Abstracts
Nonlinear eigenvalue problems,
a challenge for modern eigenvalue algorithms
Prof. Dr. Volker Mehrmann
Technische Universität Berlin
Nonlinear eigenvalue problems arise in many modern areas of key technologies, from computation of acoustics fields to magnetic and electric fields.
For linear eigenvalue problems many methods are available and mostly well understood. For nonlinear (in particular for non-polynomial) problems the situation is much less satisfactory. In this talk we will present the state of current methods including contributions of Heinrich Voss and we also discuss a challenging problem from interior car acoustics. We present new approaches for extremely large scale problems and also discuss new ideas for the construction of adaptive methods.
Rational Lanczos and Arnoldi for
the approximation of matrix functions.
Lothar Reichel
Department of Mathematical Sciences, Kent State University
The need to evaluate expressions of the form f(A)b,
where f is a nonlinear function, A is a large sparse matrix,
and b is a vector, arises in many applications. We describe short recursion
relations for the rational Lanczos method, applicable when A is symmetric and the rational approximant
has a preselected pole. We also discuss the use of the rational Arnoldi method,
applicable when A is nonsymmetric, and present error bounds.
The talk presents joint work with B. Beckermann and C. Jagels.
The quasi-Weierstraß-form:
a link between analytic and algebraic aspects of DAEs
Prof. Dr. Achim Ilchmann
Technische Universität Ilmenau
We study for regular matrix pencils
the relationship between the algebraic structure of
and the solution space of the DAE
It is well known that for ordinary differential equation
(i.e. 
)
this relationship is completely understood by invoking the Jordan canonical
form; for 
we develop a quasi-Weierstraß-form
which is simpler than the Weierstraß-form. This sets us in a position to describe
in a simple form. Moreover, the solutions of the DAE will be presented in terms of eigenvalues and
generalized eigenvectors.
This talk presents joint work with Thomas Berger and Stephan Trenn.
