Homepage of the Chair of Applied Mathematics
Chair of Applied Mathematics
The group mainly works on the development and the analysis of numerical methods,
particularly for optimization and control problems and for parameter
identification of dynamical systems:
Arithmetic Set Operations and their Visualization in Computational Geometry
Main objective of this project is the application of methods of Computational
Geometry to problems in Set-Valued Numerical Analysis. Especially,
applications to interpolation/approximation/differentiation methods of
set-valued mappings are studied. Connections to the computation of reachable
sets of differential inclusions and approximation classes like affine,
semi-affine or quasi-affine mappings as well as comparisons with several
known derivatives are part of the research.
One focus of the project lies on different definitions of addition and
difference of compact convex sets. These sets are embedded in the space of
directed sets, in which commonly used set operations known from Convex
Analysis are generalized. Directed sets are recursively constructed from
generalized intervals and can always be visualized by boundary parts and
corresponding oriented directions.
Set-Valued Numerical Analysis
Numerical algorithms for set-valued mappings are developed, analysed
theoretically and tested numerically.
Thu Oct 15 17:18:20 2008