal systems, we will
answer this question by giving an algorithm.
Abstract:
We consider linear, timevarying differentialalgebraic equations (DAEs) with critical points. By
means of projectorbased analysis critical points shall be characterized. Assuming the existence of
continuous extensions of certain projectors and the density of the regular points, one can introduce
harmless critical points that allow us to apply Radau IIA method or BDF method like in the case
of regular DAEs.
Abstract:
We consider two examples of electromechanical systems and analyse them.
We compare the index of the subsystems with the index of the whole
system and check when it differs. Later, an outlook on how to analyse general
electromechanical systems is given.
Abstract:
We consider linear discretetime descriptor systems, i.e. systems of linear equations of the form $E_{k+1} x_{k+1} = A_k x_k + f_k$, where $E_k$ and $A_k$ are matrices, $f_k$ are vectors and $x_k$ are the vectors of the solution we are looking for. Analogously to the book "DifferentialAlgebraic Equations  Analysis and Numerical Solution" by V.Mehrmann and P.Kunkel the existence and uniqueness of solutions is first studied for the constant coefficient case, i.e. where $E_k = E$ and $A_k = A$ and then for the variable coefficient case. A strangeness index is defined for such systems.
Abstract:
We consider linear higher order differentialalgebraic equations. The
classical reduction to linear first order systems leads to different
solvability results and higher smoothness requirements. We present
trimmed first order formulations for higher order DAEs based on a
derivative array approach that allow order reduction without introducing
higher smoothness requirements. Further, these trimmed first order
formulations allow an explicit representation of solutions for higher
order DAEs.
Abstract:
In signal processing we are often interested in a substitute representation of a signal and seeking some simplification for an obvious gain. This is the rationale behind the so many transforms proposed over the past several centuries, such as the Fourier, cosine, wavelets, and many others. In this talk we are interested in finding sparse solutions of underdetermined linear systems. We will show that sparsity and redundancy can be used to design new/renewed and powerful signal/image processing tools. In this way we review some known results on compressed sensing and some open problems in this area. Then we give some ideas and theoretical results on the possible relation between compressed sensing and partial differential equations. Finally we will give some experimental results on finding the sparse solutions of partial differential equations. Computational experience looks promising.
Abstract:
We consider the Hardy space $H^\infty$ of bounded and analytic
operatorvalued functions on the complex unit disc. The question whether
there exists a right inverse function G in $H^\infty$ for some given F
in $H^\infty$ is often termed "Operator Corona Problem". As right
inverse functions do not need to be unique we are interested in a right
inverse having minimum norm. The talk outlines the construction of such
a minimum norm right inverse using the socalled "lurking isometry"
method and gives results on the approximation of the minimum norm whose
apriori knowledge is required in the construction.
Impressum  Falk Ebert 07.06.2007 