Eigenvalues and model reduction
Related research
Description
Large scale eigenvalue problems arise in many applications. Excellent numerical methods are available for linear and polynomial eigenvalue problems. Currently, the focus lies on parametric eigenvalue problems arising from stability analysis of dynamical systems, graph theory, and vibrations. The parameters are physical or geometric parameters that have to be determined for an optimal design.
The focus of the NALAG research group lies in the development of the dominant pole algorithm for model reduction of linear SISO systems with parameters, moment matching model reduction methods for PDE constraint optimization, optimization methods for determining the bounds of eigenvalues of parametric matrices, and methods for the determination of Hopf bifurcations. We also work on a new class of algorithms for solving nonlinear eigenvalue problems by approximating the nonlinear matrix function by a (rational) polynomial.
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