Model Order Reduction

Course content

The students understand the of the complex links between their previous mathematical knowledge and the contents of the lecture, understand the theoretical body of the lecture as a whole and master the corresponding methods, are able to analyze and apply the methods of the lecture, understand the concept of model reduction, know and understand the most important methods of (non)linear model reduction, are able to analyze the method and understand of the basic limits of the applicability of the methods, are able to interpret the goodness and optimality of the achievable approximation

Content
Introduction to the theory of linear dynamcial systems, numerical methods for model order reduction for linear (and nonlinear) systems, in particular modal truncation (eigenvalue-based methods), balanced truncation (singular value decomposition-based methods), Pade approximation/rational interpolation (Krylov subspace-based methods) and Proper Orthogonal Decomposition (POD)/Karhunen-Loeve decomposition, Applications.