Diplomanden- und Doktorandenseminar
des Fachgebiets Numerische Mathematik
WS 2003/04


Dozenten:Volker Mehrmann, Matthias Bollhöfer, Christian Mehl
Koordination: Christian Mehl
LV-Termine:Do 10-12 in MA 313
Inhalt: Vorträge von Diplomanden, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen

Vollständige vorläufige Terminplanung:
 
Datum Uhrzeit Raum Vortragende(r) Titel
Do 30.10.2003 10:15 MA 313
 
  Vorbesprechung
Do 6.11.2003 10:15 MA 313
 
Daniel Kressner Structured Condition Numbers for Invariant Subspaces (Abstract)
Do 13.11.2003 10:15 MA 313
 
Olga Holtz M-matrices satisfy Newton's inequalities (Abstract)
Do 20.11.2003 10:15 MA 313
 
Michael Karow On Real and Complex Operator Norms of a Real Matrix
Do 4.12.2003 10:15 MA 313
 
Simone Bächle Index reduction by minimal extension for differential-algebraic equations in circuit simulation
Do 11.12.2003 12:00 MA 464
 
Prochko Prochkov Numerical Simulation of Train Traffic in Large Networks via Time-optimal Control
Do 18.12.2003 10:00 MA 313
 
Falk Ebert Controlled simulator coupling - Part II
Do 18.12.2003 11:00 MA 313
 
Tim Wichmann (Fraunhofer ITWM, Kaiserslautern) Symbolic Simplification of Nonlinear DAE-Systems in Analog Circuit Design (Abstract)
Do 15.1.2004 10:15 MA 313
 
Christian Otto The Jacobi-Davidson algorithm
Do 22.1.2004 10:00 MA 313
 
Michael Schmidt Model reduction via Karhunen-Loeve-expansion/Proper Orthogonal Decomposition
Do 22.1.2004 11:00 MA 313
 
Sonja Schlauch Analysis, Modeling and Numerical Simulation of Drop Size Distributions in Stirred Liquid-liquid Dispersions
Do 29.1.2004 10:00 MA 313
 
Ulrike Baur Model reduction of linear time-varying systems
Do 29.1.2004 11:00 MA 313
 
Andreas Hilliges Simulation of railway tracks under periodic excitation
Do 12.2.2004 10:00 MA 313
 
Chunchao Shi Characterizations of the distance to singularity for matrix pencils
Do 12.2.2004 11:00 MA 313
 
Elena Virnik Algebraic Multigrid (AMG) preconditioner applied to solving (I-A^T)x=0 with GMRES where A is transition matrix of a Markovian process
Do 19.2.2004 10:00 MA 313
 
Stefan Seidel Simulation and Optimisation of Rail Traffic in Realistic Networks
Do 19.2.2004 11:00 MA 313
 
Alex Streller Finite Element Discretization of the Navier-Stokes Equation for the Backward Facing Step

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Abstracts zu den Vorträgen:


Daniel Kressner
Structured Condition Numbers for Invariant Subspaces
Do 6.11.2003, 10:15 Uhr in MA 313

Abstract:
The purpose of this talk is to present some known and new results on the perturbation theory for invariant subspaces of matrices. The first part is a review of well-known perturbation bounds, and it is shown how the implicit function theorem can be used to derive such bounds. The condition number of an invariant subspace is introduced and connected to the singular values of a certain Sylvester operator. If the perturbation is known to preserve certain matrix structures then this condition number could severly overestimate the actual sensitivity of an invariant subspace. This question is discussed in the second part of this talk, in particular for

Corresponding structured condition numbers for the listed matrix classes are defined and compared against their unstructured counterparts. These results are used to thoroughly discuss advantages to be expected from using numerically backward stable, structure-preserving algorithms for computing invariant subspaces. Furthermore, we pose an open question concerning structured condition numbers for deflating subspaces of skew-Hamiltonian/Hamiltonian matrix pencils.
No preliminary knowledge on perturbation theory is assumed.
Olga Holtz
M-matrices satisfy Newton's inequalities
Do 13.11.2003, 10:15 Uhr in MA 313

Abstract:
Newton's inequalities c_n^2 ≤ c_{n-1}c_{n+1} are shown to hold for the normalized coefficients c_n of the characteristic polynomial of any M- or inverse M-matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes. Finally, a connection between Newton's inequlities and the inverse eigenvalue problem for nonnegative matrices is discussed.


Tim Wichman
Symbolic Simplification of Nonlinear DAE-Systems in Analog Circuit Design
Do 18.12.2003, 10:15 Uhr in MA 313

Abstract:
In general, the behaviour of an analog circuit can mathematically be described by a nonlinear differential-algebraic equation system (DAE). In the field of symbolic circuit analysis this equation system is set up symbolically using computer algebra methods. Then it is further analyzed in order to get insights into the circuit's behavior. Unfortunately, the complexity of the symbolic equation system limits this approach to very simple circuits. To extend the application field to practical examples from industry, symbolic simplification techniques have been developed which allow to generate a simplified equation system of much smaller complexity which is still accurate within a user-given error bound. For linear circuits this approach has been successfully used in industry for several years now. Recently, research started to extend these techniques to nonlinear circuits. In this talk we will present an overview of the symbolic simplification techniques for nonlinear analog circuits, i.e. for nonlinear DAE-systems. We describe the general approach as well as some details of the algorithms, especially the so-called ranking method, a technique which both improves the result and speeds up the computation. At the end we will show that the idea of symbolic simplification is general enough to be extended to additional application fields like the analysis of pipelines.


Impressum Christian Mehl 18.2.2004